[99] YX Cheng, JD Treado, BF Lonial, P Habdas, ER Weeks, MD Shattuck, CS O'Hern, Hopper Flows of Deformable Particles, Soft Matter 18(42):8071(17) 2022. PMID:36218162. Citations:4. [pdf]
Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q similar to (w/sigma(avg) - k)(beta), where sigma(avg) is the average particle diameter, k sigma(avg) is an offset where Q similar to 0, the power-law scaling exponent beta = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent beta. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent beta varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, lambda = zeta/mu. beta = d - 1/2 in the lambda -> 0 limit and d - 3/2 in the lambda -> infinity limit, with a midpoint lambda(c) that depends on the hopper opening angle theta(w). We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent beta. The offset k increases with particle stiffness until k similar to k(max) in the hard-particle limit, where k(max) similar to 3.5 is larger for lambda -> infinity compared to that for lambda -> 0. Finally, we show that the simulations of hopper flows of deformable particles in the lambda -> infinity limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.