Free-void-volume-based kinetic theory of frictional cohesive powder settling

Frictional cohesive powder (FCP) samples that are prepared by (i) starting with a dilute initial state, and then (ii) ramping the applied pressure from zero to a finite value over a time τ_ramp, have terminal packing fractions (φ_settled) that decrease logarithmically with increasing τ_ramp. This behavior is the opposite of that exhibited by their frictionless and/or noncohesive counterparts (NCPs), and indeed the opposite of that expected from the usual glass-jamming paradigm wherein slower compression or cooling produces denser final states. The difference arises from the fact that (in contrast to NCP settling, where the rate-limiting factor is the slow dynamics of densification), FCP powder settling is dominated by the even slower dynamics of structural void stabilization. We present a free-void-volume-based kinetic theory of FCP settling [K. Nan and R. S. Hoy, Phys. Rev. Lett. 130, 166102 (2023)] that is similar in spirit to but different in several crucial details from late-1990s-vintage free-volume-based kinetic theories of NCP settling, and then show that it quantitatively predicts the dramatic decrease in model FCPs’ φ_settled that occurs as τ_ramp is increased by several orders of magnitude.