“…22 Recent studies of hopper flows of spherical glass beads submerged in water have found that the scaling exponent b B 1 does not obey b = d À 1/2 from the original Beverloo equation. 29,30 In addition, studies of qausi-2D hopper flows of air bubbles immersed in water have found b B 0.5, 31 again deviating from the exponent in the original Beverloo equation. Thus, from these previous results, it is not clear whether the dissipation mechanism (i.e.…”
Section: Introductionmentioning
confidence: 93%
“…Note that the offset k has different values for λ → 0 and λ → ∞ in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30 Fig. 10Area flow rate Q (in units of Q 0 = σ avg 2 / t 0 ) versus orifice width w / σ avg for hopper flows in 2D using the SP model E sp = 10 2 (circles) and 10 5 (squares) and the frictionless DP model with K l = 10 and K b = 10 −1 (crosses) and K l = 10 and K b = 10 2 (asterisks) with (a) kinetic friction forces only (, ζ = 0) and (b) viscous drag forces only (, μ = 0).…”
Section: Appendix Amentioning
confidence: 99%
“…Note that the offset k has different values for λ → 0 and λ → ∞ in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30…”
Section: Appendix Amentioning
confidence: 99%
“…Note that the offset k has different values for l -0 and l -N in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30 For extremely soft particles, the overlaps that occur in the SP model are sufficiently large that they influence the hopper flow dynamics. For example, in Fig.…”
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 Q ∼ (w/σavg - k)β, where σavg is the average particle diameter, kσavg is an offset where Q∼0, the power-law scaling exponent β=d-1/2, and d is the spatial dimension.
“…22 Recent studies of hopper flows of spherical glass beads submerged in water have found that the scaling exponent b B 1 does not obey b = d À 1/2 from the original Beverloo equation. 29,30 In addition, studies of qausi-2D hopper flows of air bubbles immersed in water have found b B 0.5, 31 again deviating from the exponent in the original Beverloo equation. Thus, from these previous results, it is not clear whether the dissipation mechanism (i.e.…”
Section: Introductionmentioning
confidence: 93%
“…Note that the offset k has different values for λ → 0 and λ → ∞ in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30 Fig. 10Area flow rate Q (in units of Q 0 = σ avg 2 / t 0 ) versus orifice width w / σ avg for hopper flows in 2D using the SP model E sp = 10 2 (circles) and 10 5 (squares) and the frictionless DP model with K l = 10 and K b = 10 −1 (crosses) and K l = 10 and K b = 10 2 (asterisks) with (a) kinetic friction forces only (, ζ = 0) and (b) viscous drag forces only (, μ = 0).…”
Section: Appendix Amentioning
confidence: 99%
“…Note that the offset k has different values for λ → 0 and λ → ∞ in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30…”
Section: Appendix Amentioning
confidence: 99%
“…Note that the offset k has different values for l -0 and l -N in the hard-particle limit, which suggests that k is controlled by the flow dynamics and cannot be determined by the hopper geometry alone. 29,30 For extremely soft particles, the overlaps that occur in the SP model are sufficiently large that they influence the hopper flow dynamics. For example, in Fig.…”
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 Q ∼ (w/σavg - k)β, where σavg is the average particle diameter, kσavg is an offset where Q∼0, the power-law scaling exponent β=d-1/2, and d is the spatial dimension.
“…For dense particle flow, the discrete element method (DEM) is an ideal approach for studying the complex behavior of granular material [2,6,[26][27][28][29][30][31] . Anand et al [15] used DEM to study the influence of particle characteristics and hopper geometry on the granular flow.…”
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