Abstract
Drop deformation in fluid flows is investigated as an exchange between the kinetic energy of the fluid and the surface energy of the drop. We show analytically that this energetic exchange is controlled only by the stretching (or compression) of the drop surface by the rate-of-strain tensor. This mechanism is analogous to the stretching of the vorticity field in turbulence. By leveraging the non-local nature of turbulence dynamics, we introduce a new decomposition that isolates the energetic exchange arising from local drop-induced surface effects from the non-local action of turbulent fluctuations. We perform direct numerical simulations of single inertial drops in isotropic turbulence and show that an important contribution to the increments of the surface energy arises from the non-local stretching of the fluid–fluid interface by eddies far from the drop surface (outer eddies). We report that this mechanism is dominant and independent of surface dynamics in a range of Weber numbers in which drop breakup occurs. These findings shed new light on drop deformation and breakup in turbulent flows, and opens the possibility for the improvement and simplification of breakup models.
Highlights
Turbulent binary mixtures of inmiscible fluids are ubiquitous in natural phenomena and industrial applications
This paper addresses the energetic problem of particle-turbulence interactions from a local perspective, and presents an analytical derivation of the local mechanism responsible for the energetic exchange between surface energy and kinetic energy
One of our main contributions is to provide a mathematical description of the mechanism responsible for the exchange between the kinetic energy of the flow and the surface energy of the fluid-fluid interface
Summary
Turbulent binary mixtures of inmiscible fluids are ubiquitous in natural phenomena and industrial applications. The first studies of drop and bubble breakup in turbulent flows date back to the pioneering work of Kolmogorov (1949) and Hinze (1955), who proposed the idea of the maximum stable diameter based on dimensional analysis. This quantity provides a reasonable estimate of the predominant fluid-particle size in turbulent mixtures, and has been extensively validated in experiments and numerical simulations (Hinze 1955; Perlekar et al 2012; Mukherjee et al 2019; Yi et al 2021). The maximum stable diameter does not provide information on the dynamics of breakup, which is essential to predict the spatio-temporal variations of fluid-particle distributions
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