A level-set model for thermocapillary motion of deformable fluid particles

A new level-set model is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios at dynamically deformable interfaces. The Navier–Stokes equations coupled with the energy conservation equation are solved by means of a finite-volume/level-set approach, adapted to a multiple marker methodology in order to avoid the numerical coalescence of the fluid particles. The temperature field is coupled to the surface tension through an equation of state. Some numerical examples including thermocapillary driven convection in two superimposed fluid layers, and thermocapillary motion of single and multiple fluid particles are computed using the present method. These results are compared against analytical solutions and numerical results from the literature as validations of the proposed model.Peer ReviewedPostprint (author's final draft

A P1/P1 Finite Element Framework for Taking Into Account Capillary Effects in Biphasic Flow Simulations

This work describes a computational strategy, based on a stabilised finite element method, to simulate bifluid flow with capillary effects in a fibrous microstructure. In this framework, triple junction equilibrium is imposed as a natural condition in the weak formulation of the Stokes problem. Two types of 2D microstructures are then considered, hexagonal and random, and studied in terms of numerical permeability and capillary pressure

A multi-layer integral model for locally-heated thin film flow

Based on an approach used to model environmental flows such as rivers and estuaries, we develop a new multi-layered model for thin liquid film flow on a locally-heated inclined plane. The film is segmented into layers of equal thickness with the velocity and temperature of each governed by a momentum and energy equation integrated across each layer individually. Matching conditions applied between the layers ensure the continuity of down-plane velocity, temperature, stress and heat flux. Variation in surface tension of the liquid with temperature is considered so that local heating induces a surface shear stress which leads to variation in the film height profile (the Marangoni effect). Moderate inertia and heat convection effects are also included. In the absence of Marangoni effects, when the film height is uniform, we test the accuracy of the model by comparing it against a solution of the full heat equation using finite differences. The multi-layer model offers significant improvements over that of a single layer. Notably, with a sufficient number of layers, the solution does not exhibit local regions of negative temperature often predicted using a single-layer model. With Marangoni effects included the film height varies however we find heat convection can mitigate this variation by reducing the surface temperature gradient and hence the surface shear stress. Numerical results corresponding to the flow of water on a vertical plane show that very thin films are dominated by the Marangoni shear stress which can be sufficiently strong to overcome gravity leading to a recirculation in the velocity field. This effect reduces with increasing film thickness and the recirculation eventually disappears. In this case heating is confined entirely to the interior of the film leading to a uniform height profile

A particle finite element-based model for droplet spreading analysis

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Mahrous, Elaf, et al. “A Particle Finite Element-Based Model for Droplet Spreading Analysis.” Physics of Fluids, vol. 32, no. 4, American Institute of Physics, Apr. 2020, p. 42106, doi:10.1063/5.0006033. and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0006033A particle finite element method-based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses an updated Lagrangian framework to formulate the governing equations of the liquid. The curvature of the liquid surface is tracked accurately using a deforming boundary mesh. In order to predict the spreading rate of the droplet on the solid substrate and track the corresponding contact angle evolution, dissipative forces at the contact line are included in the formulation in addition to the Navier-slip boundary conditions at the solid–liquid interface. The inclusion of these boundary conditions makes it possible to account for the induced Young’s stress at the contact line and for the viscous dissipation along the solid–liquid interfacial region. These are found to be essential to obtain a mesh-independent physical solution. The temporal evolution of the contact angle and the contact line velocity of the proposed model are compared with spreading droplets and micro-sessile droplet injection experiments and are shown to be in good agreement.We are grateful to Dr. Howard Stone, Dr. James Bird, and Dr. Shreyas Mandre for their permission to use Fig. 11(a) published in Ref. 53. We thank the reviewers for their feedback and constructive comments. E.M. is thankful to Dr. Ajay Prasad for the fruitful discussion about the effect of shear stresses on droplet spreading phenomena. E.M. acknowledges the financial support by Jubail University College and the Royal Commission for Jubail and Yanbu of Saudi Arabia. M.S. and A.J. acknowledge financial support from the Natural Science and Engineering Research Council of Canada (NSERC) Collaborative Research and Development, Grant No. NSERC CRDPJ 445887-12, and the NSERC Discovery grant. P.R. was supported by the AMADEUS project (Grant No. PGC2018- 101655-B-I00) funded by the Spanish Ministry of Science, Innovation and Universities. T.C. and A.Z.W. acknowledge financial support by the Fuel Cell Performance and Durability Consortium (FC-PAD) and by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy, under Contract No. DE-AC02-05CH11231.Peer ReviewedPostprint (author's final draft

Numerical time-step restrictions as a result of capillary waves

AbstractThe propagation of capillary waves on material interfaces between two fluids imposes a strict constraint on the numerical time-step applied to solve the equations governing this problem and is directly associated with the stability of interfacial flow simulations. The explicit implementation of surface tension is the generally accepted reason for the restrictions on the temporal resolution caused by capillary waves. In this article, a fully-coupled numerical framework with an implicit treatment of surface tension is proposed and applied, demonstrating that the capillary time-step constraint is in fact a constraint imposed by the temporal sampling of capillary waves, irrespective of the type of implementation. The presented results show that the capillary time-step constraint can be exceeded by several orders of magnitude, with the explicit as well as the implicit treatment of surface tension, if capillary waves are absent. Furthermore, a revised capillary time-step constraint is derived by studying the temporal resolution of capillary waves based on numerical stability and signal processing theory, including the Doppler shift caused by an underlying fluid motion. The revised capillary time-step constraint assures a robust, aliasing-free result, as demonstrated by representative numerical experiments, and is in the static case less restrictive than previously proposed time-step limits associated with capillary waves

An implicit surface tension model for the analysis of droplet dynamics

A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.Peer ReviewedPostprint (published version

Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression

A numerical framework for modelling micro-scale multiphase flows with sharp interfaces has been developed. The suggested methodology is targeting the efficient and yet rigorous simulation of complex interface motion at capillary dominated flows (low capillary number). Such flows are encountered in various configurations ranging from micro-devices to naturally occurring porous media. The methodology uses as a basis the Volume-of-Fluid (VoF) method combined with additional sharpening smoothing and filtering algorithms for the interface capturing. These algorithms help the minimisation of the parasitic currents present in flow simulations, when viscous forces and surface tension dominate inertial forces, like in porous media. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation, which allows larger time steps at low capillary numbers to be utilised. In addition, an adaptive interface compression scheme is introduced for the first time in order to allow for a dynamic estimation of the compressive velocity only at the areas of interest and thus has the advantage of avoiding the use of a-priori defined parameters. The adaptive method is found to increase the numerical accuracy and to reduce the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model is verified against five different benchmark test cases. Moreover, numerical results are compared against analytical solutions as well as available experimental data, which reveal improved solutions relative to the standard VoF solver