Viscous flow computations with the method of lattice Boltzmann equation

Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications

Contact angle hysteresis is an important physical phenomenon. It is omnipresent in nature and also plays a crucial role in various industrial processes. Despite its relevance, there is a lack of consensus on how to incorporate a description of contact angle hysteresis into physical models. To clarify this, starting from the basic definition of contact angle hysteresis, we introduce the formalism and models for implementing contact angle hysteresis into relevant physical phenomena. Furthermore, we explain the influence of the contact angle hysteresis in physical phenomena relevant for industrial applications such as sliding drops, coffee stain phenomenon (in general evaporative self-assembly), and curtain and wire coating techniques

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Contact angle hysteresis: a review of fundamentals and applications

Surface roughness has a profound influence on the wetting properties of a material. This fact is especially true with respect to the wetting of superhydrophobic surfaces. As a result of a special surface structure, a drop of water brought into contact with such a material forms an almost perfect sphere and even a very slight tilting of the superhydrophobic object is sufficient to cause the drop to roll off. For the description of the behavior of drops on rough surfaces two theories, namely those of Cassie and Wenzel, are often employed. However, it is currently becoming well established that both models explain the wetting behavior more from a qualitative or practical point of view rather than giving a quantitative description. For a prediction of actual contact angles, a more complex description is required that, next to thermodynamics, takes into account the kinetics of wetting. In this article, we focus on a few key aspects of superhydrophobic wetting, namely the characterization of superhydrophobic surfaces, models for the movement of drops, transitions between the Cassie and Wenzel states, and the behavior of superhydrophobic materials under condensation.

Some thoughts on superhydrophobic wetting

Capillary penetration of a wetting liquid in a microtomographic image of paper board, whose linear dimension was close to the average length of wood fibers, was simulated by the lattice-Boltzmann method. In spite of the size of the system not being large with respect to the size of structural inhomogeneities in the sample, for unidirectional penetration the simulated behavior was described well by that of the Lucas-Washburn equation, while for radial penetration a radial capillary equation described the behavior. In both cases the average penetration depth of the liquid front as a function of time followed a power law over many orders of magnitude. Capillary penetration of small droplets of liquid was also simulated in the same three-dimensional image of paper. In this case the simulation results could be described by a generalized form of the radial-penetration equation.

Simulation of liquid penetration in paper.

We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity.

Lattice-Boltzmann Simulation of Capillary Rise Dynamics

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method

The behaviour of liquid droplets on inclined heterogeneous surfaces was simulated by the lattice-Boltzmann method using the Shan-Chen multiphase model. The effect of topography of the surface on the contact angle hysteresis was investigated. It is shown in particular, by using anisotropic rough surfaces, how surface topography and thereby the continuity of the three-phase contact line, affect this hysteresis. Our results clearly indicate that the superhydrophobicity of a surface cannot be judged by the contact angle alone.

Droplets on inclined rough surfaces.

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.

P. Raiskinmäki

Papers

Simulation of liquid penetration in paper.

Lattice-Boltzmann Simulation of Capillary Rise Dynamics

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method

Droplets on inclined rough surfaces.

Shear Stress in a Couette Flow of Liquid-Particle Suspensions