Hassan Farhat

Study of aggregational characteristics of emulsions on their rheological properties using the lattice Boltzmann approach

Predicting the rheological properties of emulsions is one of the most challenging and complicated problems in material and fluid sciences. Substantial complications in prediction of rheology arise due to the deformability and aggregation of emulsions. Thus a better understanding of deformation and aggregation of emulsions can lead to a better understanding of the shear thinning region of emulsions. Though numerous experimental and theoretical studies were performed to obtain rheological correlations of emulsions, their inability to visualize and understand the droplet deformation in the presence of large volume fractions has stagnated our understanding of the shear thinning behavior of emulsions. With the aid of a numerical tool, which can help in visualizing the droplet deformation and correlate it to rheological behavior of emulsions, we have made an attempt to understand the physics behind the shear thinning behavior and also predict its rheological characteristics for emulsions at different volume fractions. In this article, we try to obtain a theoretical understanding of the influence of deformation and de-aggregation of droplets on the emulsion rheology. Simulations performed in this article using a multi-component lattice Boltzmann model are used to quantify (a) relative viscosity of emulsions with change in shear rate, (b) relative viscosity of emulsions with change in time, (c) effect of deformation of droplets on the shear thinning region in emulsions, and (d) relative viscosity of emulsions with change in volume fraction.

A lattice Boltzmann model for substrates with regularly structured surface roughness

Superhydrophobic surface characteristics are important in many industrial applications, ranging from the textile to the military. It was observed that surfaces fabricated with nano/micro roughness can manipulate the droplet contact angle, thus providing an opportunity to control the droplet wetting characteristics. The Shan and Chen (SC) lattice Boltzmann model (LBM) is a good numerical tool, which holds strong potentials to qualify for simulating droplets wettability. This is due to its realistic nature of droplet contact angle (CA) prediction on flat smooth surfaces. But SC-LBM was not able to replicate the CA on rough surfaces because it lacks a real representation of the physics at work under these conditions. By using a correction factor to influence the interfacial tension within the asperities, the physical forces acting on the droplet at its contact lines were mimicked. This approach allowed the model to replicate some experimentally confirmed Wenzel and Cassie wetting cases. Regular roughness structures with different spacing were used to validate the study using the classical Wenzel and Cassie equations. The present work highlights the strength and weakness of the SC model and attempts to qualitatively conform it to the fundamental physics, which causes a change in the droplet apparent contact angle, when placed on nano/micro structured surfaces.

Accelerated Lattice Boltzmann Model for Colloidal Suspensions: Rheology and Interface Morphology

Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmannbased numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions. Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the rheology of colloids and microvasculature blood flow. The presented LBM model provides a flexible numerical platform consisting of various modules that could be used separately or in combination for the study of a variety of colloids and biological flow deformation problems.

Overview of Related Studies

This chapter reviews the lattice Boltzmann method (LBM) for single phase and multiphase flows with a focus on the Gunstensen and the Shan and Chen models. It also explains the LBM multiblock scheme, which allows the iteration to occur simultaneously in a simulation domain consisting of smooth and coarse grids. This chapter also covers surfactant-laden droplets behavior from both experimental and numerical point of view, and it highlights the main physical characteristics of this phenomenon. Emulsions rheology is reviewed here, where several empirical formulations for the calculation of the relative viscosity of non-Newtonian fluids are highlighted. Explanation for the direct calculation of emulsions’ viscosity in numerical simulations is also presented. Red blood cells as major constituent of blood determines its macrocolloid like behavior. This behavior is mainly influenced by the RBC properties, which are summarized at the end of this chapter.

Suppressing the Coalescence in the LBM: Colloids Rheology

This chapter presents a novel phenomenological approach for suppressing the coalescence in the Gunstensen multicomponent lattice Boltzmann method (LBM). The suppression of coalescence is achieved by perturbing the terminal nodes of the ambient fluid’s thin layer trapped between the approaching droplets. This additional perturbation creates a local high pressure fluid layer which eventually leads to suppressing the coalescence of the neighboring droplets while maintaining a suitable qualitative force balance representative of the physical intermolecular forces which act between them. The suppression of coalescence enables predicting the rheological properties of soft colloids, which is one of the most challenging and complicated problems in material and fluid sciences. Substantial complications in prediction of rheology arise due to the deformability and aggregation of soft colloids. Thus, a better understanding to deformation and aggregation of colloids can lead to a better understanding of the shear thinning region of colloidal solutions. This chapter provides a practical overview of the deformation and de-aggregation of droplets with change in time or increase in shear rate. Simulations performed here are used to quantify (a) relative viscosity of emulsions with change in shear rate, (b) relative viscosity of emulsions with change in time, (c) effect of deformation of droplets on the shear thinning region in emulsions, and (d) relative viscosity of emulsions with change in volume fraction.

Hybrid LBM for Surfactant-Covered Droplets

This chapter describes a novel hybrid lattice Boltzmann model for the study of the droplet flow behavior in an immiscible medium with insoluble nonionic surfactant adhering to its interface. The evolution of the surfactant concentration on the interface is modeled by the time-dependent surfactant convection-diffusion equation and solved by a finite difference scheme. The fluid velocity field, the pressure, and the interface curvature are calculated using the lattice Boltzmann method (LBM) for binary fluid mixtures. The coupling between the LBM and the finite difference scheme is achieved through the LBM macroscopic variables and the surfactant equation of state. The Gunstensen LBM is used here because it provides local and independent application of a distinct interfacial tension on the individual nodes of the droplet interface. The hybrid model is developed and successfully applied to droplets deformations and surfactant distribution under simple shear flow, uniaxial flow, and buoyancy.

Nonuniform Interfacial Tension LBM for RBC Modeling

This chapter aims at analyzing the red blood cell (RBC) deformation and velocity while streaming through venules and through capillaries whose diameters are smaller than the RBC size. The characteristics of the RBC shape change and velocity can potentially help in diagnosing diseases. In this work the RBC is considered as a surfactant covered droplet. This is justified by the fact that the cell membrane liquefies under pressure in the capillaries, and this allows the marginalization of its mechanical properties. The RBC membrane is in fact a macrocolloid containing lipid surfactant. When liquefied, it can be considered as a droplet of immiscible hemoglobin covered with lipid surfactant in a plasma surrounding. The local gradient in the surface tension due to nonuniform local interface surfactant distribution is neglected here, and a nonuniform zonal averaged value of surface tension representative of the surfactant bulk zonal concentration is rather implemented. The interplay between the surface tension geometry and the hydrodynamic conditions determines the droplet shape by affecting a change in its Weber number, and influences its velocity. The Gunstensen lattice Boltzmann model for immiscible fluids is used since it provides independent adjustment of the local surface tension, and allows the use of fluids with viscosity contrast. The proposed concept was used to investigate the dynamic shape change of the RBC while flowing through the microvasculature, and to explore the Fahraeus, and the Fahraeus–Lindqvist effects.

Accelerated Lattice Boltzmann Method

The LBM is a powerful numerical fluid solver especially in the areas of multicomponent and multiphase mixtures. However the LBM uses the particle velocity for the determination of the model time step required by the Courant-Friedrichs-Lewy (CFL) stability condition. This degrades the LBM efficiency, when compared with standard CFD solvers which use instead the macroscopic velocity for the CFL requirements. To increases the efficiency of the LBM and especially for multiphase flow simulations, the migrating multiblock (MMB) was introduced.

The Study of RBC Deformation in Capillaries With a Lattice Boltzmann Method for Surfactant Covered Droplets

This study aims at analyzing the shape change of red blood cells in the process of streaming through a capillary smaller than the red blood cell diameter. The characteristics of its shape change and velocity can potentially lead to an indicator of a variety of diseases. We approach this problem with considering red blood cells as surfactant covered droplets. This assumption is justified by the fact that the cell membrane liquefies under high pressure in small capillaries, and this allows the marginalization of the mechanical properties of the membrane. The red blood cell membrane is in fact a macro-colloid containing lipid surfactant. When liquefied, it can be treated as a droplet of immiscible hemoglobin covered with lipid surfactant in plasma surrounding. The merit is to analyze the effect of the flow condition and domain geometry on the surfactant concentration change over the droplet interface, and the effect of this change on the surface tension of the droplet. The distribution of the surfactant is calculated by enforcing conservation of the surfactant mass concentration on the interface, leading to a convection diffusion equation. The equation takes account of the effects of the normal and Marangoni stresses as a boundary condition on the interface between the immiscible fluids. The gradient in the surface tension adversely determines the droplet shape by effecting a local change in the capillary number, and influences its velocity by retarding the local surface velocity. The choice of the Gunstensen model is motivated by its capability of handling incompressible fluids, and the locality of the application of the surface tension. We used the same concept to investigate the dynamic shape change of the RBC while flowing through the microvasculature, and explore the physics of the Fahraeus, and the Fahraeus-Lindqvist effects.Copyright