On the effect of surfactant adsorption and viscosity change on apparent slip in hydrophobic microchannels

Substantial experimental, theoretical, as well as numerical effort has been invested to understand the effect of boundary slippage in microfluidic devices. However, even though such devices are becoming increasingly important in scientific, medical, and industrial applications, a satisfactory understanding of the phenomenon is still lacking. This is due to the extremely precise experiments needed to study the problem and the large number of tunable parameters in such systems. In this paper we apply a recently introduced algorithm to implement hydrophobic fluid-wall interactions in the lattice Boltzmann method. We find a possible explanation for some experiments observing a slip length depending on the flow velocity which is contradictory to many theoretical results and simulations. Our explanation is that a velocity dependent slip can be detected if the flow profile is not fully developed within the channel, but in a transient state. Further, we show a decrease of the measured slip length with increasing viscosity and demonstrate the effect of adding surfactant to a fluid flow in a hydrophobic microchannel. The addition of surfactant can shield the repulsive potential of hydrophobic walls, thus lowering the amount of slip with increasing surfactant concentration.Comment: 9 pages, 6 figure

Computational Steering of Cluster Formation in Brownian Suspensions

We simulate cluster formation of model colloidal particles interacting via DLVO (Derjaguin, Landau, Vervey, Overbeek) potentials. The interaction potentials can be related to experimental conditions, defined by the pH-value, the salt concentration and the volume fraction of solid particles suspended in water. The system shows different structural properties for different conditions, including cluster formation, a glass-like repulsive structure, or a liquid suspension. Since many simulations are needed to explore the whole parameter space, when investigating the properties of the suspension depending on the experimental conditions, we have developed a steering approach to control a running simulation and to detect interesting transitions from one region in the configuration space to another. The advantages of the steering approach and the restrictions of its applicability due to physical constraints are illustrated by several example cases.Comment: 9 pages, 4 figures, submitted to Proceedings of the Fourth International Conference on Mesoscopic Methods in Engineering and Science (ICMMES) 2007 (Munich, Germany), revised version, 2 figures exchanged, some parts rephrase

Evaluation of pressure boundary conditions for permeability calculations using the lattice-Boltzmann method

Lattice-Boltzmann (LB) simulations are a common tool to numerically estimate the permeability of porous media. For valuable results, the porous structure has to be well resolved resulting in a large computational effort as well as high memory demands. In order to estimate the permeability of realistic samples, it is of importance to not only implement very efficient codes, but also to choose the most appropriate simulation setup to achieve accurate results. With the focus on accuracy and computational effort, we present a comparison between different methods to apply an effective pressure gradient, efficient boundary conditions, as well as two LB implementations based on pore-matrix and pore-list data structures.Comment: 16 pages, 6 figure

Self-assembled porous media from particle-stabilized emulsions

We propose a new mechanism to create self-assembled porous media with highly tunable geometrical properties and permeabilities: We first allow a particle-stabilized emulsion to form from a mixture of two fluids and colloidal particles. Then, either one fluid phase or the particle layer is solidified, which can be achieved by techniques such as polymerization or freezing. Based on computer simulations we demonstrate that modifying only the particle wettability or concentration results in porous structures with a wide range of pore sizes and a permeability that can be varied by up to three orders of magnitude. We then discuss optimization of these properties for self-assembled filters or reactors and conclude that structures based on so-called "bijels" are most suitable candidates.Comment: 4 pages, 4 figure

Domain and droplet sizes in emulsions stabilized by colloidal particles

Particle-stabilized emulsions are commonly used in various industrial applications. These emulsions can present in different forms, such as Pickering emulsions or bijels, which can be distinguished by their different topologies and rheology. We numerically investigate the effect of the volume fraction and the uniform wettability of the stabilizing spherical particles in mixtures of two fluids. For this, we use the well-established three-dimensional lattice Boltzmann method, extended to allow for the added colloidal particles with non-neutral wetting properties. We obtain data on the domain sizes in the emulsions by using both structure functions and the Hoshen-Kopelman (HK) algorithm, and demonstrate that both methods have their own (dis-)advantages. We confirm an inverse dependence between the concentration of particles and the average radius of the stabilized droplets. Furthermore, we demonstrate the effect of particles detaching from interfaces on the emulsion properties and domain size measurements.Comment: 9 pages, 9 figure

Towards a continuum model for particle-induced velocity fluctuations in suspension flow through a stenosed geometry

Non-particulate continuum descriptions allow for computationally efficient modeling of suspension flows at scales that are inaccessible to more detailed particulate approaches. It is well known that the presence of particles influences the effective viscosity of a suspension and that this effect has thus to be accounted for in macroscopic continuum models. The present paper aims at developing a non-particulate model that reproduces not only the rheology but also the cell-induced velocity fluctuations, responsible for enhanced diffusivity. The results are obtained from a coarse-grained blood model based on the lattice Boltzmann method. The benchmark system comprises a flow between two parallel plates with one of them featuring a smooth obstacle imitating a stenosis. Appropriate boundary conditions are developed for the particulate model to generate equilibrated cell configurations mimicking an infinite channel in front of the stenosis. The averaged flow field in the bulk of the channel can be described well by a non-particulate simulation with a matched viscosity. We show that our proposed phenomenological model is capable to reproduce many features of the velocity fluctuations.Comment: 6 pages, 6 figure

Direct simulation of liquid-gas-solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid-gas-solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary -- in particular if the bubble-particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble-particle interaction at a size ratio of 1-2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than $100\,000$ fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully-resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble-particle interaction problems correctly.Comment: submitted to International Journal of Computational Fluid Dynamic

Accurate lubrication corrections for spherical and non-spherical particles in discretized fluid simulations

Discretized fluid solvers coupled to a Newtonian dynamics method are a popular tool to study suspension flow. As any simulation technique with finite resolution, the lattice Boltzmann method, when coupled to discrete particles using the momentum exchange method, resolves the diverging lubrication interactions between surfaces near contact only insufficiently. For spheres, it is common practice to account for surface-normal lubrication forces by means of an explicit correction term. A method that additionally covers all further singular interactions for spheres is present in the literature as well as a link-based approach that allows for more general shapes but does not capture non-normal interactions correctly. In this paper, lattice-independent lubrication corrections for aspherical particles are outlined, taking into account all leading divergent interaction terms. An efficient implementation for arbitrary spheroids is presented and compared to purely normal and link-based models. Good consistency with Stokesian dynamics simulations of spheres is found. The non-normal interactions affect the viscosity of suspensions of spheres at volume fractions \Phi >= 0.3 but already at \Phi >= 0.2 for spheroids. Regarding shear-induced diffusion of spheres, a distinct effect is found at 0.1 <= \Phi <= 0.5 and even increasing the resolution of the radius to 8 lattice units is no substitute for an accurate modeling of non-normal interactions.Comment: 19 pages, 10 figure

Timescales of emulsion formation caused by anisotropic particles

Particle stabilized emulsions have received an enormous interest in the recent past, but our understanding of the dynamics of emulsion formation is still limited. For simple spherical particles, the time dependent growth of fluid domains is dominated by the formation of droplets, particle adsorption and coalescence of droplets (Ostwald ripening), which eventually can be almost fully blocked due to the presence of the particles. Ellipsoidal particles are known to be more efficient stabilizers of fluid interfaces than spherical particles and their anisotropic shape and the related additional rotational degrees of freedom have an impact on the dynamics of emulsion formation. In this paper, we investigate this point by means of simple model systems consisting of a single ellipsoidal particle or a particle ensemble at a flat interface as well as a particle ensemble at a spherical interface. By applying combined multicomponent lattice Boltzmann and molecular dynamics simulations we demonstrate that the anisotropic shape of ellipsoidal particles causes two additional timescales to be of relevance in the dynamics of emulsion formation: a relatively short timescale can be attributed to the adsorption of single particles and the involved rotation of particles towards the interface. As soon as the interface is jammed, however, capillary interactions between the particles cause a local reordering on very long timescales leading to a continuous change in the interface configuration and increase of interfacial area. This effect can be utilized to counteract the thermodynamic instability of particle stabilized emulsions and thus offers the possibility to produce emulsions with exceptional stability.Comment: 14 pages, 14 figure