Spreading, pinching, and coalescence: the Ohnesorge units

TL;DR

This paper introduces Ohnesorge units, a universal scaling framework based on intrinsic timescales and lengthscales derived from fluid properties, which unifies and simplifies the analysis of drop spreading, pinching, and coalescence across diverse experiments.

Contribution

It proposes the Ohnesorge units as a new scaling system that extends beyond traditional VI, VC, and IC units, enabling better comparison and understanding of drop dynamics.

Findings

Ohnesorge units unify diverse experimental data.

Scaling collapse reveals universal features of drop dynamics.

Enhanced analysis of spreading, pinching, and coalescence processes.

Abstract

Understanding the kinematics and dynamics of spreading, pinching, and coalescence of drops is critically important for a diverse range of applications involving spraying, printing, coating, dispensing, emulsification, and atomization. Hence experimental studies visualize and characterize the increase in size over time for drops spreading over substrates, or liquid bridges between coalescing drops, or the decrease in the radius of pinching necks during drop formation. Even for Newtonian fluids, the interplay of inertial, viscous, and capillary stresses can lead to a number of scaling laws, with three limiting self-similar cases: visco-inertial (VI), visco-capillary (VC) and inertio-capillary (IC). Though experiments are presented as examples of the methods of dimensional analysis, the lack of precise values or estimates for pre-factors, transitions, and scaling exponents presents difficulties for quantitative analysis and material characterization. In this tutorial review, we reanalyze and summarize an elaborate set of landmark published experimental studies on a wide range of Newtonian fluids. We show that moving beyond VI, VC, and IC units in favor of intrinsic timescale and lengthscale determined by all three material properties (viscosity, surface tension and density), creates a complementary system that we call the Ohnesorge units. We find that in spite of large differences in topological features, timescales, and material properties, the analysis of spreading, pinching and coalescing drops in the Ohnesorge units results in a remarkable collapse of the experimental datasets, highlighting the shared and universal features displayed in such flows.