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US-12625100-B2 - Magnetic resonance method and system for characterizing circular Couette flow of fluids

US12625100B2US 12625100 B2US12625100 B2US 12625100B2US-12625100-B2

Abstract

A method and system of characterizing flow behavior of a fluid sample including providing a magnet with a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient, inducing circular Couette flow in the fluid in at least the sensitive region, generating an NMR pulse sequence comprising at least two pulses with a delay between the pulses, acquiring at least one echo from the pulse sequence from the sensitive region, measuring the magnitude of the NMR signal of the at least one acquired echo, normalizing the measured magnitude to a reference magnitude, and using the normalized magnitude to derive a shear rate for the fluid sample.

Inventors

  • William Selby
  • Igor Mastikhin

Assignees

  • William Selby
  • Igor Mastikhin

Dates

Publication Date
20260512
Application Date
20230818

Claims (20)

  1. 1 . A method of characterizing flow behavior of a fluid sample comprising: i) providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient; ii) inducing circular Couette flow in the fluid in at least the sensitive region and providing a rotation speed of the sample; iii) generating an NMR pulse sequence comprising at least two pulses with a delay between the pulses; iv) acquiring at least one echo from the pulse sequence from the sensitive region v) measuring the magnitude of the NMR signal of the at least one acquired echo; vi) normalizing the measured magnitude to a reference magnitude; and vii) determining a flow behavior index for the fluid sample though fitting the measured magnitudes using a numerical integration equation.
  2. 2 . The method of claim 1 , wherein the fluid is a non-Newtonian fluid.
  3. 3 . The method of claim 2 , wherein the magnet is a unilateral magnet.
  4. 4 . The method of claim 3 , wherein the echoes from the pulse sequence are acquired from a slice in the at least a portion of the sample.
  5. 5 . The method of claim 2 , wherein the fluid is located in the interstitial space between inner and outer concentric cylinders where the inner cylinder is located within the outer cylinder, the circular Couette flow is induced by rotating one of the cylinders while maintaining the other cylinder stationary, and the rotation speed is the rotation speed of the stationary cylinder.
  6. 6 . The method of claim 1 , wherein the integration equation is S = ∫ R 1 R 2 ρ ⁡ ( r ) ⁢ ∫ θ 1 θ 2 e - i ⁢ ( γ ⁢ G ⁢ υ θ ( r ) ⁢ cos ⁢ θτ 2 ) ⁢ rdrd ⁢ θ where S is the NMR signal, R 1 and R 2 , are the radii of the inner and outer cylinders, γ is the gyromagnetic ratio, G is the magnetic field gradient, v is a kinematic viscosity of the fluid sample, r is a radial position inside the sample, θ is the angle between the velocity and magnetic field gradient and d is the gap between the inner and outer cylinders, τ is a delay between pulses, and p(r) is spin density distribution.
  7. 7 . The method of claim 1 , wherein the pulse sequence is a Carr-Purcell-Meiboom-Gill sequence.
  8. 8 . The method of claim 1 , wherein the reference magnitude is acquired by carrying out steps i) and iii) to v), where the fluid sample is stationary.
  9. 9 . The method of claim 8 , wherein the NMR pulse sequence used in step iii) for the stationary sample is a DANTE sequence and wherein the echo time is varied.
  10. 10 . The method of claim 1 , wherein the reference magnitude is the magnitude of the NMR signal acquired from a Newtonian reference sample.
  11. 11 . The method of claim 8 , wherein the echo time for the NMR pulse sequence is shorter than the echo time used for the stationary sample.
  12. 12 . The method of claim 1 , further comprising in step iv), acquiring a first plurality of echoes where the echo times are varied, and in step v), measuring the magnitudes of the first plurality of echoes.
  13. 13 . The method of claim 1 , further comprising in step iv), acquiring a second plurality of echoes where the echo times of the second plurality of echoes are shorter than or equal to the echo times of the first plurality of echoes.
  14. 14 . The method of claim 1 , wherein the fluid sample is housed in the interstitial space between an inner and an outer cylinder, and wherein in step vii), the integration equation is S = ∫ R 1 R 2 e ( - i ⁢ γ ⁢ G ⁢ υ θ ( r ) ⁢ cos ⁢ θτ 2 ) ⁢ rdr + ∫ R 1 R 2 e ( i ⁢ γ ⁢ G ⁢ υ θ ( r ) ⁢ cos ⁢ θτ 2 ) ⁢ rdr = ∫ R 1 R 2 cos ( γ ⁢ G ⁢ υ θ ( r ) ⁢ cos ⁢ θτ 2 ) ⁢ rdr ( 13 ) where S is the NMR signal, R 1 and R 2 , are the radii of the inner and outer cylinders, γ is the gyromagnetic ratio, G is the magnetic field gradient, v is a kinematic viscosity of the fluid sample, r is a radial position inside the sample, θ is the angle between the velocity and magnetic field gradient, d is the gap between the inner and outer cylinders, and τ is a delay between pulses.
  15. 15 . The method of claim 1 , wherein step vii) the integration equation is S = 2 ⁢ π ⁢ ∫ R 1 R 2 J 0 ( γ ⁢ G ⁢ υ θ ( r ) ⁢ τ 2 ) ⁢ rdr where S is the NMR signal, R 1 and R 2 , are the radii of the inner and outer cylinders, γ is the gyromagetic ratio, G is the magnetic field gradient, v is a kinematic viscosity of the fluid sample, J 0 is a Bessel function of the first kind, and τ is a delay time.
  16. 16 . The method of claim 1 , further comprising using the normalized magnitude to derive a shear rate for the fluid sample.
  17. 17 . An NMR system comprising: a portable unilateral magnetic having a constant gradient perpendicular to a surface of the magnet; a tubular stator vessel suitable for holding a sample fluid, wherein the stator is adjacent the surface and at least partially located in the constant gradient; a tubular rotor located inside of the stator vessel along the central longitudinal axis of the stator vessel; a motor operably connected to the tubular rotor for rotating the rotor around the central axis; a radio frequency coil around the tubular stator; and an NMR console operably connected to the radio frequency coil.
  18. 18 . The NMR system of claim 17 , further comprising a sensor for measuring the rotation speed of the tubular rotor.
  19. 19 . The NMR system of claim 17 , wherein the NMR console comprises a radio frequency generator and a radio frequency detector both operably connected to the radio frequency coil, and a computer system operably connected to the radio frequency detector.
  20. 20 . The NMR system of claim 19 , wherein the computer system comprising computer program instructions for computer implemented steps comprising generating an NMR pulse sequence comprising at least two pulses with a delay between the pulses; acquiring at least one echo from the pulse sequence from the sensitive region; measuring the magnitude of the NMR signal of the at least one acquired echo; normalizing the measured magnitude to a reference magnitude; and determining a flow behavior index for the fluid sample though fitting the measured magnitudes using a numerical integration equation.

Description

CROSS-REFERENCE TO RELATED APPLICATION This application claims the benefit of U.S. Provisional Patent Application Ser. No. 63/399,952 filed Aug. 22, 2022. FIELD In one of its aspects, the present disclosure relates generally to a method and system for characterizing circular Couette flow of fluids. BACKGROUND Even prior to the invention of magnetic resonance imaging (MRI) [1], nuclear magnetic resonance (NMR) has found recurring applications in rheological measurements with varying degrees of complexity [2, 3, 4]. Over the years, the methods for characterizing fluid flow using NMR have improved significantly, allowing for the characterization of increasingly complex flow regimes [5, 6, 7, 8, 9]. MRI-based methods can provide significant advantages over conventional rheometric techniques that characterize macroscopic properties such as the force or torque exerted on a boundary and the relative velocity between boundaries. Bulk measurements of rheological properties are then deduced by assuming that the material and the shear rate are homogeneous in the gap between boundaries [5]. Sophisticated MRI-based methods offer spatial resolution that carries information on the inner structures of a flow system. Furthermore, unlike optical scattering methods, NMR allows for the characterization of opaque samples. Rheological-NMR (Rheo-NMR) methods have been applied in many fields such as: food science [10, 11], biomedicine [12, 13], and pharmaceuticals [14, 15]. While informative, conventional methods often require large and expensive MRI scanners and can be difficult to implement without extensive experience in NMR. Several low-field Rheo-NMR techniques have previously been developed that employ permanent magnet systems in the characterization of rheological properties. Some techniques integrate permanent magnet arrays into commercially available rheometers [12, 16] and measure NMR relaxation parameters in conjunction with rheological properties. Others make use of permanent magnets and gradient coils to image velocity distributions [17], requiring a relatively large and homogeneous instrument (approx. 150 kg). Portable, low-field NMR sensors such as the NMR MOUSE [18] and more recent developments such as the PROTEUS magnet for flow allow for an alternative approach to be considered. While being more compact and affordable, portable magnets offer many advantages typically associated with NMR. Reduced size and cost require sacrificing field homogeneity and sensitivity; therefore, portable NMR sensors are not as versatile as conventional MRI scanners and are often designed and optimized around a specific class of applications. Various techniques have been developed that employ portable, low-field instruments in flow characterization. Previous work has shown that the flow behavior of non-Newtonian fluids can be characterized by employing simple constant gradient magnet arrays and observing the signal phase interference caused by the velocity distribution within the sensitive volume [20, 21]. While the size and cost of the NMR instrumentation are significantly reduced, pipe flow methods often require complex flow networks and large sample volumes (>10 L). SUMMARY In one aspect, the present disclosure relates to a novel method for characterizing circular (laminar) Couette flow of fluids, particularly non-Newtonian fluids, and also Newtonian fluids. Symmetry of the flow system combined with a constant magnetic field gradient leads to phase interference, affecting the signal magnitude, and net phase cancellation when averaging across an excited slice, preventing the use of phase-sensitive methods. Therefore, utilized is the dependence of signal magnitude at variable echo times and shear rates to characterize rheological properties. In one aspect, equations, as detailed in the present disclosure, governing the velocity distributions of fluids that obey a simple power-law model are used to obtain integral expressions for signal magnitude. Integral expressions can be simplified by approximating a thin excited slice or complete excitation of the Couette cell depending on experimental parameters. In one aspect, with simple data acquisition and analysis procedures employed, measurements of the flow behavior indices of non-Newtonian xanthan gum dispersions are in close agreement with conventional rheological magnetic resonance measurements. The present disclosure in one aspect relates to a method for measuring the flow behavior index using a low-cost portable NMR instrument and a circular Couette flow system, wherein rotation effects are encoded in a first echo acquired with a variable echo time and optional subsequent echoes with short echo times are acquired. In one aspect, a short echo time is shorter than or equal to the shortest variable echo time, in another aspect a short echo time is on the order of tens of microseconds, in another aspect, a short echo time is in the range of about 200 μs to about 400 μs and in another aspe