Obtaining Self-similar Scalings in Focusing Flows

TL;DR

This paper introduces two methods to extract self-similar scaling exponents from data of converging thin fluid films, covering regimes from gravity-driven to surface tension-driven flows, and confirms theoretical relations through experiments and simulations.

Contribution

It provides novel methods for determining self-similar scaling exponents in focusing flows, applicable across a range of driving forces, and extends previous work to mixed regimes.

Findings

Methods successfully extract scaling exponents from experimental and numerical data.

Scaling exponents vary smoothly with Bond number, including small values.

Experimental results agree with numerical simulations and theoretical predictions.

Abstract

The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or experimental data is non-trivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semi-analytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface tension driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.