Abstract
In this work we study the deformation of clean and surfactant-laden droplets in laminar shear-flow. The simulations are based on Direct Numerical Simulation of the Navier–Stokes equations coupled with a Phase Field Method to describe interface topology and surfactant concentration. Simulations are performed considering both 2D (circular droplet) and 3D (spherical droplet) domains. First, we focus on clean droplets and we characterize the droplet shape and deformation. This enables us to define the range of parameters in which theoretical models well predict the results obtained from 2D and 3D simulations. Then, surfactant-laden droplets are considered; the main factors leading to larger droplet deformation are carefully described and quantified. Results obtained indicate that the average surface tension reduction and the accumulation of surfactant at the tips of the deformed droplet have a dominant role, while tangential stresses at the interface (Marangoni stresses) have a limited effect on the overall droplet deformation. Finally, the distribution of surfactant over the droplet surface is examined in relation to surface deformation and shear stress distribution.
Highlights
The deformation of a droplet in a simple shear flow is of fundamental relevance in a number of flowing system of industrial and biological interest
We will focus on clean-droplets (C-series): the shape and the deformation of the droplet obtained from our 2D and 3D simulations will be compared against previous works [10, 14, 17, 41] and with analytic predictions [24, 34]
The capillary number is the ratio between these two contributions, and, when a clean system is considered, is the main parameter that controls the final shape of the droplet
Summary
The deformation of a droplet in a simple shear flow is of fundamental relevance in a number of flowing system of industrial and biological interest. Possible applications include the formation and rheology of emulsions [7], emulsifying devices [18], polymer blending [9], oil recovery [19] and the study of red blood cells [36] This problem was first tackled by Taylor [33, 34], who developed an analytic formula able to predict the deformation of a droplet in shear flow. This formula, developed under the hypotheses of small deformations and negligible inertia effects, constitutes a simple tool for the calculation of droplet deformation. The capillary number highlights the two principal factors involved in droplet deformation: the shear rate, which tries to deform the droplet, and surface tension, which acts to restore the spherical shape of the droplet
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