Simulation of Granular Flow Dynamics

Department of Applied Mathematics
The University of Western Ontario
May 2004-August 2004

Granular materials containing a mixture of grain types often segregate over time, given sufficient energy input to create significant motion of the grains. This effect is seen in everyday situations, such as in boxes of breakfast cereal containing mixtures of flakes and dried berries. Typically, one finds that the concentration of dried berries is much higher at the top of the box than at the bottom. While the reasons for this segregation are reasonably well understood, the mechanisms and processes that can be used to remix such granular materials are not. Simulation of the dynamics of granular systems composed of grains with different sizes and masses was done using an existing software. The microscopic dynamics of the granular systems in question are described by Newton's equations and collision rules. For instance, by varying the value of the coefficient of restitution and wall loss parameters of the balls, the collisions can be controlled so that they are completely or partially elastic or vice versa.

In order to produce a phase diagram for a specific number of balls in a 2-D system, density profiles for sample points were produced then used in plotting density versus height graphs. Using these graphs, the behavior of the system can be predicted. Each curve shape characterizes a specific system behavior.

For specific configurations of flows and initial conditions, we mapped out the conditions that lead to mixing and segregation in a 2-D system. By varying parameters such as the total density, relative density, elastic properties of the grains, and rate of energy input (via gravity or motion of the container) we mapped out a dynamic phase diagram.

Temperature is a measure of the kinetic energy of particles. Since the kinetic energy is directly related to the velocity of the particles, temperature is also related to the velocity of the particles. By changing the sieve-size coefficient, the velocity of the balls in our system can be controlled. N. Menon and D.J. Durian* proposed a relationship between flow velocity (V_f) and random velocity ( $delta$ V) for a 3-D system given by the law $delta$ V $prop$ V_f2/3. By plotting the log of this relationship we examined its accuracy and got a result that agreed with Menon's and Durian's proposal within 4% confidence level.

Adding balls of different sizes affects the dynamics of the system. for example, Adding balls of bigger size and higher density causes segregation between the two types of balls. while Adding balls of bigger size and same density,shortens the life time of the clumped regions. This movie indicates the behavior of a system containing 10% of balls of bigger size but same density.

* Narayanan Menon and Douglas J. Durian, 28 March 1997. Diffusing-Wave Spectroscopy of Dynamics in a Three-Dimensional Granular Flow. Science, Vol 275, Issue 5308, 1920-1922.

Supervised by: Dr. Colin Denniston
Prepared by: Nehal Al Tarhuni
Last updated: August 13 2004