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

Impact and spreading of microdrops on homo- and heterogeneous solids: Modelling and benchmark simulations

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The finite element framework developed for the high accuracy computation of dynamic wetting phenomena in Sprittles & Shikhmurzaev, Int. J. Num. Meth. Fluids 2011 is used to develop a code for the simulation of unsteady flows such as microdrop impact and spreading. The accuracy of the code for describing free-surface flows is tested by comparing its results to those obtained in previous numerical studies for the large amplitude oscillations of free liquid drops in zero gravity. The capability of our code to produce high resolution benchmark calculations for dynamic wetting flows, using either conventional modelling or the more sophisticated interface formation model, is demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the drop shape which are beyond the resolution of experiments. Directions of our research programme that follows the presented study are outlined

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

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

The Formation of a Bubble from a Submerged Orifice

The formation of a single bubble from an orifice in a solid surface, submerged in an in- compressible, viscous Newtonian liquid, is simulated. The finite element method is used to capture the multiscale physics associated with the problem and to track the evolution of the free surface explicitly. The results are compared to a recent experimental analysis and then used to obtain the global characteristics of the process, the formation time and volume of the bubble, for a range of orifice radii; Ohnesorge numbers, which combine the material parameters of the liquid; and volumetric gas flow rates. These benchmark calculations, for the parameter space of interest, are then utilised to validate a selection of scaling laws found in the literature for two regimes of bubble formation, the regimes of low and high gas flow rates.Comment: Accepted for publication in the European Journal of Mechanics B/Fluid

Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.Comment: 14 pages, 11 Figures, 4 Table

Air Entrainment in Dynamic Wetting: Knudsen Effects and the Influence of Ambient Air Pressure

Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the gas' mean free path and hence the Knudsen number $Kn$. These effects first manifest themselves through Maxwell slip at the gas' boundaries so that for sufficiently small $Kn$ they can be incorporated into a continuum model for dynamic wetting flows. The resulting mathematical model contains flow structures on the nano-, micro- and milli-metre scales and is implemented into a computational platform developed specifically for such multiscale phenomena. The coating flow geometry is used to show that for a fixed gas-liquid-solid system (a) the increased Maxwell slip at reduced pressures can substantially delay air entrainment, i.e. increase the `maximum speed of wetting', (b) unbounded maximum speeds are obtained as the pressure is reduced only when slip at the gas-liquid interface is allowed for and (c) the observed behaviour can be rationalised by studying the dynamics of the gas film in front of the moving contact line. A direct comparison to experimental results obtained in the dip-coating process shows that the model recovers most trends but does not accurately predict some of the high viscosity data at reduced pressures. This discrepancy occurs because the gas flow enters the `transition regime', so that more complex descriptions of its non-equilibrium nature are required. Finally, by collapsing onto a master curve experimental data obtained for drop impact in a reduced pressure gas, it is shown that the same physical mechanisms are also likely to govern splash suppression phenomena.Comment: Accepted for publication in the Journal of Fluid Mechanic