Haverford College and University of Pennsylvania

Chaos and the Origins of Irreversibility: Fluids and Particles

Abstract: Although much of the microscopic world is governed by time-reversible equations of motion, the macroscopic world is Irreversible. Precisely how does this happen in classical systems such as the motion of fluids? This issue is fundamental to statistical physics. To elucidate it, we can consider the slow flow of a Newtonian fluid at very low Reynolds number, which is known to be reversible. As a simple example, consider what happens if you stir a jar of honey and then un-stir it. All fluid elements return precisely to their starting positions. Now consider fluids containing solid particles that are too large to exhibit Brownian motion, i.e. "suspensions". The accepted wisdom is that they are also governed by reversible equations, but we have shown experimentally that in fact the particles in a sheared suspension do not return to their starting positions if the fluid sheared beyond a certain threshold. Instead they appear to undergo a random walk after one or more cycles. I will compare the experiments with numerical simulations demonstrating that the particles interact chaotically with each other, and that the strength of the chaos grows dramatically above the threshold for irreversibility. The comparison illuminates the connections between chaos, reversibility, and predictability.[1] Finally, I will give a second example showing how irreversibility is responsible for the mixing or inter-penetration of two stirred fluids. If time remains, I will explain why an introduction to fluid and nonlinear dynamics belongs in the education of any physics student.

[1] This work was done jointly with D.J. Pine, J. Brady, and A. Leshansky.

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