Hopper flows of deformable particles

Abstract

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 $w$: $Q\sim (w/{\sigma }_{\mathrm{avg}}-k{)}^{\beta }$, where ${\sigma }_{\mathrm{avg}}$ is the average particle diameter, $k{\sigma }_{\mathrm{avg}}$ is an offset where $Q\sim 0$, 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 $\lambda \to 0$ limit and $d-3/2$ in the $\lambda \to \infty$ 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 $k\sim k_{\max }$ in the hard-particle limit, where $k_{\max }\sim 3.5$ is larger for $\lambda \to \infty$ compared to that for $\lambda \to 0$. Finally, we show that the simulations of hopper flows of deformable particles in the $\lambda \to \infty$ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.

arXiv comment15 pages, 12 figures

References in corpus (14)

• Statistics of the contact network in frictional and frictionless granular packings
• Jamming of Deformable Polygons
• Granular discharge and clogging for tilted hoppers
• Clogging of soft particles in 2D hoppers
• Isostaticity at Frictional Jamming
• Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming
• Orientation, Flow, and Clogging in a Two-Dimensional Hopper: Ellipses vs. Disks
• Silo outflow of soft frictionless spheres
• Granular discharge rate for submerged hoppers
• The role of deformability in determining the structural and mechanical properties of bubbles and emulsions
• Dense bubble flow in a silo: an unusual flow of a dispersed medium
• The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions
• Computational studies of the glass-forming ability of model bulk metallic glasses
• Details of soft particle clogging in two-dimensional hoppers

Cited by in corpus (4)

• Mechanical Plasticity of Cell Membranes Enhances Epithelial Wound Closure
• Computational modeling of the physical features that influence breast cancer invasion into adipose tissue
• Flow and clogging of capillary droplets
• Clogging of cohesive particles in a two-dimensional hopper