Description:TECHNICAL FIELD
Embodiments of the present disclosure relate determining rheological parameters associated with a fluid, and more specifically to measuring the properties associated with a fluid based on a measure of the rheological parameters associated with the fluid.

BACKGROUND
Generally, rheology is associated with the flow and deformation phenomena of materials, especially fluids. Rheology is based on continuum mechanics and combines principles of fluid mechanics and elasticity for determining mechanical behaviour of materials related to elasticity, viscosity, plasticity and other associated properties. Usually, rheology is associated with the transient behaviour of materials under the influence of stress. Determination of rheological parameters can provide crucial information that may be used in fabrication of materials, for example rubbers, plastics etc., since the mechanical performance of such materials are normally influenced by their properties of the material, such as the associated viscoelastic properties. Additionally, rheology also finds application in physiology, where for example viscoelastic properties of bodily fluids may be determined to aid in diagnostics.
In the recent times, rheology techniques as in microrheology have been increasingly adopted to determine rheological parameters associated with fluids by measuring trajectories of microscopic tracer particles that are present in the fluids. Microrheology offers advantages of requiring lesser quantity of fluid samples for performing analysis, requiring smaller experimental setup, and incurring lesser cost. Further, microrheology also allows for the measurement of rheological properties of a fluid down to microscopic scales, which are around the size of the tracer particles that are inserted in the fluids.
Currently employed microrheology techniques use optically trapped tracer particles, typically spherical beads, suspended in a fluid medium. Normally, the trajectories of such tracer particles in the fluid are statistically averaged to determine rheological properties associated with the fluid. A disadvantage of such techniques is that data collected by are unreliable in providing a complete analysis of the rheological parameters for the fluid. Furthermore, the measured rheological parameters are also sensitive to heating effects associated with the trapping laser on the fluid medium. Hence, conventional microrheology techniques suffer from a number of drawbacks in systems where the fluids exhibit transient behaviour. Thus, there is a need to overcome one or more of the aforementioned problems in these know techniques of the prior art.
SUMMARY
Embodiments of the present disclosure relate to a method of determining rheological properties of a fluid. In an embodiment, particles are magnetized to create magnetic probes, which are inserted into a fluid. The magnetic probe in the fluid forms a suspension. A finite quantity of the suspension is aspirated and placed in a sample cell that is sealed to prevent evaporation of the fluid from the sample cell. The sample cell containing the suspension is then placed within a coil, wherein the coil is configured to produce a magnetic field when switched to an ON state. After placing the sample cell within the coil, the coil is switched to an ON state. An external magnetic field is generated by the coil and the external magnetic field is applied to the sample cell. The frequency of the external magnetic field generated by the coil may vary, and the applied external magnetic field to determine the rheological parameters of the fluid is kept above a pre-defined threshold. The magnetic probes in the suspension respond to the external magnetic field depending on the type of the fluid and rheological properties associated with the fluid are determined based on a response of the magnetic probes to the applied external magnetic field. Other embodiments are also disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS
The detailed description is described with reference to the accompanying figures. Features, aspects, and advantages of the subject matter of the present disclosure will be better understood with regard to the following description and the accompanying drawings. The figures are intended to be illustrative, not limiting, and are generally described in context of the embodiments, and it should be understood that it is not intended to limit the scope of the disclosure to these particular embodiments. In the figures, the same numbers may be used throughout the drawings to reference features and components. In order that the present disclosure may be readily understood and put into practical effect, reference will now be made to exemplary embodiments as illustrated with reference to the accompanying figures. The figures together with detailed description below, are incorporated in and form part of the specification, and serve to further illustrate the embodiments and explain various principles and advantages.
Figure 1 illustrates an exemplary pictorial representation of the system used for measuring the response of magnetic probes in the fluid and computing the rheological parameters of the fluid in accordance with an embodiment of the present disclosure.
Figure 2 illustrates an exemplary sample cell placed within a coil for measuring the rheological parameters of the fluid by generating a magnetic field when the coil is switched to an ON state in accordance with an embodiment of the present disclosure.
Figure 3A illustrates an exemplary scanning electron microscope (SEM) image indicating a view of a magnetic probe used in for determining the response of the magnetic field on the magnetic probes in the fluid on application of a magnetic field, where the bright portions in the SEM image illustrate a Fe-Co layer in accordance with an embodiment of the present disclosure.
Figure 3B illustrates an exemplary scanning electron microscope (SEM) image indicating an alternate view of a magnetic probe used in for determining the response of the magnetic field on the magnetic probes in the fluid on application of a magnetic field, where the bright portions in the SEM image illustrate a Fe-Co layer in accordance with an embodiment of the present disclosure.
Figure 4 is an exemplary illustration of relevant coordinates to describe rotational motion of the magnetic probe in two dimensions in accordance with an embodiment of the present disclosure.
Figure 5 illustrates an exemplary motion of a magnetic probe indicating a long axis and a short axis along which the response of the magnetic probe is measured on application of the magnetic field in accordance with an embodiment of the present disclosure.
Figure 6A is an exemplary illustration of a time evolution of the angular coordinate ? obtained when the magnetic probe is rotated about the short axis (the second axis) when the applied magnetic field strength is B=30 G and the applied frequency is ?_B=3 Hz in accordance with an embodiment of the present disclosure.
Figure 6B is an exemplary illustration of a typical trajectory of the magnetic probe when rotated about the long axis on application of an external magnetic field in accordance with an embodiment of the present disclosure.
Figure 7A is an exemplary illustration of a method for preparing a sample and determining the rheological parameters of a fluid containing the magnetic probes in accordance with an embodiment of the present disclosure.
Figure 7B is an exemplary illustration of a method for preparing the magnetic probes in accordance with an embodiment of the present disclosure.
Figure 7C is an exemplary illustration of a method of preparing the sample for testing the rheological parameters of the fluid in accordance with an embodiment of the present disclosure.
Figure 7D is an exemplary illustration of a method of measuring the rheological parameters of the fluid from the response of the magnetic probes in the fluid in accordance with an embodiment of the present disclosure.
Figure 8A is an exemplary illustration of a measure of the time progression of angular coordinate ? measured in the viscoelastic surfactant solution at various applied field frequencies? ??_B in accordance with an embodiment of the present disclosure.
Figure 8B is an exemplary illustration of a measure of the angular frequency O of the magnetic probe as a function of applied field frequency, which correspond to the viscoelasticity measurement in the fluid in accordance with an embodiment of the present disclosure.
Figure 8C is an exemplary illustration of the dependence of the translational probe velocity v on ? ??_B measured at B=50 G in the viscoelastic polymer solution (solid square) and in the Newtonian solution.
Figure 8D is an exemplary illustration of the pitch of the magnetic probe as a function of the applied field amplitude for a Newtonian case (open circle) and for the viscoelastic fluid (solid square).
Figure 8E is an exemplary illustration of the numerically obtained time progression of the viscoelastic torque T_v, the torque induced by the magnetic field T_m, the sum of viscoelastic and magnetic torques T_T = T_v +T_m, the phase difference ß between magnetic field vector B and the magnetic moment m of the rod and angular velocity O of the magnetic probe obtained for the rheological parameter corresponding to 7 mM CpyCl/NaSaI solution at B = 30 G and ?_B = 200 rad s^(-1) in accordance with an embodiment of the present disclosure.
Figure 8F is an exemplary illustration of a typical sequence of an input chirped pulse in the time domain where the frequency varies linearly from 1Hz to 15 Hz within a timeframe of 1 s in accordance with an embodiment of the present disclosure.
Figure 8G is an exemplary illustration of the resulting linear magnetic probe displacement for the applied chirped pulses of various timeframes, wherein the shaded portion represents the cut-off regime.
Figure 8H is an exemplary illustration of a time evolution of the magnetic probe angle ? in response to the applied chirped sequences of various durations, wherein the shaded portion represents the cut-off regime.

DETAILED DESCRIPTION
The following describes technical solutions in exemplary embodiments of the subject matter of the present disclosure with reference to the accompanying drawings. In this application as disclosed herein, "at least one" means one or more, and "a plurality of" means two or more. The term "and/or" describes an association relationship for describing associated objects and represents that three relationships may exist. For example, A and/or B may represent the following cases: Only A exists, both A and B exist, and only B exists, where A and B may be singular or plural. The character "/" usually indicates an "or" relationship between the associated objects. "At least one item (piece) of the following" or a similar expression thereof means any combination of the items, including any combination of singular items (piece) or plural items (pieces). For example, at least one item (piece) of a, b, or c may represent a, b, c, a and b, a and c, b and c, or a, b, and c, where a, b, and c each may be singular or plural.
It should be noted that in this application articles “a”, “an” and “the” are used to refer to one or to more than one (i.e., to at least one) of the grammatical object of the article. The terms “comprise” and “comprising” are used in the inclusive, open sense, meaning that additional elements may be included. It is not intended to be construed as “consists of only”. Throughout this specification defined above, unless the context requires otherwise the word “comprise”, and variations such as “comprises” and “comprising”, will be understood to imply the inclusion of a stated element or step or group of elements or steps but not the exclusion of any other element or step or group of elements or steps. The term “including” is used to mean “including but not limited to”. “Including” and “including but not limited to” are used interchangeably. In the structural formulae given herein and throughout the present disclosure, the following terms have been indicated meaning, unless specifically stated otherwise.
Unless otherwise defined, all terms used in the disclosure, including technical and scientific terms, have meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. By means of further guidance, term definitions are included for better understanding of the present disclosure. The term ‘about’ as used herein when referring to a measurable value such as a parameter, an amount, a temporal duration, and the like, is meant to encompass variations of ±10% or less, preferably ±5% or less, more preferably ±1% or less and still more preferably ±0.1% or less of and from the specified value, insofar such variations are appropriate to perform the present disclosure. It is to be understood that the value to which the modifier ‘about’ refers is itself also specifically, and preferably disclosed.
It should be noted that in this application, the term such as "example" or "for example" or “exemplary” is used to represent giving an example, an illustration, or descriptions. Any embodiment or design scheme described as an "example" or "for example" in this application should not be explained as being more preferable or having more advantages than another embodiment or design scheme. Exactly, use of the word such as "example" or "for example" is intended to present a related concept in only a specific manner.
It should be understood that in the embodiments of the present subject matter that "B corresponding to A" indicates that B is associated with A, and B can be determined based on A. However, it should be further understood that determining B based on A does not mean that B is determined based on only A. B may alternatively be determined based on A and/or other information.
In the embodiments of this application, "a plurality of" means two or more than two. Descriptions such as "first", "second" in the embodiments of this application are merely used for indicating and distinguishing between described objects, do not show a sequence, do not indicate a specific limitation on a quantity of devices in the embodiments of this application, and do not constitute any limitation on the embodiments of this application.
Exemplary embodiments of the present disclosure relate to measuring the properties associated with a fluid based on a measure of the rheological parameters associated with the fluid. An exemplary embodiment of the present disclosure relates to a method for determining rheological properties of a fluid. In an exemplary embodiment, first a fluid may be selected whose rheological parameters or properties need to be ascertained in order to understand various other associated properties of the fluid such as viscosity, viscoelasticity etc. In an exemplary embodiment, the fluid may be a Newtonian fluid and/or a non-Newtonian fluid and/or a combination thereof. In an exemplary embodiment, magnetic probes may be inserted into a fluid forming a suspension (sample), wherein the suspension may be in a colloidal state. In an exemplary embodiment, a small portion of the suspension (hereinafter also broadly referred to as sample in this document) may be aspirated and placed in sample holding means, such as a sample cell.
In an exemplary embodiment, the sample cell may be placed within a coil, for example a Helmholtz coil, wherein the coil may be configured to produce a magnetic field when switched to an ON state. In an exemplary embodiment, the magnetic field may be a rotating magnetic field or a pulsating magnetic field or a combination thereof. In an exemplary embodiment, the coil may be initial in an OFF state and may be switched to an ON state to generate a magnetic field. In an exemplary embodiment, on switching the coil to an ON state, an external magnetic field (B) may be applied to the sample in the sample cell, which is placed within the coil. In an exemplary embodiment, a frequency of the external magnetic field applied to the sample in the sample cell may be above a pre-defined threshold. In an exemplary embodiment, rheological properties associated with the fluid may be determined and/or computed based on a response of the magnetic probes to the applied external magnetic field in the sample. In an exemplary embodiment, the response of the magnetic probes may be considered as a measure of the asynchronous motion of the magnetic probes in the fluid.
In an exemplary embodiment, the magnetic probes generally includes particles that can be easily magnetized, for example by means of a magnet. In an exemplary embodiment, the particles forming the magnetic probes are selected form at least one of Iron or Nickel or cobalt or an alloy or steel or samarium or neodymium. In an exemplary embodiment, in a two-dimensional plane, wherein the particles are magnetized either along a first axis (for example the x-axis) or a second axis (for example the y-axis), wherein magnetization of the particles induces a magnetic moment to the particle along either the first axis or the second axis.
In an exemplary embodiment. on application of the external magnetic field the response of the magnetic probes may include aligning the magnetic moment of the magnetic probes along the direction of the applied external magnetic filed. In an exemplary embodiment, aligning may include the magnetic probes in the sample tending to be aligned along the direction of the magnetic field. In an exemplary embodiment, during the process of the magnetic probes being aligned along the direction of the magnetic field, the magnetic probes in the sample may face resistance due to a number of parameters associated with the fluid, unique to each fluid, such as the viscosity, elasticity etc.
In an exemplary embodiment, aligning the magnetic probes to the applied external magnetic field may include generating at least a motion of the magnetic probes along a degree of freedom. In an exemplary embodiment, the degree of freedom may include a number of independent parameters defining a configuration or a state of the magnetic probe in the sample. In an exemplary embodiment, on application of the external magnetic field to the sample containing the magnetic probes, wherein the external magnetic field may be considered as a rotating magnetic field, the response of the magnetic probes may be a rotation or rotational motion. In an exemplary embodiment the rotation or rotational motion may be produced by the magnetic moment of the magnetic probes along an axis of the magnetic probe.
In an exemplary embodiment, if the magnetic moment of the magnetic probe is aligned along the first axis the response may be a rotation or rotational motion produced about the second axis, in a two-dimensional plane. In an exemplary embodiment, when the applied external magnetic field is below a certain threshold frequency the magnetic moment of the magnetic probe may be aligned along the second axis the response may be a rotation or rotational motion produced about the second axis. In an exemplary embodiment, if the magnetic moment is along the second axis, the response may be a rotation about second axis below a certain threshold (step-in) frequency of the external magnetic field. In an exemplary embodiment, the rotation axis may undergoes a gradual transition from the second axis to about the first axis as the external field frequency is increased. In an exemplary embodiment, above the threshold frequency (step-out), the magnetic probes in the sample may perform asynchronous rotation which dynamically switches between the rotation about the first axis and the second axis.
In an exemplary embodiment, when the frequency of the external magnetic (also refers to the applied external magnetic field on the sample) is around the threshold frequency, the rotation or rotational motion along the second axis undergoes a gradual transition or a translation motion along the first axis. In an exemplary embodiment, when the frequency of the external magnetic is above the threshold frequency, the response of the magnetic probes may be an asynchronous rotation about the first axis and the second axis. In an exemplary embodiment, on application of the high frequency external magnetic field to the sample, wherein the external magnetic field is a rotating magnetic field, the response of the magnetic probes in the sample may be a rotation along the first axis and an additionally induced translation motion. In an exemplary embodiment, this may be considered as like a cork-screw mechanism because of the coupling of the rotation motion to the translation motion, i.e., rotational motion along one axis being coupled with translational motion along the axis.
In an exemplary embodiment, when the frequency of the applied external magnetic field is above a pre-defined threshold frequency, above the cut-off frequency or high frequency, the magnetic moment of the magnetic probes is not able to align with the magnetic field and the magnetic probes may rotate asynchronously with respect to the applied external magnetic field.
In an exemplary embodiment, the response of the magnetic probes may be directly related to a measure or degree of rotational (angular) motion. In an exemplary embodiment, a measure or degree of rotational motion may be translated to a viscosity measurement and a relaxation time (elasticity) measurement for the fluid. In an exemplary embodiment, the response of the magnetic probe may be a measure of the translational motion. In an exemplary embodiment, a pitch associated with the translation motion may be translated into a relaxation time measurement of the fluid.
In an exemplary embodiment, when the frequency of the external magnetic field is a chirp frequency, where the frequency of the external magnetic field is varying or increasing non-linearly, i.e., wherein chirp may be defined as a single where the frequency increases or decreases with time, the threshold frequency may be determined within a pre-determined time frame, for example 1-2 sec, and the threshold frequency may be inversely related to viscosity of the fluid. In an exemplary embodiment, successive repetition of the chirp frequency may enable in determining an accuracy of the threshold frequency, and hence the viscosity. In an exemplary embodiment, the method may include performing cross-correlation of simultaneous translation motion and rotational motion results in a high signal to noise ratio, thereby providing accurate rheological parameter measurements.
In an exemplary embodiment, the magnetic probes may have a length in the range of about 0.5 µm to about10mm, and not limiting to these boundaries. In an exemplary embodiment, the first axis (also referred to as the long axis) defined to be extending along the length of the magnetic probe. In an exemplary embodiment, the magnetic probes have a width in the range of about 0.05 µm to 5mm and a second axis (also referred to as a short axis) defined to be extending through the width of the magnetic probe.
In an exemplary embodiment, the magnetic probes may be at least one of a permanent magnet or a temporary magnet or an electromagnet. In an exemplary embodiment, the external magnetic field may be rotating magnetic field and/or an oscillating magnetic field. In an exemplary embodiment, the magnetization of the magnetic probe comprises at least one of a diamagnetic or a paramagnetic or a ferromagnetic or an antiferromagnetic or a ferrimagnetic or superparamagnetic.
Reference is now made to Figure 1, which illustrates an exemplary pictorial representation of the system 100 used for measuring the response of magnetic probes in the fluid and computing the rheological parameters of the fluid in accordance with an embodiment of the present disclosure. System 100 illustrates sample cell 110 placed within coil 120, and the sample cell 110 may be configured to hold sample 112. Coil 120 is a tri-axial Helmholtz coil and is in an initial OFF state. Switching on power to coil 120 induces a magnetic field, which may be applied to the sample in sample cell 110. Recording device 130 is placed in line, for example within a field of view, to observe the reaction or response of sample 112 on application of the magnetic field by coil 120. Recording device 130 is configured to be coupled to computing device 140. Computing device 140 is configured to receive the data from recording device 130 and perform analysis on the data. Control unit 150 is interfaced with computing device 140, wherein control unit 150 may be configured to control the frequency of the magnetic field or the power to coil 120 to control the frequency of the magnetic field.
Sample 112 may be an admixture of a fluid containing particulate matter, wherein the particulate matter is magnetized and referred to as magnetic probes. The particulate matter may be an organic material or an inorganic material or a combination thereof of a different organic material or combination of different inorganic materials (alloys). The particulate matter is magnetized first, for example by placing the particulate matter in the presence of a magnetic field. It should be obvious to a person of ordinary skill in the art that various techniques are available to magnetize particulate matter and all such techniques fall within the scope of the present disclosure. In an exemplary embodiment, the particulate matter may include at least one of Iron or Nickel or cobalt or an alloy or steel or samarium or neodymium. In an exemplary embodiment, the particulate matter (hereinafter also referred to as particle) may be magnetized along a first axis or a second axis. In an exemplary embodiment, magnetization of the particles induces a magnetic moment to the particle along the first axis or the second axis.
The magnetized particles (also hereinafter referred to as magnetic probes) may be mixed with the fluid to form a suspension (hereinafter referred to as a sample). Sample 112 formed by inserting the magnetic probes into the fluid will be in a colloidal state. A small portion of sample 112 may be aspirated and placed in sample cell 110 and sample cell 110 may be tightly sealed. Sealing sample cell 110 is done to ensure that there is no evaporation of the sample 112 from sample cell 110 and no air within sample cell 110 while performing the experiment to detect rheological parameters for the fluid. In an exemplary embodiment, sample cell 110 may be a narrow hollow tube sealed at one end and open at the other end into which sample 112 is placed into sample cell 110 from the open end, and sample cell 110 is tightly sealed such that there is no air gap in sample cell 110. In another exemplary embodiment, sample 112 may be placed on a glass substrate and covered with another glass substrate, where sample 112 is sandwiched between two glass substrates and sealed tightly such that there is no air in the area where sample 112 is placed. Tightly sealing of sample 112 between the substrates ensures there is no evaporation of sample 112 from sample cell 110. It should be obvious to a person of ordinary skill in the art that any non-magnetic transparent material, organic or inorganic may be used for forming sample cells 110. It should also be obvious to a person of ordinary skill in the art that various other methods ad techniques may be employed to form a sample cell containing the sample and all such variations of techniques and method for forming the sample cell fall within the scope of the present disclosure.
Coil 120 is typically a triaxial Helmholtz coil that may produce a rotating magnetic field or oscillating magnetic field. It should be obvious here to a person of ordinary skill in the art that various other coils 120 may be used where sample 112 may be placed within coil 120. Initially coil 120 is in an OFF state and there is no magnetic field present or no external magnetic field acting on sample 112.
Recording device 130 may be any device configured to record data and transmit data of the recording to a computing device 140. In an exemplary embodiment, recording device 130 may include a camera or any other imaging device which is kept in the field of view (FOV) of the sample to record the motion of the magnetic probes in sample 112. In an exemplary embodiment, on switching coil 120 to an ON state the magnetic probes tend to align along the direction of the magnetic field and the movement of the magnetic probe on application of the magnetic field may be recorded by recording device 130 and sent to computing device 140.
Computing device 140 essentially may include any device that includes at least a memory and a processor, which is capable of receiving data from recording device 130, performing analysis on the data and providing the results of the analysis to an end user. In an exemplary embodiment, computing device 140 may include a computer, a laptop, a mobile phone, PDA etc. Computing device 140 may also include storage to store data. Computing device 140 may include application programs that may be loaded onto the memory and executed to perform actions based on tasks.
Control unit 150 is also coupled to computing device 140. Control unit 150 essentially monitors the frequency of coil 120 to ensure that the required frequency is applied to coil 120. Control unit 150 may also monitor switching OFF and ON coil 120 for application of the external magnetic field on sample 112 placed within coil 120. In an exemplary embodiment, control unit 150 may be part of computing device 140 and directly interfaced with coil 120.
In an exemplary embodiment, the colloidal probes (which are also referred to as probes or rods) were grown on a Si wafer consisting of pillars with spacing 1 µm using the glancing angle deposition technique. The process or technique is not explained in detail as it is well known, and the actual process does not fall within the scope of the present disclosure. In an exemplary case of making the probes, the rotation speed was maintained at a relatively low velocity in the range of about 0.03 rad s-1, which advantageously leads to the growth of rod structures or the probes. The length L of the probes is about 5 µm and thickness s of the probes is about 1 µm. In an exemplary embodiment, in order to impart a magnetic moment to the probes, the probes two iron-cobalt layers are alternatively sandwiched, each having a thickness of about 150 nm between the SiO2 during the growth process. In an exemplary case, the probes are then magnetized such that their magnetic moment vector orients parallel to their long axis.
In an exemplary case, the suspension of the developed probes is then obtained in ultra-pure water by sonication of the wafer. In an exemplary case, as a viscoelastic fluid, e an equimolar solution of surfactant cetylpyridinium chloride monohydrate (CPyCl) and sodium salicylate (NaSaI) in water at a concentration of 7 Mm was employed. In an exemplary embodiment, the fluid exhibits a viscoelastic nature. In an exemplary embodiment, using passive micro rheology, the zero shear viscosity ?0 of the fluid was determined to be about 0.25 ± 0.02 Pa s, viscosity at infinite shear ?8 of the fluid was determined to be about 0.04 ± 0.01 Pa s, and the stress-relaxation time t of the fluid was determined to be about 1.73 ± 0.03 s. In an exemplary embodiment, a small volume or fractions of the probes suspended in the viscoelastic fluid (sample) is confined using a thin sample cell 120, the sample cell having a height of about 100 µm and the sample cell with the sample placed between the two Helmholtz coils (along the defined x and y axis).
In an exemplary embodiment, owing to the magnetic moment of the probes being aligned along the long axis, the probes display an in-plane rotational motion when the probes are subjected to a rotating magnetic field B along the X-Y plane. In an exemplary embodiment, in order to identify and analyze the distinct features of the rotational probe motion, an amplitude B of the magnetic field is varied between 10 - 30 G and the frequency ?B of the magnetic field is varied between 1 - 100 Hz. It should be obvious to a person of ordinary skill in the art that for applied B values, the magnetic moment remains parallel to the long axis of the rod, which may be verified separately by a response of the probes to the applied field direction.
Reference is now made to Figure 2, which illustrates an exemplary sample cell 110 placed within coil 120 for measuring the rheological parameters of the fluid by generating a magnetic field when coil 120 is switched to an ON state in accordance with an embodiment of the present disclosure. As disclosed previously with respect to Figure 1, sample cell 110 contains sample 112, which is placed on substrate or stand 115 within coil 120. Coil 120 as discussed previously is a triaxial Helmholtz coil preferably with copper windings or windings consisting of material with a high conductivity. Though coil 120 is a triaxial, response of the magnetic probes in sample 112 is monitored along two-dimensions, for example in the x and y direction. It should be obvious that response of the magnetic probes in sample 112 may be monitored along all 3 axes (three-dimensional plane), but the measurements along the third axes is neglected as measurements in the two-dimensional plane provide sufficient data to determine rheological properties of the fluid. In an exemplary embodiment, sample cell 120 is placed within coil 120 in the XY plane and hence the sample is presumed to be in the XY place as well. It should also be obvious to a person of ordinal skill in the art that variation of coil 120 and sample cell 110 may be possible and all such variation fall within the scope of the present disclosure. The strength and frequency of the magnetic field applied to sample 120 may be controlled by an external device coupled to coil 120. For example, the frequency of the magnetic field may be chosen by varying the current supplied to coil 120.
Reference is now made to Figure 3A, which illustrates an exemplary scanning electron microscope (SEM) image 300A indicating a view of a magnetic probe which is helical in nature and used for determining the response of the magnetic field on the magnetic probes in the fluid on application of a magnetic field, where bright portions 302, 304 in the SEM image illustrate a Fe-Co layer in accordance with an embodiment of the present disclosure. The scale bar for the image is about 1 µm. In an exemplary case, the length “L” of the probes is about 5 µm and the thickness “s” of the probes is about 1 µm. It should be obvious to a person of ordinary skill in the art that these numbers mentioned are only exemplary in nature and probes having different lengths and thickness may be used, and all such variation of probes fall within the scope of the present disclosure. In an exemplary embodiment, in order to impart a magnetic moment to the probes, sandwiched two iron-cobalt layers are alternatively sandwiched, each of thickness 150 nm between the SiO2 during the growth process. The probes are then magnetized such that their magnetic moment vector orients parallel to their long axis.
Reference is now made to Figure 3B, which illustrates an exemplary scanning electron microscope (SEM) image 300B indicating an alternate view of a magnetic probe which is rod shaped and used for determining the response of the magnetic field on the magnetic probes in the fluid on application of a magnetic field, where bright portions 312, 314 in the SEM image illustrate a Fe-Co layer in accordance with an embodiment of the present disclosure. The scale bar for the image is about 1 µm. In Figure3A and Figure 3B the SEM images as illustrated are only illustrative in nature, and other SEM images are a possibility.
Reference is now made to Figure 4, which is an exemplary illustration 400 of relevant coordinates to describe rotational motion of the magnetic probe 112 in two dimensions in accordance with an embodiment of the present disclosure. The probe 112 (reference to probe(s) in this document means magnetic probe(s))is illustrated as being placed in a three dimensional plane (XYZ). R denotes the axis of rotation of the probe in the XY plane. On application of the external magnetic field magnetic moment m of the probe is aligned along axis of rotation R. Angle ? between the x-axis and the long axis of the probe is (here the long axis coincides with the magnetic moment of the particle) while beta ß is the angle between magnetic moment m and the magnetic field vector B.
Reference is now made to Figure 5, which illustrates an exemplary motion of a magnetic probe indicating a long axis and a short axis along which the response of the magnetic probe is measured on application of the magnetic field in accordance with an embodiment of the present disclosure. Probe 112 has a long axis L and a short axis S. Long axis L of the probe is aligned along the direction of the magnetic field vector B. An exemplary trajectory of probe 112 is illustrated, and the trajectory of probe 112 in the sample will be based on the amplitude and frequency of the applied magnetic field on the sample, which may rotate along the long axis L or along the short axis S based on the amplitude and frequency of the magnetic field B.
Reference is now made to Figure 6A, which is an exemplary illustration of a time evolution 600A of the angular coordinate ? obtained when the magnetic probe is rotated about the short axis (the second axis) when the applied magnetic field strength is B=30 G and the applied frequency is ?_B=3 Hz in accordance with an embodiment of the present disclosure. The x-axis represents time in seconds and the y-axis represents the angular coordinates ? in radians. In an exemplary case, the time evolution of the probe with respect to the angular coordinates illustrates a linear increase 610 when the magnetic field applied to the probe is about 30 G and the applied frequency to the probe is about 3 Hz and the probe is rotate about the short axis S. At time 0 seconds the angular coordinate ? is 0 radians. At a time of about 0.5 seconds, the angular coordinate ? is about 10 radians. At a time of about 1 second the angular coordinate ? is about 20 radians. At a time of about 1.5 second the angular coordinate ? is about 30 radians, and at a time of about 2 second the angular coordinate ? is about 40 radians. In the exemplary case when the applied magnetic field strength is B=30 G and the applied frequency is ?_B=3 Hz with increasing time a linear 610 increase is observed with respect to the angular coordinates of the probes.
Reference is now made to Figure 6B, which is an exemplary illustration of a typical trajectory 600B of the magnetic probe when rotated about the long axis on application of an external magnetic field in accordance with an embodiment of the present disclosure. As illustrated in the exemplary case on application of the applied external magnetic field to probe 112, a typical trajectory 620 of probe 112 is illustrated which the probes rotates along the long axis, which is almost flat linear path, when at the applied magnetic field strength B is about 30 G and frequency ?_B is about 3 Hz. Figure 6B is an SEM image taken at a resolution of about 2 µm.
Reference is now made to Figure 7A, which is an exemplary illustration of a method 700A.
for preparing a sample and determining the rheological parameters of a fluid containing the magnetic probes in accordance with an embodiment of the present disclosure. In step 710 first a fluid is selected, where the fluid may be a Newtonian fluid or a non-Newtonian fluid or a combination thereof. The fluid characteristics, such as elasticity, viscosity, viscoelasticity etc., need to be ascertained, for which rheological parameters will be obtained and analyzed to obtain these properties associated with the fluid. In step 720, after selection of the fluid, magnetic probes are inserted into the fluid to create a suspension, the magnetic probes in the fluid will be in a colloidal state and may be referred to as the sample (as previously disclosed). Magnetic probes essentially contain particles that are magnetized and inserted into the fluid to study the rheological properties associated with a fluid.
In step 730, the sample (fluid with the magnetic probes) is placed in a sample cell. The sample cell has been described previously with respect to Figure 1. A small quality of the sample prepared is aspirated and placed into a sample cell and the sample cell is sealed to prevent any evaporation of the sample. In step 740, once the sample cell is prepared, the sample cell containing the sample is placed within a coil. The coil is preferably a Helmholtz coil or any other coil that can generate a rotating or oscillating magnetic field. The coil is initially in an OFF state and there will be no magnetic field present when the coil is in the OFF state.
In step 750, the coil is switched to an ON state and the strength/amplitude of the magnetic field and the frequency of the magnetic field may be chosen to be above a certain threshold region where it may be suitable to study the response of the magnetic probes in the sample to determine the rheological properties associated with the fluid. In response to the applied magnetic field, as discussed previously, the magnetic moment of the probes align along the direction of the magnetic field and the particle shows either translational motion or rotational motion or a combination thereof. In step 760, the response of the probes to the applied magnetic field are recorded, for example using an imaging device and then transmitted to a computing device. In step 770, based on the response of the probes to the applied magnetic field the rheological properties of the fluid may be ascertained. Several other changes may be made to these steps to determine the rheological properties of a chosen fluid, and all such changes and variations fall within the scope of the present disclosure.
Reference is now made to Figure 7B, which is an exemplary illustration of method 700B for preparing the magnetic probes in accordance with an embodiment of the present disclosure. In step 722 a suitable material, which may be an organic material or an inorganic material or a combination of different organic material or a combination of different inorganic material that can be magnetized are chosen. In an exemplary case as disclosed previously Iron-cobalt or iron-nickel may be chosen. In step 724 the particles are magnetized, and the process for magnetization as an exemplary case has been discussed previously. In an exemplary embodiment, the particles may be placed in a strong magnetic field and magnetized thereby creating magnetic probes. Magnetization may be performed either along a long axis L or along a short axis S of the probe. In Step 724A, magnetization of the particle to create the magnetic probes by the process of magnetization is to induce a magnetic moment to the particle along the axis of magnetization.
Reference is now made to Figure 7C, which is an exemplary illustration of a method 700C of preparing the sample for testing the rheological parameters of the fluid in accordance with an embodiment of the present disclosure. In step 732 a sample cell or a substrate is taken. The substrate is preferably glass or a transparent material which does not react to an external magnetic field. In step 734 a small portion of the suspension (fluid with the magnetic probes) may be aspirated from the suspension prepared and the aspirated portion of the suspension may be placed in the sample cell or on the substrate. In step 736, the sample cell is sealed such that the suspension inside the sample cell does not evaporate or leak out. In case the suspension of placed on a substrate, the substrate with the suspension is covered with another substrate and sealed, such that the suspension is sandwiched between the two substrates, and essentially the two substrates may mimic the sample cell.
Reference is now made to Figure 7D, which is an exemplary illustration of a method 700D of measuring the rheological parameters of the fluid from the response of the magnetic probes in the fluid in accordance with an embodiment of the present disclosure. In step 742, the sample cell along with the sample (suspension) which contains a small portion of the fluid with the magnetic probes is placed in the coil, and the coil is switched to an ON state. Switching ON the coil will generate a magnetic field and the magnetic field generated is applied to the sample place within the coil. As discussed previously, because the suspension contains magnetic probes, the magnetic probes in the sample will respond to the applied magnetic field. In step 744 a check is made on the threshold of the applied magnetic field frequency. The frequency of the applied magnetic field is monitored to be above a certain threshold limit. In step 730, once the applied magnetic field is above a certain threshold the magnetic probes in the sample tend to align along the direction of the field, but face resistance due to the elasticity, viscosity and other parameters associated with the fluid. Recording and analyzing these responses will provide vital information regarding the rheological properties of the fluid.
Reference is now made to Figure 8A, which is an exemplary illustration 800A of a measure of the time progression of angular coordinate ? measured in the viscoelastic surfactant solution at various applied field frequencies? ??_B in accordance with an embodiment of the present disclosure. The x-axis represents time in seconds and the y-axis represents the angular coordinates ? measured in radians. Measurements are performed between a time interval of 0 seconds to 2 seconds, and the angular coordinates ? is computed. The graph 800A illustrates a time progression of the angular coordinates ? measured for a viscoelastic surfactant solution. When the applied magnetic field frequency ? ??_B is about 1Hz, from a time of 0 second to a time of 2 seconds, the angular coordinates ? linearly increases from 0 radians to about 10 radians, for 7 mM CPyCl/NaSal as the sample solution at magnetic field strength B of about 30G the linearity being at an angle of about 20 degrees (line 810). When the applied magnetic field frequency ? ??_B is about 60 Hz, from a time of 0 second to a time of 1.5 seconds, the angular coordinates ? linearly increases from 0 radians to about 30 radians steeply, for 7 mM CPyCl/NaSal solution as the sample at magnetic field strength B of about 30G the linearity being at an angle of about 50 degrees (line 812). The linearity is additionally followed with a periodic back and forth behavior of the angular coordinate ?.
When the applied magnetic field frequency ? ??_B is about 3 Hz, from a time of 0 second to a time of 1.5 seconds, for 7 mM 7 mM CPyCl/NaSal solution as the sample solution at magnetic field strength B about 30G the angular coordinates ? linearly increases from 0 radians to about 30 radians steeply, for the linearity being at an angle of about 50 degrees (line 814). When the applied magnetic field frequency ? ??_B is about 40 Hz, from a time of 0 second to a time of 1.5 seconds, for 7 mM CPyCl/NaSal solution as a sample solution at magnetic field strength B of about 30G the angular coordinates ? linearly increases from 0 radians to about 30 radians steeply, for the linearity being at an angle of about 70 degrees (line 816). In addition to the linear evolution, the angular coordinate ? also exhibits, back and forth osciallations. When the applied magnetic field frequency ? ??_B is about 8 Hz, from a time of 0 second to a time of 1.5 seconds, for water-glycerol mixture as a sample solution at magnetic field strength B of about 30G the angular coordinates ? linearly increases from 0 radians to about 30 radians steeply, for the linearity being at an angle of about 80 degrees (line 818). The graphs 800A illustrates how the angular coordinates change rapidly as a function of time for different sample solutions as a function of the applied magnetic field frequencies. In particular, the angular coordinate ? displays a transition from a linear increase at low applied field frequencies ? ??_B to an oscillatory linear increase at high applied frequencies. The transition point depends on magnetic drive and viscous drag of the fluid.
Reference is now made to Figure 8B, which is an exemplary illustration 800B of a measure of the angular frequency O of the magnetic probe as a function of applied field frequency, and the corresponding viscoelasticity measurement in the sample in accordance with an embodiment of the present disclosure. As illustrated the solid curve 821 is related to numerically obtained results for the viscoelastic fluid and the dashed curve 823 is the numerically obtained results for Newtonian cases. The solid symbols in the graph 800B correspond to the measurement in the viscoelastic fluid of 7 mM CPyCl/NaSal solution at magnetic field strength of about B=30 G (square, 822) and for a viscoelastic fluid of 7 mM CPyCl/NaSal solution as sample at magnetic field strength B=10 G (circle, 820) while the open symbols represent the Newtonian case of water-glycerol mixture at a magnetic field of about B=30 G (square, 826) and at a magnetic field of about B=30 G (circle, 828). For 7 mM CTAB/NaSal as sample solution at magnetic field strength of about B = 30G the measurements are indicated as inverted triangles (824), and the numerically obtained results are represented by the solid line 825
Each curve is normalized by the cut-off value i.e., O_C. The solid curve and the dashed curve are the numerically obtained results for the viscoelastic and Newtonian cases, respectively. There is a steep increase when the applied frequency is below the cut off frequency and then subsequently a gradual decrease in the measured valued as the frequency is increased. The decrease is faster in Newtonian fluids compared to non-Newtonian fluids used. The vertical stabs indicate the error margin for the measurements. For the non-Newtonian fluids the gradual decrease between the different samples is varying whereas for the Newtonian fluids it appears that the frequency of the field does not affect the decrease in angular frequency. For both frequencies 10G and 30G there is a large overlap region for Newtonian fluids.
Reference is now made to Figure 8C, which is an exemplary illustration 800C of the dependence of the translational probe velocity v on ? ??_B measured at B=50 G in the viscoelastic polymer solution (solid square) and in the Newtonian solution. The x-axis represents the frequency of the magnetic field in Hertz and the y-axis represents the velocity of the magnetic probes is measured in µm/s. The solid squares 832 represent the velocity of the magnetic probes as a function of frequency for a viscoelastic sample (polymer solution as sample), where a there is a sharp increase in the velocity from 0 µm/s to about 0.9 µm/s as the frequency increases from 2 Hz to 6 Hz, then a sharp fall in the velocity from about 0.9 µm/s to about 0.3 µm/s at a frequency of 6 Hz, a slight increase at 7 Hz to 0.4 µm/s and then a gradually tapering off from about 0.4 µm/s at a frequency of 7 Hz to about 0.35 µm/s at a frequency of about 10 Hz. For a Newtonian fluid at the same magnetic field amplitude of about 50G, the velocity increases from 0 µm/s at a frequency of about 2 Hz to about 0.83 µm/s at a frequency of about 8 Hz, and then tapers off from 0.93 µm/s at 8 Hz to about 0.3 µm/s at a frequency of about 10 Hz. An abrupt drop in the measured velocity v is a typical signature of the viscoelastic case, here, the elastic contribution of the fluid strongly modifies the translational-rotatioanal coupling of the elongated probe particle. Such a sudden drop is completely absent in the counterpart Newtonian fluid.
Reference is now made to Figure 8D, which is an exemplary illustration 800D of the pitch of the magnetic probe as a function of the applied field amplitude for a Newtonian case (open circle) and for the viscoelastic fluid (solid square). As illustrated as the strength of the magnetic field increases, for a Newtonian sample the pitch is almost a constant at 0.15 µm (line 834) and for a non-Newtonian sample the pitch increases gradually from 0.23 µm at a field strength of 3 mT to about 0.26 µm at a field strength of 6 mT. In a Newtonian, the pitch only depends on the geometry of the particle and is independent of applied magnetic field and the viscosity of the surrounding fluid. However, it exhibits a strong dependence on the magnitude of the applied field and the elastic nature of the viscoelastic fluid. Therefore, a feature which can be used to determine the elasticity of the surrounding viscoelastic fluid.
Reference is now made to Figure 8E, which is an exemplary illustration 800E of the numerically obtained time progression of the viscoelastic torque T_v, in accordance with the embodiments of the present disclosure. In an exemplary case the torque (total Torque TT) induced by a magnetic field T_m is the sum of viscoelastic torque and magnetic torque and may be represented by the formula T_T = T_v +T_m. In the exemplary case the phase difference ß between magnetic field vector B and the magnetic moment m of the probe and angular velocity O of the magnetic probe is obtained for the rheological parameter corresponding to 7 mM CpyCl/NaSaI as the sample solution at a magnetic field strength B = 30 G and the frequency at about ?_B = 200 rad s^(-1) in accordance with an embodiment of the present disclosure.
In the exemplary case, the x-axis represents time in seconds and the y-axis illustrated measurements of different parameters associated with the magnetic probes in the fluid measured for the exemplary case of 7mM CpyCl/NaSaI solution as a sample when the magnetic field strength was maintained at 30 G and the frequency of the filed was ?B of about 200 rad/sec. A measure of the viscoelastic torque T? of the viscoelastic fluid versus time T is illustrated in graph 840 that the torque measurement between time 0 seconds and 2 seconds is cyclic in nature oscillating between a value of -1.02 to -1.04. For example, one cycle of the graph 840 begins at time T = 0 seconds and the torque measured in fNm is about -1.025 goes down to -1.04 at a time of about 0.02 seconds the raises sharply up back to -1.02 at a time of about 0.03 seconds and the fall back to about -1.025 at about 0.035 second completing one cycle full cycle and the pattern was found to be repetitive for every 0.035, the second cycle starting from 0.035 seconds and repeating every 0.035 secs until about 2 secs.
A measure of the torque Tm versus time T is illustrated in graph 842 that the torque measurement between time 0 seconds and 2 seconds is cyclic in nature oscillating between a value of about 2 to -2. For example, one cycle of the graph 842 begins at time 0 seconds and the torque measured in fNm is about 2 goes down to -2 at a time of about 0.025 seconds the raises back to 2 at a time of about 0.045 seconds completing one cycle, and the pattern was found to be repetitive for every 0.045 second cycle from 0.045 seconds until about 2 seconds.
A measure of the total torque TT which is the sum of the torque of the viscoelasticity and the torque of the magnetic moment versus time T is illustrated in graph 844 that the torque measurement between time 0 seconds and 2 seconds is cyclic in nature oscillating between a value of about 1.5 to -2.5. For example, one cycle of the graph 844 begins at time 0 seconds and the torque measured in fNm is about 1.5 goes down to -2.5 at a time of about 0.025 seconds the raises back to 1.5 at a time of about 0.045 seconds completing one cycle, and the pattern was found to be repetitive for every 0.045 second cycle from 0.045 seconds until about 2 seconds. The total torque follows the same pattern as the torque of the magnetic moment.
A measure of the phase difference ß versus time T is illustrated in graph 846 where the measurement between time 0 seconds and 2 seconds is cyclic in nature oscillating between a value of about -p and p, with discrete discontinuities when the total torque is at a minimum. . For example, one cycle of graph 846 begins at time 0.025 seconds the phase difference is – p and gradually increases to a value of p at time 0.06 secs. There is a discrete discontinuity in the phase difference when the total torque reaches a minimum value of -2.5.
A measure of the angular velocity of the probe ? versus time T is illustrated in graph 848 where the measurement between time 0 seconds and 2 seconds is cyclic in nature oscillating between a value of about 400 at 0 secs going down to -400 at about 0.025 sec and back to 400 at a time of about 0.035 secs, and repeating in cycles after that. The pattern is similar as that of the total magnetic moment measured between 0 secs and 0.2 secs except for the range of values in the y-axis being different. The time evolution of ß with two distinct slopes at such a high frequency is a generic signature of the viscoelastic fluid. Accordingly, the observed asymmetry in T_m between the positive and negative part. This signature manifests due to strong coupling of the magnetic probe particle to the surrounding viscoelastic fluid.
Reference is now made to Figure 8F, which is an exemplary illustration 800F of a typical sequence of an input chirped pulse in the time domain where the frequency varies linearly from 1Hz to 15 Hz within a timeframe of 1 s in accordance with an embodiment of the present disclosure. The plot 800F illustrates a measure of current versus time. The current measurement oscillates between a value of -1 to 1, initially each cycle is separated apart and after about 0.5 secs the measurements seems to be periodic at every 0.1 sec or lesser and with increase in time the periodicity of the signals occurs closer.
Figure 8G is an exemplary illustration 800G of the resulting linear magnetic probe displacement for the applied chirped pulses of various timeframes, wherein the shaded portion represents the cut-off regime. The graph illustrates the displacement µm as a measure of the frequency ?B. The shaded region in the plot shows the cut-off regime, which occurs at about a frequency of about 6 Hz. The first line 860 measured at a response time of 5 seconds illustrates the displacement with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the displacement from 0 to about 2 µm and beyond the cutoff at 6 Hz till about 15 Hz, the displacement increases from 2 µm to about 3 µm. The second line 862 measured at a response time of 3 seconds illustrates the displacement with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the displacement from 0 to about 1 µm and beyond the cutoff at 6 Hz till about 15 Hz, the displacement increases from 1 µm to about 1.5 µm. The third line 864 measured at a response time of 1 seconds illustrates the displacement with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the displacement from 0 to about 0.3 µm and beyond the cutoff at 6 Hz till about 15 Hz, the displacement increases from remains fairly constant around 0.3 µm, with slight variations around the 0.3 µm region. As a result of the increase in the time for the frequency span, the magnetic probe experiences more time to translate, particularly before the cut-off regime, thus, it exhibits large translational displacement. The cut-off occurs when the magnetic drive is not able to contract the viscous drag of the fluid, hence, provide us a direct measure of the viscosity of the fluid medium.
Figure 8H is an exemplary illustration of a time evolution of the magnetic probe angle ? in response to the applied chirped sequences of various durations, wherein the shaded portion represents the cut-off regime. The graph illustrates the probe angle ? as a measure of the frequency ?B. The shaded region in the plot shows the cut-off regime, which occurs at about a frequency of about 6 Hz. The first line 870 measured at a response time of 5 seconds illustrates the probe angle with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the probe angle from 0 to about 2200 degrees and beyond the cutoff at 6 Hz till about 15 Hz, the probe angle increases from 2200 degrees to about 4000 degrees. The second line 872 measured at a response time of 3 seconds illustrates the probe angle with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the probe angle from 0 degrees to about 1500 degrees and beyond the cutoff at 6 Hz till about 15 Hz, the probe angle increases from 1500 degrees to about 2500 degrees. The third line 874 measured at a response time of 1 seconds illustrates the probe angle with frequency. As the frequency increases from 1 to 6 Hz, there is an increase in the probe angle from 0 degrees to about 450 degrees and beyond the cutoff at 6 Hz till about 15 Hz, the displacement increases from remains fairly constant or shows a graduly increase from 450 degrees to about 500 degrees, with slight variations between 450-500 degrees. As a result of the increase in the time for the frequency span, the magnetic probe experiences more time to rotate, particularly before the cut-off regime, thus, it leads to large angular displacement. The angular cut-off occurs when the magnetic drive is not able to contract the rotational viscous drag of the fluid, hence, provide us a direct measure of the viscosity of the fluid medium.
Although the present disclosure has been described with reference to several preferred embodiments, it should be understood that the present disclosure is not limited to the preferred embodiments disclosed here. Embodiments of the present disclosure are intended to cover various modifications and equivalent arrangements within the spirit and scope of the appended claims. Although the foregoing disclosure has been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may be practised within the scope of the appended claims. Examples of the present disclosure have been described in language specific to structural features and/or methods. It should be noted that there are many alternative ways of implementing both the process and apparatus of the present invention. Accordingly, embodiments of the present disclosure are to be considered illustrative and not restrictive, and the invention is not to be limited to the details given herein but may be modified within the scope and equivalents of the appended claims. It should be understood that the appended claims are not necessarily limited to the specific features or methods described. Rather, the specific features and methods are disclosed and explained as examples of the present disclosure. , Claims:We Claim

1. A method for determining rheological properties of a fluid, the method comprising:
inserting magnetic probes (110, 110A) into a fluid forming a suspension;
placing the suspension in a sample cell;
placing the sample cell within a coil, wherein the coil is configured to produce a magnetic field when switched to an ON state;
switching the coil to an ON state, and applying an external magnetic field (B) to the sample cell, wherein a frequency of the external magnetic field applied to the suspension in the sample cell is above a pre-defined threshold; and
determining rheological properties associated with the fluid based on a response of the magnetic probes to the applied external magnetic field in the suspension, wherein the response of the magnetic probes is a measure of the asynchronous motion of the magnetic probes in the fluid.

2. The method as claimed in claim 1, wherein the magnetic probes comprise:
particles comprising at least one of Iron or Nickel or cobalt or an alloy or steel or samarium or neodymium, and
wherein the particles are magnetized along a first axis or a second axis, wherein magnetization of the particles induces a magnetic moment to the particle along the first axis or the second axis.

3. The method as claimed in claim 1, wherein on application of the external magnetic field the response of the magnetic probes comprises:
aligning the magnetic moment of the magnetic probes along the direction of the applied external magnetic field.

4. The method as claimed in claim 3, wherein aligning the magnetic probes to the applied external magnetic field comprises:
generating at least a motion of the magnetic probes along a degree of freedom, wherein the degree of freedom includes a number of independent parameters defining a configuration or a state of the magnetic probe.

5. The method as claimed in claim 5, wherein on application of the external magnetic field to the suspension containing the magnetic probes, wherein the external magnetic field is a rotating magnetic field, the response of the magnetic probes is a rotation or rotational motion produced by the magnetic moment of the magnetic probes along an axis of the magnetic probe.

6. The method as claimed in claim 5, wherein if the magnetic moment of the magnetic probe is aligned along the first axis the response is a rotation or rotational motion produced about the second axis.

7. The method as claimed in claim 5, wherein when the external magnetic field is below a certain threshold frequency the magnetic moment of the magnetic probe is aligned along the second axis the response is a rotation or rotational motion is produced about the second axis.

8. The method as claimed in claim 7, wherein when the frequency of the external magnetic is around the threshold frequency, the rotation or rotational motion along the second axis undergoes a gradual transition or a translation motion along the first axis.

9. The method as claimed in claim 7, wherein when the frequency of the external magnetic is above the threshold frequency, the response of the magnetic probes is an asynchronous rotation about the first axis and the second axis.

10. The method as claimed in claim 4, wherein on application of the high frequency external magnetic field, wherein the external magnetic field is a rotating magnetic field,
the response of the magnetic probes is a rotation along the second first axis and an additionally induced translation motion.

11. The method as claimed in claim 1, wherein the fluid is a Newtonian fluid or a non-Newtonian fluid or a combination thereof.

12. The method as claimed in claim 1, wherein when the frequency of the applied external magnetic field is above a pre-defined threshold frequency the magnetic probes rotate asynchronously with respect to the applied external magnetic field.

13. The method as claimed in claim 6 or 7, wherein the response of the magnetic probes includes a measure or degree of rotational (angular) motion, wherein the measure or degree of rotational motion is translated to a viscosity measurement and a relaxation time (elasticity) measurement for the fluid.

14. The method as claimed in claim 8, wherein the response of the magnetic probe is a measure of the translational motion, and wherein a pitch associated with the translation motion is translated into a relaxation time measurement of the fluid.

15. The method as claimed in Claim 10, wherein when the frequency of the external magnetic field is a chirp frequency, the threshold frequency is determined within a pre-determined time frame (1-2 sec), and wherein the threshold frequency is inversely related to viscosity of the fluid.

16. The method as claimed in claim 15, wherein successive repetition of the chirp frequency enables determining an accuracy of the threshold frequency, and hence the viscosity.

17. The method as claimed in claim 16, comprises:
performing cross-correlation of simultaneous translation motion and rotational motion results in a high signal to noise ratio, thereby providing accurate rheological parameter measurements.

18. The method as claimed in claim 1, wherein the magnetic probes (110, 110A) have a length in the range of about 0.5 µm to 10mm and the first axis (long axis) defined to be extending along the length of the magnetic probe.

19. The method as claimed in claim 1, wherein the magnetic probes (110, 110A) have a width in the range of about 0.05 µm to 5mm and a second axis (short axis) defined to be extending through the width of the magnetic probe.

20. The method as claimed in claim 1, wherein the magnetic probes is at least one of a permanent magnet or a temporary magnet or an electromagnet.

21. The method as claimed in claim 1, wherein the external magnetic field is rotating magnetic field and/or an oscillating magnetic field.

22. The method as claimed in claim 1, wherein the magnetization of the magnetic probe comprises at least one of a diamagnetism or a paramagnetism or a ferromagnetism or an antiferromagnetism or a ferrimagnetism or a superparamagnetism.

Dated this 09th day of November 2023
Indian Institute of Science
By their Agent & Attorney

Dr. Eric W B Dias
Reg No IN/PA- 1058
of Khaitan & Co