Deformation of drops by outer eddies in turbulence

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.

Comparison of Experimental and Numerical Transient Drop Deformation during Transition through Orifices in High-Pressure Homogenizers

The droplet deformation in dispersing units of high-pressure homogenizers (HPH) is examined experimentally and numerically. Due to the small size of common homogenizer nozzles, the visual analysis of the transient droplet generation is usually not possible. Therefore, a scaled setup was used. The droplet deformation was determined quantitatively by using a shadow imaging technique. It is shown that the influence of transient stresses on the droplets caused by laminar extensional flow upstream the orifice is highly relevant for the droplet breakup behind the nozzle. Classical approaches based on an equilibrium assumption on the other side are not adequate to explain the observed droplet distributions. Based on the experimental results, a relationship from the literature with numerical simulations adopting different models are used to determine the transient droplet deformation during transition through orifices. It is shown that numerical and experimental results are in fairly good agreement at limited settings. It can be concluded that a scaled apparatus is well suited to estimate the transient droplet formation up to the outlet of the orifice.

ANALYTICAL STUDY OF THE MECHANISM OF DROPLET DEFORMATION AND BREAKUP IN SHEAR FLOWS

The problem of drop deformation and breakup in shear flow represents academic and practical interest and has attracted close attention over the intervening decades. Drop breakup is important for a wide range of engineering and biomedical applications including production and processing of emulsions, aerosols, etc. Although drop breakup operations are widely used in various industries, however, till quite presently there is no unequivocal treatment of the physical mechanism, which causes the fragmentation of dispersions in shear flows. In this paper the principles of constructing a mathematical model, which predicts the evolution of initially spherical droplet in shear flows of viscous liquid over a wide range of flow regimes as well physical parameters of both liquid phases, are considered. A mathematical model is presented that describes the deformation of a single drop suspended in another immiscible liquid under the combined action of three forces, namely, hydrodynamic force, capillary force and dissipative viscous force. The influence of each of these forces on the process of droplet deformation is discussed in the paper. The focus of the study is to more deeply analyze the dynamics of droplet deformation in shear flows and the transitional effects associated with current droplet shapes. Particular attention is paid to the analysis of critical conditions for the onset of irreversible deformation of droplets, which leads to their destruction. The deformed droplet is assumed to be in the form of prolate ellipsoid of revolution. The drop deformation is regarded as motion of the centers mass of the half-drops, symmetrical with respect to the drop center. The results of numerical calculations for droplet deformation in shear flows in comparison with experimental data of other authors are presented. A simple criterion for destruction of droplets in shear flows has been obtained. The results of the analysis confirm the reliability of the model and the competency of the assumption made. The model is able to predict the nature of droplet deformation and the conditions for their destruction in shear flows with known operating parameters with a greater degree of accuracy than the existing empirical relationships.

Viscosity Ratio Effect on Drop Deformation in the Boundary Layer

In the present study, the motion of a droplet in the boundary layer is investigated numerically. Volume of Fluid method is employed to solve the governing equations. It is found that the presence of the droplet leads to an increase in the pressure inside the boundary layer and on the wall. The results show that the droplets create a vortex on the bottom surface. The friction coefficient increases due to the presence of the droplets and is reduced before and after the droplet due to the formation of a vortex. It is concluded that increasing the viscosity and reducing the density at the same time will not affect the velocity and friction coefficient. It is shown that increasing the radius of the droplet increases the stress and thus decreases the boundary layer velocity. As the Reynolds number increases, the amount of surface friction coefficient decreases. By adding nanoparticles into the pure water, surface friction coefficient increases, especially in the region where the droplet is present.

Viscoelastic Effects on Drop Deformation Using a Machine Learning-Enhanced, Finite Element method

This paper presents a numerical study of the viscoelastic effects on drop deformation under two configurations of interest: steady shear flow and complex flow under gravitational effects. We use a finite element method along with Brownian dynamics simulation techniques that avoid the use of closed-form, constitutive equations for the “micro-”scale, studying the viscoelastic effects on drop deformation using an interface capturing technique. The method can be enhanced with a variance-reduced approach to the stochastic modeling, along with machine learning techniques to reconstruct the shape of the polymer stress tensor in complex problems where deformations can be dramatic. The results highlight the effects of viscoelasticity on shape, the polymer stress tensor, and flow streamlines under the analyzed configurations.