Phase Transition in Liquid Drop Fragmentation

TL;DR

This study investigates a phase transition in liquid drop fragmentation induced by gas pressure, revealing a critical point where the droplet size distribution follows a power-law, indicating a phase transition with unique critical behavior.

Contribution

It introduces a novel experimental method using scanner imaging to analyze droplet fragmentation and identifies a non-percolative phase transition characterized by a sharp change in size distribution.

Findings

Power-law size distribution at critical pressure

Sign change in surface correction term

Sharp transition in dominance probability

Abstract

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl. Upon varying the gas pressure, a critical value is found where the size-distribution becomes a pure power-law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in Nuclear Multifragmentation studies [1,2]. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2. The sizes of the largest and average fragments, on the other hand, do not go to zero but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian [3,4].