Influence of surface viscosity on droplets in shear flow

Abstract

The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq-Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number B q . Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number Ca, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram (B q ; Ca) of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.

Capillary waves with surface viscosity

“…For such a thin film geometry of high wavenumber, we may consider a two-dimensional flow structure as well as a low Reynolds number under the Stokes' limit. Foreshadowed by the previous numerical work (Gounley et al 2016;Ponce-Torres et al 2017), we anticipate a similar importance of the Marangoni and surface viscosity effects on the capillary wave in the two-dimensional thin film case under the Stokes' limit.…”

“…In insoluble surfactant solutions, the surface shear viscosity is often much higher than O(10 −8 Nsm −1 ), in particular, in the case of 1-eicosanol, it is found (Zell et al 2014;Gavranovic et al 2006) to be at least 10 3 -10 4 times higher than that of soluble SDS solutions. Moreover, recent numerical (Gounley et al 2016) and experimental studies conclude that surface viscosity effects in insoluble surfactants can give rise to noticeable behaviours on the resulting dynamics, which cannot otherwise be fully understood if we considered the Marangoni effect alone (Ponce-Torres et al 2017). In this paper, we shall investigate both the effects of Marangoni and surface viscosity in insoluble surfactant solutions with a particular focus on the dynamics of very thin films with capillary waves close to critical damping.…”

Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment

“…Viscosity, which describes momentum transfer in a flowing fluid, is a transport coefficient used widely in fluid mechanics [1][2][3], materials science [4,5], nanoscience [6], particle physics [7], biophysics [8] and other fields. At a microscopic level, viscosity arises from collisions, but at a macroscopic or hydrodynamic level it is defined by a constitutive relation [9],…”

Tank-treading of microcapsules in shear flow

“…A first response could be that, in shear flow, the shape is dominated by the contribution of the shear membrane viscosity due to the rotation of the surface, a result recently observed numerically in the case of droplets with both surface viscosities in shear flow (Gounley et al 2015). Thus, to be optimal, the numerical simulations and models should consider various constitutive laws and notably the generalized Hooke's model for HSA microcapsules (de Loubens et al 2015), the bending resistance and the dilatational and shear membrane viscosities, which is not the case currently.…”