Alex Wray

Electrostatic Suppression of the "Coffee Stain Effect"

The dynamics of a slender, evaporating, particle-laden droplet under the effect of electric fields are examined. Lubrication theory is used to reduce the governing equations to a coupled system of evolution equations for the interfacial position and the local, depth-averaged particle concentration. The model incorporates the effects of capillarity, viscous stress, Marangoni stress, elecrostatically induced Maxwell stress, van der Waals forces, concentration-dependent rheology, and evaporation. Via a parametric numerical study, the one-dimensional model is shown to recover the expected inhomogeneous ring-like structures in appropriate parameter ranges due to a combination of enhanced evaporation close to the contact line, and resultant capillarity-induced flow. It is then demonstrated that this effect can be significantly suppressed via the use of carefully chosen electric fields. Finally, the three-dimensional behavior of the film and the particle concentration field is briefly examined.

Reduced Models for Thick Liquid Layers with Inertia on Highly Curved Substrates

A method is presented for deriving reduced models for fluid flows over highly curved substrates with wider applicability and accuracy than existing models in the literature. This is done by reducing the Navier--Stokes equations to a novel system of boundary layer like equations in a general geometric setting. This is accomplished using a new, relaxed set of scalings that assert only that streamwise variations are “slow”. These equations are then solved using the method of weighted residuals, which is demonstrated to be applicable regardless of the geometry selected. A large number of results in the literature can be derived as special cases of our general formulation. A few of the more interesting cases are demonstrated. Finally, the formulation is applied to two thick annular flow systems as well as a conical system in both linear and nonlinear regimes, which traditionally has been considered inaccessible to such reduced models. Comparisons are made with direct numerical simulations of the Stokes equatio...