Maximum angle of stability of a wet granular pile

Abstract

Anyone who has built a sandcastle recognizes that the addition of liquid to granular materials increases their stability. However, measurements of this increased stability often conflict with theory and with each other [1,2,3,4,5,6,7]. A friction-based Mohr-Coulomb model has been developed [3,8]. However, it distinguishes between granular friction and inter-particle friction, and uses the former without providing a physical mechanism. Albert, et al.[2] analyzed the geometric stability of grains on a pile's surface. The frictionless model for dry particles is in excellent agreement with experiment. But, their model for wet grains overestimates stability and predicts no dependence on system size. Using the frictionless model and performing stability analysis within the pile, we reproduce the dependence of the stability angle on system size, particle size, and surface tension observed in our experiments. Additionally, we account for past discrepancies in experimental reports by showing that sidewalls can significantly increase the stability of granular material.The experimental apparatus consists of a clear plexiglass drum which is rotated about an horizontal axis. We primarily use a drum with a diameter D of 28.5 cm and a width W which can be varied from 0 cm to 14.5 cm. A drum with D = 12.5 cm and W = 11.5 cm is also used to vary system size. The rotation rate ω is varied from 9.0×10 −4 rpm to 5.6×10 −1 rpm. Soda-lime glass spheres which have a density ρ of 2.4 g cm −3 , and with radius r = 0.25 mm, 0.3 mm, 0.5 mm, and 1.5 mm and size dispersity within 0.1 mm were used. The drum was 40% filled with grains premixed with a small amount of liquid. We report the amount of liquid added in terms of the volume fraction, V f , which is defined as the volume of the liquid divided by the volume occupied by the grains alone. The effect of surface tension of the liquid Γ was tested by using silicone oil and water which have Γ = 20 ± 1 dyne cm −1 and Γ = 70 ± 1 dyne cm −1 , respectively. Silicone oil with viscosity ν ranging from 5 cS to 1000 cS is used to study its impact on the measured inclination angles.The drum is back lit so that light could pass through a thin layer of grains that tends to accumulate on the sides of the drum, but is unable to pass through the bulk of the pile. Images were acquired with a mega-pixel resolution digital camera at a rate of three frames per second 100 50 time (s) (b) 32 30 28 26 Surface angle (deg.) 100 50 0 time (s) (a) FIG. 1: Avalanching regimes Glass spheres (radius r 0.5 mm) mixed with silicone oil in a rotating drum (width W 14.5 cm). (a) Stick-slip flow is observed for a rotation rate ω of 0.028 rpm and viscosity ν = 5 cS. (b) Continuous flow is observed for rotation rate of 0.28 rpm.and used to determine the surface slope with automated code. At this rate, the slope of the pile changed no more than 0.2 degrees between frames. This error in measurement is not significant given that the slope of the pile at the moment of avalanche was distributed over about two degrees in a given run....

Effect of cohesive force on the formation of a sandpile

“…2. Note ș r is obtained after a sandpile is stable, and is smaller than the maximum angle of stability [6][7][8]. Similar to the observations in experiments, the surface of the pile may not be very smooth, especially when the cohesive force is high, thus ș r is obtained by the linear regression of the coordinates y and z for the surface particles.…”

“…The cohesive force between particles is found to have a very significant effect on sandpiles [6][7][8]. The presence of a small amount of liquid can have a considerable influence on the properties of granular matter, e.g., the angle of repose of a wet granular pile is much greater than that of a dry pile because of the capillary forces due to the liquid bridges formed between particles.…”

“…The presence of a small amount of liquid can have a considerable influence on the properties of granular matter, e.g., the angle of repose of a wet granular pile is much greater than that of a dry pile because of the capillary forces due to the liquid bridges formed between particles. A number of experimental, theoretical and numerical studies have been conducted on this topic, and the maximum angle of stability is modeled by considering the force balance and mechanical stability of the surface or near surface particles [6][7][8].…”

Capillary adhesion at the nanometer scale

“…The meniscus formed between clay particles binds them together with capillary forces, increasing the unconfined yield strength of the granular assembly. The same physics is involved when wet sand is used to build sand castles, which would not be possible to make with dry sand [6][7][8][9][10].…”

Subglacial till behaviour derived from in situ wireless multi-sensor subglacial probes: Rheology, hydro-mechanical interactions and till formation

“…Schiffer, 2005;Nowak et al, 2005) have argued that even a very small percentage of water can affect its physical behaviour, because capillary action can produce interstitial liquid bridges between grains. This acts to strengthen the material at low water contents (Helsey and Levine, 1998;Herminghaus, 2005) (water content regimes I, II and III) and results in a granular regime, dominated by the motion of individual grains.…”