“…Moreover, we highlight that the curves in figure 8( b ) exhibit a monotonic trend similar to the size ratio dependence of the segregation velocity in previous cyclic shear (Trewhela et al. 2021) and bedload transport studies (Chassagne et al. 2020; Rousseau et al.…”
Section: Discussionsupporting
confidence: 81%
“…In particular, the form of our segregation velocity expression (4.2), after substituting in the expression for , resembles a recent experimental scaling law for the intruder velocity in cyclic shear (Trewhela et al. 2021), , where and are empirical fits, which is based on velocity measurements and dimensional analysis. Figure 8.( a ) Solid curves (left-hand axis) are for and (see text) according to the empirical fit (3.2); colours from blue to red indicate increasing .…”
Section: Discussionmentioning
confidence: 58%
“…the intruder rises), keeping in mind that the negative sign for w i due to the downward applied F ext has been omitted in the plots throughout this paper. The previously known effects of the (local) pressure (P) and shear rate ( γ ) on the segregation velocity (Fry et al 2018;Trewhela, Ancey & Gray 2021) are captured in (4.2) by the (local) effective viscosity, η = μ(I)P/ γ , although c also depends on I (figure 7). In particular, the form of our segregation velocity expression (4.2), after substituting in the expression for η, resembles a recent experimental scaling law for the intruder velocity in cyclic shear (Trewhela et al 2021), w i ∝ F(R)ρg γ d 2 /(Cρgd + P), where F(R) and C are empirical fits, which is based on velocity measurements and dimensional analysis.…”
Section: Implications For Gravity-driven Segregationmentioning
The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations.
“…Moreover, we highlight that the curves in figure 8( b ) exhibit a monotonic trend similar to the size ratio dependence of the segregation velocity in previous cyclic shear (Trewhela et al. 2021) and bedload transport studies (Chassagne et al. 2020; Rousseau et al.…”
Section: Discussionsupporting
confidence: 81%
“…In particular, the form of our segregation velocity expression (4.2), after substituting in the expression for , resembles a recent experimental scaling law for the intruder velocity in cyclic shear (Trewhela et al. 2021), , where and are empirical fits, which is based on velocity measurements and dimensional analysis. Figure 8.( a ) Solid curves (left-hand axis) are for and (see text) according to the empirical fit (3.2); colours from blue to red indicate increasing .…”
Section: Discussionmentioning
confidence: 58%
“…the intruder rises), keeping in mind that the negative sign for w i due to the downward applied F ext has been omitted in the plots throughout this paper. The previously known effects of the (local) pressure (P) and shear rate ( γ ) on the segregation velocity (Fry et al 2018;Trewhela, Ancey & Gray 2021) are captured in (4.2) by the (local) effective viscosity, η = μ(I)P/ γ , although c also depends on I (figure 7). In particular, the form of our segregation velocity expression (4.2), after substituting in the expression for η, resembles a recent experimental scaling law for the intruder velocity in cyclic shear (Trewhela et al 2021), w i ∝ F(R)ρg γ d 2 /(Cρgd + P), where F(R) and C are empirical fits, which is based on velocity measurements and dimensional analysis.…”
Section: Implications For Gravity-driven Segregationmentioning
The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations.
“…Note that the value of obtained here is very close to those reported in the literature for dry granular flows (Fry et al., 2018) and water‐driven flows in bedload configurations (Chassagne et al., 2020). Recent experiments of Trewhela et al., (2020) investigating the segregation of single particle intruders, that is, large or small particles immersed in a sea of oppositely sized constituents, reveal a similar dependence on the material and flow properties although the scaling of the segregation rate with pressure is somewhat different. Specifically, they report a dependence whereas scaling with the inertial number gives .…”
Section: Resultsmentioning
confidence: 98%
“…Specifically, they report a 1 / G P dependence whereas scaling with the inertial number gives /2 1 / G P . This is probably because, in this study, the segregation rate is obtained from the bulk center of mass of segregating large particles in three-dimensional flows while the experiments of Trewhela et al (2020) focused on the trajectory of single large and small particle intruders in a quasi-two-dimensional configuration. Further investigation is needed to confirm this difference in scaling behavior and would be an interesting direction for future research.…”
Granular flows composed of differently sized particles tend to segregate into different layers whereby large particles rise to the free surface and small particles settle to the base (Gray, 2018;Umbanhowar et al., 2019). Particle size segregation is an important process in the motion of geophysical mass flows, such as debris flows (
The influence of silo width on dense granular flow in a two‐dimensional silo is investigated through experiments and simulations. Though the flow rate remains stable for larger silo widths, a slight reduction in silo width results in a significant increase in flow rate for smaller silo widths. Both Beverloo's and Janda's formula accurately capture the relationship between the flow rate and outlet size. Flow characteristics in the regions near the outlet exhibit local self‐similarity, supporting Beverloo and Janda's principles. Moreover, global self‐similarity is analyzed, indicated by the transition in flow state from mass flow in regions far from the outlet to funnel flow near the outlet. The earlier occurrence of this transition favors to enhance the grain velocity and consequently increases the dense flow rate. An exponential scaling law is proposed to describe the dependencies of flow rate, grain velocity, and transition height on silo width.
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