Controlling wetting with electrolytic solutions: phase-field simulations of a droplet-conductor system

The wetting properties of immiscible two-phase systems are crucial in a wide range of applications, from lab-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is impermeable. Using nonlinear Poisson--Boltzmann theory, we present a theoretical prediction of the dependency of the apparent contact angle on the applied electric potential. We then present well-resolved dynamic simulations of electrowetting using a phase-field model, where the entire two-phase electrokinetic problem, including the electric double layers (EDLs), is resolved. The simulations show that, while the contact angle on scales smaller than the EDL is unaffected by the application of an electric field, an apparent contact angle forms on scales beyond the EDL. This contact angle relaxes in time towards a saturated apparent contact angle. The dependency of the contact angle upon applied electric potential is in good compliance with the theoretical prediction. The only phenomenological parameter in the prediction is shown to only depend on the permeability ratio between the two phases. Based on the resulting unified description, we obtain an effective expression of the contact angle which can be used in more macroscopic numerical simulations, i.e. where the electrokinetic problem is not fully resolved

Electrohydrodynamic channeling effects in narrow fractures and pores

In low-permeability rock, fluid and mineral transport occur in pores and fracture apertures at the scale of micrometers and below. At this scale, the presence of surface charge, and a resultant electrical double layer, may considerably alter transport properties. However, due to the inherent non-linearity of the governing equations, numerical and theoretical studies of the coupling between electric double layers and flow have mostly been limited to two-dimensional or axisymmetric geometries. Here, we present comprehensive three-dimensional simulations of electrohydrodynamic flow in an idealized fracture geometry consisting of a sinusoidally undulated bottom surface and a flat top surface. We investigate the effects of varying the amplitude and the Debye length (relative to the fracture aperture) and quantify their impact on flow channeling. The results indicate that channeling can be significantly increased in the plane of flow. Local flow in the narrow regions can be slowed down by up to $5 \%$ compared to the same geometry without charge, for the highest amplitude considered. This indicates that electrohydrodynamics may have consequences for transport phenomena and surface growth in geophysical systems

Transient electrohydrodynamic flow with concentration dependent fluid properties: modelling and energy-stable numerical schemes

Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier-Stokes-Poisson-Nernst-Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where solving the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes

A hierarchy of non-equilibrium two-phase flow models

We review and extend a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer–Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. In the context of two-phase flow models, the subcharacteristic condition implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models Methods Appl. Sci., 21 (12), 2011, 2379–2407] and Lund [SIAM J. Appl. Math. 72, 2012, 1713–1741] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense

An implicit local time-stepping method based on cell reordering for multiphase flow in porous media

We discuss how to introduce local time-step refinements in a sequential implicit method for multiphase flow in porous media. Our approach relies heavily on causality-based optimal ordering, which implies that cells can be ordered according to total fluxes after the pressure field has been computed, leaving the transport problem as a sequence of ordinary differential equations, which can be solved cell-by-cell or block-by-block. The method is suitable for arbitrary local time steps and grids, is mass-conservative, and reduces to the standard implicit upwind finite-volume method in the case of equal time steps in adjacent cells. The method is validated by a series of numerical simulations. We discuss various strategies for selecting local time steps and demonstrate the efficiency of the method and several of these strategies by through a series of numerical examples.publishedVersio

Electrochemically Assisted Growth of Hopper and Tabular Calcite under Confinement

Crystallization under confinement is commonplace in nature and offers new pathways to engineer crystals with the desired morphologies in a controlled and reproducible manner. In this work, we demonstrate the electrochemically assisted, in situ formation of hopper and tabular calcite crystals within a wedge-like pore formed by confinement induced by the surface force apparatus (SFA). In this geometry, the distance between the confining surfaces decreases continuously from hundreds of micrometers to a few nanometers in a single experimental setup. Calcium carbonate precipitation followed in real-time is triggered by elevating the pH and thus supersaturation directly inside the pore. The pH increase is tracked with a fluorophore tracer and calculated analytically. The unusual calcite crystal habits are obtained in the absence of precipitation-modifying additives and vary as a function of the distance between the confining walls, where at the largest surface separations, hopper crystals form on the gold surface, whereas flat, tabular calcite forms on mica when the confining distance was below 5 μm. Hexagonal or triangular calcite plates exhibit surfaces dominantly defined by rough (001) planes and increase in their surface area-to-volume ratios with decreasing SFA pore thickness. Stabilization of calcite plates bound by (001) faces is a cooperative effect of the oriented growth of calcite on the confining, negatively charged mica walls and the confinement shape, which promotes the development of calcite morphology in the rapid crystal growth directions. The heterogeneous crystallization of calcite is preceded by the nucleation and spreading of a front composed of submicrometer-sized calcium carbonate particles visualized in situ in the SFA pore. Our work demonstrates abundant crystal growth under nanoscale confinement facilitated by elevated pH and a high surface charge of the confining walls.publishedVersio