A system of glass beads or steel balls is an example of a granular system. In su
ID: 2075103 • Letter: A
Question
A system of glass beads or steel balls is an example of a granular system. In such a system the beads are macroscopic objects and the collisions between the beads are inelastic. Because the collisions in such a system are inelastic, a gas-like steady state is achieved only by inputting energy, usually by shaking or vibrating the walls of the container. Suppose that the velocities of the particles are measured in a direction perpendicular to the direction of shaking. Do the assumptions we used to derive the Maxwell-Boltzmann velocity distribution apply here? See for example, the experiments by Daniel L. Blair and Arshad Kudrolli, "Velocity correlations in dense granular gases," Phys. Rev. E 64, 050301 (R) (2001) and the theoretical arguments by J. S. van Zon and F. C. MacKintosh, "Velocity distributions in dissipative granular gases," Phys. Rev. Lett. 93, 038001 (2004).Explanation / Answer
No, the assumptions used for deriving the Maxwell-Boltzmann distribution would not remain valid here because the Maxwell-Boltzmann relation is valid for an ideal gas(whose molecules undergo elastic collisions) sytem which is isotropic that is every direction is equivalent for that systerm.
However for the granular system, the direction in which the wall is shaken is unique and thus not equivalent to any other direction. Also since in the direction of vibration we are transfering the momentum to the system, The net momentum of the system at every instant would not be zero as it was the case for ideal gas system.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.