Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics

The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the solvability conditions of the density field equation with appropriate boundary conditions imposed on the solid support. The equation describing the motion of a spreading film are derived in the lubrication approximation. In the case of quasi-equilibrium spreading, is shown that the correct sharp-interface limit is obtained, and sample solutions are obtained by numerical integration. It is further shown that evaporation or condensation may strongly affect the dynamics near the contact line, and accounting for kinetic retardation of the interphase transport is necessary to build up a consistent theory.Comment: 14 pages, 5 figures, to appear in PR

Molecular scale contact line hydrodynamics of immiscible flows

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy. Our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular-scale vicinity of the contact line. In particular, the behavior at high capillary numbers, leading to the breakup of the fluid-fluid interface, is accurately predicted.Comment: 33 pages for text in preprint format, 10 pages for 10 figures with captions, content changed in this resubmissio

Buckling-induced lock-up of a slender rod injected into a horizontal cylinder

We investigate the buckling and post-buckling behavior of an elastic rod injected into a horizontal, frictional, cylindrical constraint through experiments, numerical simulations, and scaling analyses. Particular emphasis is given to the onset of helical buckling which can lead to lock-up and prevent further injection. This problem is of timely importance to the petroleum industry due to the prevalence of Coiled Tubing (CT) technology in horizontal wells. An experiment is developed at the desktop scale to allow for a precise exploration of parameter space, including the important effects of radial clearance and natural curvature of the injected rod. In parallel, we perform computer simulations derived from first principles, implementing a dynamic Kirchhoff rod model that includes the frictional interaction between the rod and constraint. Our numerical simulations allow a direct comparison with experiments, as well as a systematic exploration of the parameter space. Moreover, a scaling analysis is performed to identify the key dimensionless parameter(s) that justifies using these findings at the field scale, thereby enabling the direct application of the results from our desktop experiments and numerical simulations to a problem of industrial relevance

Relaxation of nonspherical sessile drops towards equilibrium

We present a theoretical study related to a recent experiment on the coalescence of sessile drops. The study deals with the kinetics of relaxation towards equilibrium, under the action of surface tension, of a spheroidal drop on a flat surface. For such a nonspherical drop under partial wetting conditions, the dynamic contact angle varies along the contact line. We propose a new nonlocal approach to the wetting dynamics, where the contact line velocity depends on the geometry of the whole drop. We compare our results to those of the conventional approach in which the contact line velocity depends only on the local value of the dynamic contact angle. The influence on drop dynamics of the pinning of the contact line by surface defects is also discussed