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1. Shear rheology of a dilute suspension of thin rings

   https://doi.org/10.1122/8.0000628  

   Borker, Neeraj S.; Koch, Donald L. (April 2023, Journal of Rheology)

   The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ). 

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2. Extensional rheology of a dilute particle-laden viscoelastic solution

   https://doi.org/10.1103/PhysRevFluids.4.091301  

   Jain, Anika; Einarsson, Jonas; Shaqfeh, Eric S. (September 2019, Physical Review Fluids)
3. Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers

   https://doi.org/10.1103/PhysRevFluids.1.013301  

   Koch, Donald L.; Lee, Eric F.; Mustafa, Ibrahim (May 2016, Physical Review Fluids)
4. Velocity fluctuations in a dilute suspension of viscous vortex rings

   https://doi.org/10.1103/PhysRevFluids.4.044501  

   Morrell, Thomas A.; Spagnolie, Saverio E.; Thiffeault, Jean-Luc (April 2019, Physical Review Fluids)
5. Entrainment of particles during the withdrawal of a fibre from a dilute suspension

   https://doi.org/10.1017/jfm.2020.643  

   Dincau, B. M.; Mai, E.; Magdelaine, Q.; Lee, J. A.; Bazant, M. Z.; Sauret, A. (November 2020, Journal of Fluid Mechanics)

   null (Ed.)

   A fibre withdrawn from a bath of a dilute particulate suspension exhibits different coating regimes depending on the physical properties of the fluid, the withdrawal speed, the particle sizes and the radius of the fibre. Our experiments indicate that only the liquid without particles is entrained for thin coating films. Beyond a threshold capillary number, the fibre is coated by a liquid film with entrained particles. We systematically characterize the role of the capillary number, the particle size and the fibre radius on the threshold speed for particle entrainment. We discuss the boundary between these two regimes and show that the thickness of the liquid film at the stagnation point controls the entrainment process. The radius of the fibre provides a new degree of control in capillary filtering, allowing greater control over the size of the particles entrained in the film. 

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