Clark shearing experiments
This page describes some preliminary simulation results matching some shearing experiments carried out at Clark University. The experimental setup is a cuboid, with walls at x=±30d, y=±6.5d, and z=0d, with all friction coefficients set to 0.2 to approximately model the glass material used in the experiment. The initial particle packing is created by pouring 141480 particles in from a height of z=205d, to fill up the container to approximately z=150d.
A layer of particles (whose centers satisfy y<-5.5d) are then frozen in place on the back wall. A slit of size 4d is opened in center of the base of the simulation. This creates a converging flow in the bottom of the container, but in the upper section of the container, the flow becomes roughly uniform in the x and z directions, and the shear with back wall becomes the dominant effect. We are specifically interested in looking at this in the region 80d<z<100d, |x|<10d.
Creating the inital packing of particles took approximately one week of computation time on twenty processors. Creating 250 snapshots of the drainage took another week of computation on the same system.
Movie of a cuboid of the simulation
The above movie is a cutaway of the shearing simulation, showing all particles in the region 80d<z<100d, and |x|<10d. Particles shown in light yellow are fixed to the back wall. Also available is a movie showing particles in the region 80d<z<100d, -3.8d<y<-3.2d, and |x|<10d, plus a variation movie simulating the effect of observing a laser sheet in the experiment. A further variation movie tracks the particles by subtracting off the background velocity.
The graph below shows the number density as a function of the y coordinate in the region $80d<z<100d and |x|<10d, from frame 50 to frame 250.
The strong peaks show that particles are strongly correlated in layers. By fitting the peaks to a gaussian form, the first four layers were defined to be y=-5.09d, y=-4.19d, y=-3.31d, and y=-2.47d.
Particle motion in the first four layers
The above images are taken from a movie showing a 0.1d-wide slice of particles for the first four layers of the shearing region. In the movie the layers are ordered top-left, top-right, bottom-left, bottom-right. Also available is a movie showing the four layers in a moving frame, to subtract off the background velocity.
The graph below shows the velocity profile in the primary test region, in the simulation units.
To make a direct comparison to the experiment, we need to convert to physical units. The density of the fluid used in the experiment is 1100 kg/m³, and the density of the soda lime glass particles is approximately 2440 kg/m³. Thus the effective gravity is
Since d=1mm, the time unit of the simulation corresponds to
This tells us that average downward speed in the center of the container corresponds to approximately 0.661 cm/s.
Evolution of the overall downwards velocity
While the overall downwards velocity is roughly constant on intermediate scales, there are several issues which make defining a overall background velocity difficult. The plot below shows the average downward velocity in each of the four layers.
Layers 1, 2, 3, and 4 use the colors red, blue, cyan, and magenta respectively. It is clear that there are large fluctuations from frame to frame, and many of these fluctuations are correlated between layers. Also, there is an slow decrease in the average velocity over long times. The background velocity can be roughly fitted to a quadratic over the region 100<t/tau<600.