Finite Element Simulation of Dynamic Wetting Flows as an\ud Interface Formation Process

A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows — the dynamic contact angle — depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the ‘hydrodynamic resist to dynamic wetting’, is discovered where the influence of the capillary’s radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a userfriendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations

Wetting Front Dynamics in Isotropic Porous Media

A new approach to the modelling of wetting fronts in porous media on the Darcy scale is developed, based on considering the types (modes) of motion the menisci go through on the pore scale. This approach is illustrated using a simple model case of imbibition of a viscous incompressible liquid into an isotropic porous matrix with two modes of motion for the menisci, the wetting mode and the threshold mode. The latter makes it necessary to introduce an essentially new technique of conjugate problems that allows one to link threshold phenomena on the pore scale with the motion on the Darcy scale. The developed approach (a) makes room for incorporating the actual physics of wetting on the pore scale, (b) brings in the physics associated with pore-scale thresholds, which determine when sections of the wetting front will be brought to a halt (pinned), and, importantly, (c) provides a regular framework for constructing models of increasing complexity

Coalescence of Liquid Drops: Different Models Versus\ud Experiment

The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the ‘conventional’ one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this ‘internal interface’ that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different ‘scaling laws’ advanced as approximate solutions to the problem formulated using the conventional model is\ud established

A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces

It is known from both experiments and molecular dynamics simulations that chemically patterning a solid surface has an effect on the flow of an adjacent liquid. This fact is in stark contrast with predictions of classical fluid mechanics where the no-slip boundary condition is insensitive to the chemistry of the solid substrate. It has been shown that the influence on the flow caused by a steep change in the wettability of the solid substrate can be described in the framework of continuum mechanics using the interface formation theory. The present work extends this study to the case of intermittent patterning. Results show that variations in wettability of the substrate can significantly affect the flow, especially of thin films, which may have applications to the design of microfluidic devices

Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin and Removal

We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable singularities in the distribution of the fluid's pressure. The origin of this difficulty is that, near a corner formed by smooth parts of the piece-wise smooth boundary, in addition to the solution of the inhomogeneous problem, there is also an eigensolution. For obtuse corner angles this eigensolution (a) becomes dominant and (b) has a singular radial derivative of velocity at the corner. A method is developed that uses the knowledge about the eigensolution to remove multivaluedness and nonintegrability of the pressure. The method is first explained in the simple case of a Stokes flow in a corner region and then generalised for the full-scale unsteady Navier-Stokes flow in a domain with a free surface.Comment: Under consideration for publication in the Journal of Fluid Mechanics. Figure bouding box problems resolve

Colloidal deposits from evaporating sessile droplets:Coffee ring versus surface capture

Suppression of the coffee ring effect is desirable in many industrial applications which utilize colloidal deposition from an evaporating liquid. Here we focus on the role of particle arrest at the liquid-air interface (surface capture) which occurs at high evaporation rates. It is known experimentally that this phenomenon inhibits particles from reaching the contact line, leading to a deposit which is closer to uniform. We are able to describe this effect using a simple 1D modeling framework and, utilizing asymptotic theory, parametrize our model by the ratio of the vertical advection and diffusion timescales. We show that our model is consistent with existing frameworks for small values of this parameter, but also predicts the surface layer formation seen experimentally at high evaporation rates. The formation of a surface layer leads to a deposit morphology which mimics the evaporative flux density and so is closest to uniform when evaporation has a constant strength across the liquid-air interface.</p

Finding the point of no return : dynamical systems theory applied to the moving contact-line instability

The wetting and dewetting of solid surfaces is ubiquitous in physical systems across a range of length scales, and it is well known that there are maximum speeds at which these processes are stable. Past this maximum, flow transitions occur, with films deposited on solids (dewetting) and the outer fluid entrained into the advancing one (wetting). These new flow states may be desirable, or not, and significant research effort has focused on understanding when and how they occur. Up until recently, numerical simulations captured these transitions by focussing on steady calculations. This review concentrates on advances made in the computation of the time-dependent problem, utilising dynamical systems theory. Facilitated via a linear stability analysis, unstable solutions act as ‘edge states’, which form the ‘point of no return’ for which perturbations from stable flow cease decaying and, significantly, show the system can become unstable before the maximum speed is achieved

The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites

Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquid drops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed