Cheng Yuxuan, Treado John D, Lonial Benjamin F, Habdas Piotr, Weeks Eric R, Shattuck Mark D, O'Hern Corey S
Department of Physics, Yale University, New Haven, Connecticut, 06520, USA.
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, 06520, USA.
Soft Matter. 2022 Nov 2;18(42):8071-8086. doi: 10.1039/d2sm01079h.
Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate and the orifice width : ∼ (/ - ), where is the average particle diameter, is an offset where ∼ 0, the power-law scaling exponent = - 1/2, and 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 . 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 varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, = /. = - 1/2 in the → 0 limit and - 3/2 in the → ∞ limit, with a midpoint that depends on the hopper opening angle . We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent . The offset increases with particle stiffness until ∼ in the hard-particle limit, where ∼ 3.5 is larger for → ∞ compared to that for → 0. Finally, we show that the simulations of hopper flows of deformable particles in the → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.
大量实验和计算研究表明，颗粒材料的连续料斗流遵循贝弗洛方程，该方程将体积流率与孔口宽度联系起来： ∼ (/ - )，其中 是平均粒径， 是一个偏移量， ∼ 0，幂律标度指数 = - 1/2， 是空间维度。最近对不同背景流体中可变形颗粒料斗流的研究表明，颗粒刚度和耗散机制也会强烈影响幂律标度指数 。我们对具有动摩擦和背景流体耗散的可变形颗粒在二维和三维空间中的料斗流进行了计算研究。我们表明，指数 随粘性阻力与动摩擦系数之比 = / 连续变化。在 → 0 极限下 = - 1/2，在 → ∞ 极限下 = - 3/2，中间点 取决于料斗开口角度 。我们还描述了流的空间结构，并将料斗流空间结构的变化与指数 的变化联系起来。偏移量 随颗粒刚度增加，直到在硬颗粒极限下 ∼ ，其中对于 → ∞， ∼ 3.5 比 → 0 时更大。最后，我们表明，在 → ∞ 极限下可变形颗粒料斗流的模拟重现了水中油滴准二维料斗流的实验结果。
