ALBERT

Description: Abstract The spreading of an incompressible viscous liquid over an isotropic homogeneous unsaturated porous substrate is considered. It is shown that, unlike the dynamic wetting of an impermeable solid substrate, where the dynamic contact angle has to be specified as a boundary condition in terms of the wetting velocity and other flow characteristics, the 'effective' dynamic contact angle on an unsaturated porous substrate is completely determined by the requirement of existence of a solution, i.e. the absence of a non-integrable singularity in the spreading fluid's pressure at the 'effective' contact line. The obtained velocity dependence of the 'effective' contact angle determines the critical point at which a transition to a different flow regime takes place, where the fluid above the substrate stops spreading whereas the wetting front inside it continues to propagate. © Cambridge University Press 2013.

Description: The interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this model's predictions differ from those of the conventionally used one, (b) what influence the ambient fluid has on the evolution of the shape of the coalescing drops and (c) the coupling of the intrinsic dynamics of coalescence and that of the ambient fluid. The key feature of the interface formation model in its application to the coalescence phenomenon is that it removes the singularity inherent in the conventional model at the onset of coalescence and describes the part of the free surface 'trapped' between the coalescing volumes as they are pressed against each other as a rapidly disappearing 'internal interface'. Considering the simplest possible formulation of this model, we find experimentally verifiable differences with the predictions of the conventional model showing, in particular, the effect of drop size on the coalescence process. According to the new model, for small drops a non-monotonic time dependence of the bridge expansion speed is a feature that could be looked for in further experimental studies. Finally, the results of both models are compared to recently available experimental data on the evolution of the liquid bridge connecting coalescing drops, and the interface formation model is seen to give a better agreement with the data. © 2014 Cambridge University Press.

Description: The coalescence of two liquid drops surrounded by a viscous gas is considered in the framework of the conventional model. The problem is solved numerically with particular attention paid to resolving the very initial stage of the process which only recently has become accessible both experimentally and computationally. A systematic study of the parameter space of practical interest allows the influence of the governing parameters in the system to be identified and the role of viscous gas to be determined. In particular, it is shown that the viscosity of the gas suppresses the formation of toroidal bubbles predicted in some cases by early computations where the gas' dynamics was neglected. Focusing computations on the very initial stages of coalescence and considering the large parameter space allows us to examine the accuracy and limits of applicability of various 'scaling laws' proposed for different 'regimes' and, in doing so, reveal certain inconsistencies in recent works. A comparison with experimental data shows that the conventional model is able to reproduce many qualitative features of the initial stages of coalescence, such as a collapse of calculations onto a 'master curve' but, quantitatively, overpredicts the observed speed of coalescence and there are no free parameters to improve the fit. Finally, a phase diagram of parameter space, differing from previously published ones, is used to illustrate the key findings. © © 2014 Cambridge University Press.

Description: Fundamental solutions (Green's functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier-Stokes-Fourier equations). Incorporation of these new fundamental solutions into a numerical framework based on the method of fundamental solutions (MFS) allows for efficient computation of three-dimensional gas microflows at remarkably low computational cost. The R13-MFS approach accurately recovers analytic solutions for low-speed flow around a stationary sphere and heat transfer from a hot sphere (for which a new analytic solution has been derived), capturing non-equilibrium flow phenomena missing from lower-order solutions. To demonstrate the potential of the new approach, the influence of kinetic effects on the hydrodynamic interaction between approaching solid microparticles is calculated. Finally, a programme of future work based on the initial steps taken in this article is outlined. © 2017 Cambridge University Press.

Description: We consider the linearized form of the regularized 13-moment equations (R13) to model the slow, steady gas dynamics surrounding a rigid, heat-conducting sphere when a uniform temperature gradient is imposed far from the sphere and the gas is in a state of rarefaction. Under these conditions, the phenomenon of thermophoresis, characterized by forces on the solid surfaces, occurs. The R13 equations, derived from the Boltzmann equation using the moment method, provide closure to the mass, momentum and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extend the Navier-Stokes-Fourier model to include non-equilibrium effects. We obtain analytical solutions for the field variables that characterize the gas dynamics and a closed-form expression for the thermophoretic force on the sphere. We also consider the slow, streaming flow of gas past a sphere using the same model resulting in a drag force on the body. The thermophoretic velocity of the sphere is then determined from the balance between thermophoretic force and drag. The thermophoretic force is compared with predictions from other theories, including Grad's 13-moment equations (G13), variants of the Boltzmann equation commonly used in kinetic theory, and with recently published experimental data. The new results from R13 agree well with results from kinetic theory up to a Knudsen number (based on the sphere's radius) of approximately 0.1 for the values of solid-to-gas heat conductivity ratios considered. However, in this range of Knudsen numbers, where for a very high thermal conductivity of the solid the experiments show reversed thermophoretic forces, the R13 solution, which does result in a reversal of the force, as well as the other theories predict significantly smaller forces than the experimental values. For Knudsen numbers between 0.1 and 1 approximately, the R13 model of thermophoretic force qualitatively shows the trend exhibited by the measurements and, among the various models considered, results in the least discrepancy. © 2019 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Description: The theoretical framework developed by Rayleigh and Plateau in the 19th century has been remarkably accurate in describing macroscale experiments of liquid cylinder instability. Here we re-evaluate and revise the Rayleigh-Plateau instability for the nanoscale, where molecular dynamics experiments demonstrate its inadequacy. A new framework based on the stochastic lubrication equation is developed that captures nanoscale flow features and highlights the critical role of thermal fluctuations at small scales. Remarkably, the model indicates that classically stable (i.e. 'fat') liquid cylinders can be broken at the nanoscale, and this is confirmed by molecular dynamics. © 2019 Cambridge University Press A.

Description: 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. © 2012 Cambridge University Press.

Description: Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier-Stokes-Fourier, regularised 13-moment and regularised 26-moment frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number , whilst providing clear insight into non-equilibrium phenomena occurring adjacent to the interface. © 2018 Cambridge University Press.