On the evolution equations of interfacial variables in two-phase flows

TL;DR

This paper reviews and analyzes the evolution equations for geometric interface variables in two-phase flows, clarifying their physical significance and assessing different formulations through numerical simulations.

Contribution

It provides a comprehensive review and clarification of the evolution equations for interfacial geometry, including new analytical relations and validation through simulations.

Findings

Analytical relations for interfacial area density are clarified.

Different formulations of evolution equations are assessed.

Numerical simulations demonstrate the impact of various formulations.

Abstract

Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the interface. We analyze the evolution equations for a set of geometrical quantities that characterize the interface in two-phase flows. Several analytical relations for the interfacial area density are reviewed and presented, clarifying the physical significance of the different quantities involved and specifying the hypotheses under which each transport equation is valid. Moreover, evolution equations for the unit normal vector and for the curvature are analyzed. The impact of different formulations is then assessed in numerical simulations of rising bubble benchmarks.