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Thermal diffusivity measurements in a sheared particle-laden suspension

A. P. Merin and Vinod Srinivasan*

  • *Contact author: vinods@umn.edu

Phys. Rev. Fluids 11, 094302 – Published 8 September, 2026

DOI: https://doi.org/10.1103/7b71-gckp

Abstract

This study examines the effective thermal diffusivity of sheared particle-fluid suspensions with non-Brownian neutrally buoyant particles in a thin gap Taylor-Couette cell. A steady canonical shear flow is generated with Taylor instabilities suppressed by outer cylinder rotation. Spherical acrylic particles of 1.93 mm diameter were used with a density-matched propylene glycol-glycerol solution. Thermal diffusivity of the medium is deduced by applying a thermal pulse to the stationary inner cylinder and monitoring temporal temperature decay on the inner cylinder surface. The study documents the effects of the particle Peclet number (<1400) for four different particle volume fractions of 0.14, 0.22, 0.30, and 0.36. Here the Peclet number is defined as the ratio of timescales of thermal diffusion in the liquid over the particle scale to the timescale of the imposed shear. The applied shear corresponded to particle Reynolds numbers ranging from Stokes flow (Rep1) to a maximum of 0.85, where weak inertial effects are likely present. At low Peclet number Pe<100, the enhancement due to shear is roughly linear with the Peclet number. At higher Pe (100<Pe<700), the enhancement displays power-law behavior with an exponent of 1/2, which has been predicted by some models for concentrated suspensions, but is also consistent with the emergence of a particle-free fluid layer near one wall. At still higher Pe, the 1/2 power-law behavior is retained for all but the highest volume fractions, with ϕ=0.35 exhibiting a 1/11 power-law behavior, which has been previously predicted, albeit for dilute suspensions, for the high-Pe limit. The thermal diffusivity measurements are complemented by limited measurements of particle velocity through particle tracking, which suggest that particle motion does not contribute significantly to the observed enhancement at high Peclet numbers.

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References (50)

  1. C. Qian and G. Gao, Reduction of interior temperature of mass concrete using suspension of phase change materials as cooling fluid, Constr. Build. Mater. 26, 527 (2012).
  2. A. Kijo–Kleczkowska, Combustion of coal–water suspensions, Fuel 90, 865 (2011).
  3. R. L. Wu, J. R. Grace, C. J. Lim, and C. M. Brereton, Suspension-to-surface heat transfer in a circulating-fluidized-bed combustor, AIChE J. 35, 1685 (1989).
  4. B.-S. Kang, S. G. Kim, and J.-S. Kim, Thermal degradation of poly (methyl methacrylate) polymers: Kinetics and recovery of monomers using a fluidized bed reactor, J. Anal. Appl. Pyrolysis 81, 7 (2008).
  5. J. Dufek, The fluid mechanics of pyroclastic density currents, Annu. Rev. Fluid Mech. 48, 459 (2016).
  6. N.-H. L. Wang and K. Keller, Augmented transport of extracellular solutes in concentrated erythrocyte suspensions in Couette flow, J. Colloid Interface Sci. 103, 210 (1985).
  7. A. L. Zydney and C. K. Colton, Augmented solute transport in the shear flow of a concentrated suspension, Physicochem. Hydrodynam. 10, 77 (1988).
  8. A. Einstein, Effect of suspended rigid spheres on viscosity, Ann. Phys. 324, 289 (1906).
  9. É. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, P1 (2018).
  10. E. C. Eckstein, D. G. Bailey, and A. H. Shapiro, Self-diffusion of particles in shear flow of a suspension, J. Fluid Mech. 79, 191 (1977).
  11. D. Leighton and A. Acrivos, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech. 181, 415 (1987).
  12. P. R. Nott and J. F. Brady, Pressure-driven flow of suspensions: Simulation and theory, J. Fluid Mech. 275, 157 (1994).
  13. P. M. Kulkarni and J. F. Morris, Suspension properties at finite Reynolds number from simulated shear flow, Phys. Fluids 20, 040602 (2008).
  14. P. R. Nott, E. Guazzelli, and O. Pouliquen, The suspension balance model revisited, Phys. Fluids 23, 043304 (2011).
  15. M. Souzy, H. Lhuissier, E. Villermaux, and B. Metzger, Stretching and mixing in sheared particulate suspensions, J. Fluid Mech. 812, 611 (2017).
  16. D. G. Wang, S. S. Sadhal, and C. S. Campbell, Particle rotation as a heat transfer mechanism, Int. J. Heat Mass Transf. 32, 1413 (1989).
  17. A. S. Ahuja, Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results, J. Appl. Phys. 46, 3408 (1975).
  18. A. S. Ahuja, Augmentation of heat transport in laminar flow of polystyrene suspensions. II. Analysis of the data, J. Appl. Phys. 46, 3417 (1975).
  19. L. Leal, Macroscopic transport properties of a sheared suspension, J. Colloid Interface Sci. 58, 296 (1977).
  20. Y. Chung and L. Leal, An experimental study of the effective thermal conductivity of a sheared suspension of rigid spheres, Int. J. Multiphase Flow 8, 605 (1982).
  21. B. Metzger, O. Rahli, and X. Yin, Heat transfer across sheared suspensions: Role of the shear-induced diffusion, J. Fluid Mech. 724, 527 (2013).
  22. A. Nir and A. Acrivos, The effective thermal conductivity of sheared suspensions, J. Fluid Mech. 78, 33 (1976).
  23. A. Nadim, R. Cox, and H. Brenner, Taylor dispersion in concentrated suspensions of rotating cylinders, J. Fluid Mech. 164, 185 (1986).
  24. C. W. Sohn and M. Chen, Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment, ASME J. Heat Transf. 103, 47 (1981).
  25. S. Shin and S.-H. Lee, Thermal conductivity of suspensions in shear flow fields, Int. J. Heat Mass Transf. 43, 4275 (2000).
  26. K. Yeo and M. R. Maxey, Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow, Phys. Fluids 25, 053303 (2013).
  27. F. Picano, W.-P. Breugem, D. Mitra, and L. Brandt, Shear thickening in non-Brownian suspensions: An excluded volume effect, Phys. Rev. Lett. 111, 098302 (2013).
  28. G. Subramanian and D. L. Koch, Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field, Phys. Fluids 18, 073302 (2006).
  29. A. P. Merin and V. Srinivasan, Heat transfer measurements in neutrally buoyant suspensions in the inertial regime, in Proceedings of the ASME 2022 Heat Transfer Summer Conference collocated with the ASME 2022 16th International Conference on Energy Sustainability, Philadelphia, USA (ASME, New York, 2022), p. V001T13A009.
  30. L. Wang, D. L. Koch, X. Yin, and C. Cohen, Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres, Phys. Fluids 21, 033303 (2009).
  31. M. N. Ardekani, O. Abouali, F. Picano, and L. Brandt, Heat transfer in laminar Couette flow laden with rigid spherical particles, J. Fluid Mech. 834, 308 (2018).
  32. J.-P. Matas, J. F. Morris, and E. Guazzelli, Transition to turbulence in particulate pipe flow, Phys. Rev. Lett. 90, 014501 (2003).
  33. P. Chossat and G. Iooss, Primary and secondary bifurcations in the Couette-Taylor problem, Jpn. J. Appl. Math. 2, 37 (1985).
  34. D. Coles, Transition in circular Couette flow, J. Fluid Mech. 21, 385 (1965).
  35. E. Linares-Guerrero, M. L. Hunt, and R. Zenit, Effects of inertia and turbulence on rheological measurements of neutrally buoyant suspensions, J. Fluid Mech. 811, 525 (2017).
  36. Y. Song and M. Hunt, Rheological measurements and transition to turbulence for moderate Reynolds number inertial suspensions, J. Fluid Mech. 988, A19 (2024).
  37. J. A. Balderas-López, A. Mandelis, and J. A. Garcia, Thermal-wave resonator cavity design and measurements of the thermal diffusivity of liquids, Rev. Sci. Instrum. 71, 2933 (2000).
  38. W. E. Acree, Jr. and J. S. Chickos, Phase transition enthalpy measurements of organic and organometallic compounds, in NIST Chemistry WebBook, edited by P. J. Linstrom and W. G. Mallard, NIST Standard Reference Database Number 69 (National Institute of Standards and Technology, Gaithersburg, MD, 2026).
  39. N. Ravi, V. Gabeur, Y.-T. Hu, R. Hu, C. Ryali, T. Ma, H. Khedr, R. Rädle, C. Rolland, L. Gustafson, et al., SAM 2: Segment anything in images and videos, in International Conference on Learning Representations (OpenReview.net, 2025), Vol. 2025, pp. 28085–28128.
  40. A. D. Brailsford and K. G. Major, The thermal conductivity of aggregates of several phases, including porous materials, Br. J. Appl. Phys. 15, 313 (1964).
  41. A. Karnis, H. Goldsmith, and S. Mason, The kinetics of flowing dispersions: I. Concentrated suspensions of rigid particles, J. Colloid Interface Sci. 22, 531 (1966).
  42. M. V. Majji and J. F. Morris, Inertial migration of particles in Taylor-Couette flows, Phys. Fluids 30, 033303 (2018).
  43. M. V. Majji, S. Banerjee, and J. F. Morris, Inertial flow transitions of a suspension in Taylor–Couette geometry, J. Fluid Mech. 835, 936 (2018).
  44. P. Ramesh, S. Bharadwaj, and M. Alam, Suspension Taylor–Couette flow: Co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals, J. Fluid Mech. 870, 901 (2019).
  45. G. Segre and A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow part 2. Experimental results and interpretation, J. Fluid Mech. 14, 136 (1962).
  46. B. Ho and L. Leal, Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech. 65, 365 (1974).
  47. J.-P. Matas, J. F. Morris, and É. Guazzelli, Inertial migration of rigid spherical particles in Poiseuille flow, J. Fluid Mech. 515, 171 (2004).
  48. C. D. Andereck, S. Liu, and H. L. Swinney, Flow regimes in a circular Couette system with independently rotating cylinders, J. Fluid Mech. 164, 155 (1986).
  49. M. Ghosh and M. Alam, Instabilities and particle-induced patterns in co-rotating suspension Taylor–Couette flow, J. Fluid Mech. 995, R4 (2024).
  50. S. P. Singh, M. Ghosh, and M. Alam, Counter-rotating suspension Taylor–Couette flow: Pattern transition, flow multiplicity and the spectral evolution, J. Fluid Mech. 944, A18 (2022).

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