Paper Number
RI2 

Session
Rheology and Mobility at Interfaces

Title
Influence of interfacial viscosity on the stability of droplet shapes during sedimentation

Presentation Date and Time
October 12, 2021 (Tuesday) 4:10

Track / Room
Track 6 / Ballroom 1

Authors (Click on name to view author profile)

1. Singh, Natasha (Purdue University, Davidson School of Chemical Engineering)
2. Narsimhan, Vivek (Purdue University, Davidson School of Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Natasha Singh and Vivek Narsimhan
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47906

Speaker / Presenter 
Singh, Natasha

Keywords
None

Text of Abstract
In this study, we examine how interfacial viscosity affects the stability of droplet shapes during sedimentation. The viscous interface of the droplet is modeled using the Boussinesq-Scriven constitutive relationship, and the interfacial velocity is computed using the boundary-integral method. We observe that below a critical value of the capillary number, Ca_C, the initially perturbed droplet eventually reverts to its spherical shape. Above this Ca_C, the droplet deforms continuously and becomes unstable, resulting in a growing tail at the rear end for initial prolate perturbations and a cavity for initial oblate perturbations. We observe that interfacial shear viscosity stabilizes the droplet, i.e., it increases the Ca_C compared to a clean droplet by inhibiting/delaying the growth of the instability at the droplet’s rear end. In contrast, the interfacial dilational viscosity destabilizes the droplet, i.e., it reduces the Ca_C compared to a clean droplet by increasing the rate at which instability grows at the droplet’s rear end. Interestingly, both surface shear and dilational viscosity appear to increase the time at which pinch-off occurs compared to a clean droplet, although the mechanisms are distinct. We also examine the combined influence of surface viscosity and surfactant transport on droplet stability by assuming a linear dependence of surface tension on surfactant concentration and an exponential dependence of interfacial viscosities on the surface pressure. We find that pressure-thinning/thickening effects are not very pronounced for dilational viscosities but are significant for the shear viscosity case. Lastly, we provide phase diagrams for the critical capillary number to demonstrate how interfacial viscosity alters the stability for different values of the droplet's viscosity ratio and the initial Taylor deformation parameter.