Understanding the dynamics of surface-trapped particles is crucial to the understanding of a range of problems such as the formations of Pickering (solid-stabilized) emulsions and particle monolayers. The application of Pickering emulsions, where colloidal particles are applied to the fluid interface to stabilize emulsions, has become increasingly useful in the industries of food, cosmetics, petroleum, and biomedicine.
This research aims to provide a deeper understanding of the dynamics of particles trapped at a liquid interface in an applied flow field via mathematical modeling and analytical/numerical methods.
I presented my results at the APS DFD November Meetings (2021, 2022), APS March Meeting (2022), the SIAM Annual Meeting (2022) and Dynamical Systems (2023)
Abstract
The dynamics of particles attached to an interface separating two immiscible fluids are encountered in a wide variety of applications. Here we present a combined asymptotic and numerical investigation of the fluid motion past spherical particles attached to a deformable interface undergoing uniform creeping flows in the limit of small Capillary number and small deviation of the contact angle from 90 degrees. Under the assumption of a constant three-phase contact angle, we calculate the interfacial deformation around an isolated particle and a particle pair. Applying the Lorentz reciprocal theorem to the zeroth-order approximation corresponding to spherical particles at a flat interface and the first correction in Capillary number and correction contact angle allows us to obtain explicit analytical expressions for the hydrodynamic drag in terms of the zeroth-order approximations and the correction deformations. The drag coefficients are computed as a function of the three-phase contact angle, the viscosity ratio of the two fluids, the Bond number, and the separation distance between the particles. In addition, the capillary force acting on the particles due to the interfacial deformation is calculated.
Keywords
Low-Reynolds number flows, Interfacial flows, Particle interactions
Reference:
Zhou, Z., Vlahovska, P. M., Miksis, M. J., The Translational and Rotational Motions of a Spherical Particle at a Gas-Liquid Interface (In Preparation)
ArXiv Preprint: arXiv:2206.14949 [physics.flu-dyn]