Jacob H. Masliyah

Modeling forced liquid convection in rectangular microchannels with electrokinetic effects

Abstract The effects of the electric double layer near the solid–liquid interface and the flow induced electrokinetic field on the pressure-driven flow and heat transfer through a rectangular microchannel are analyzed in this work. The electric double layer field in the cross-section of rectangular microchannels is determined by solving a non-linear, two-dimensional Poisson–Boltzmann equation. A body force caused by the electric double field and the flow-induced electrokinetic field is considered in the equation of motion. For steady-state, fully-developed laminar flows, both the velocity and the temperature fields in a rectangular microchannel are determined for various conditions. The flow and heat transfer characteristics with⧹without consideration of the electrokinetic effects are evaluated. The results clearly show that, for aqueous solutions of low ionic concentrations and a solid surface of high zeta potential, the liquid flow and heat transfer in rectangular microchannels are significantly influenced by the presence of the electric double layer field and the induced electrokinetic flow.

On water-in-oil emulsions stabilized by fine solids

Abstract The stability of water-in-oil emulsions stabilized by fine solids with different hydrophobicities were studied with model organic solvents, such as light mineral oil (Bayol-35), decane and toluene. The fine solids used in this study include kaolinite clay particles treated with asphaltenes, hydrophilic and hydrophobic colloidal silica, hydrophobic polystyrene latex microspheres, as well as fumed silica dry powders treated with silanization. Experimental results showed that hydrophilic colloidal silica could only stabilize oil-in-water emulsions for a short period of time. If hydrophobic particles (colloidal silica or polystyrene latex microspheres) were suspended in the aqueous phase prior to emulsification, they could only produce oil-in-water emulsions. Only hydrophobic particles suspended in organic phase prior to emulsification could stabilize water-in-oil emulsions. The size of the water droplets in emulsion was as small as 2 μm when the solids were 12 nm in diameter. The stability of the produced emulsions depended on the hydrophobicity of the particles. Only particles with intermediate hydrophobicity could produce very stable water-in-oil emulsions, and in some cases the volume of the produced emulsions was triple that of water present in the system.

Analysis of electroosmotic flow of power-law fluids in a slit microchannel.

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

Mathematical Modelling of Flow Through Consolidated Isotropic Porous Media

A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively.

Creeping flow over a composite sphere: Solid core with porous shell

Abstract Creeping flow past a solid sphere with a porous shell has been solved using the Stokes and Brinkman equations. The dimensionless solid core and shell radii, normalized by the square root of the shell permeability, are the two parameters that govern the flow. In the limiting cases, the analytical solution describing the flow past the composite sphere reduces to that for flow past a solid sphere and a homogeneous porous sphere. The settling rates of a solid sphere with attached threads are measured experimentally. This system can be considered a model for rigid linear molecules anchored or adsorbed onto a colloidal particle. The analytical solution for the composite sphere is in excellent agreement with the experimental results.

An experimental and numerical study of the Dean problem: flow development towards two-dimensional multiple solutions

An experimental and numerical study investigating the flow development and fully developed flows of an incompressible Newtonian fluid in a curved duct ofsquare cross section with a curvature ratio of 15.1 is presented. Numerical simulations of flow development from a specified inlet profile were performed using a parabalized form of the steady three-dimensional Navier-Stokes equations

Axially invariant laminar flow in helical pipes with a finite pitch

Steady axially invariant (fully developed) incompressible laminar flow of a Newtonian fluid in helical pipes of constant circular cross-section with arbitrary pitch and arbitrary radius of coil is studied. A loose-coiling analysis leads to two dominant parameters, namely Dean number, Dn = Re λ ½ , and Germano number, Gn = Re η, where Re is the Reynolds number, λ is the normalized curvature ratio and η is the normalized torsion. The Germano number is embedded in the body-centred azimuthal velocity which appears as a group in the governing equations. When studying Gn effects on the helical flow in terms of the secondary flow pattern or the secondary flow structure viewed in the generic (non-orthogonal) coordinate system of large Dn , a third dimensionless group emerges, γ = η/(λ Dn ) ½ . For Dn * = Gn Dn -2 = η/(λ Re ) takes the place of γ. Numerical simulations with the full Navier-Stokes equations confirmed the theoretical findings. It is revealed that the effect of torsion on the helical flow can be neglected when γ ≤ 0.01 for moderate Dn. The critical value for which the secondary flow pattern changes from two vortices to one vortex is γ * > 0.039 for Dn 0.2 for Dn ≥ 20. For flows with fixed high Dean number and A, increasing the torsion has the effect of changing the relative position of the secondary flow vortices and the eventual formation of a flow having a Poiseuille-type axial velocity with a superimposed swirling flow. In the orthogonal coordinate system, however, the secondary flow generally has two vortices with sources and sinks. In the small-γ limit or when Dn is very small, the secondary flow is of the usual two-vortex type when viewed in the orthogonal coordinate system. In the large-γ limit, the appearance of the secondary flow in the orthogonal coordinate system is also two-vortex like but its orientation is inclined towards the upper wall. The flow friction factor is correlated to account for Dn , A and γ effects for Dn ≤ 5000 and γ

Effects of physical environment on induction time of air–bitumen attachment

Abstract Induction time is a key parameter in flotation. It is defined as the time needed for attachment of an air bubble with particles or a layer of bitumen when they are in contact. It has been reported that induction time is a function of many physical parameters. However, no systematic experimental study of these parameters has been reported. A refined induction timer was built to investigate the effects of physical parameters on induction time. The induction time, measured by moving an air bubble toward and then away from a silica particle bed, was found to be affected by the initial gap between the air bubble and the particle bed, the displacement and size of the air bubble, and the velocities of the air bubble approach to and retraction from the particle bed. Air bubble–bitumen attachment in different solutions (de-ionized water, clear process water and process water containing 0.5% fine solids) with or without calcium ion addition was studied at different temperatures. The results showed that induction time decreased with increasing temperature. The induction time was lowest in de-ionized water and highest in process water containing 0.5% fine solids with 50 ppm calcium ions.

Characterization and demulsification of solids-stabilized oil-in-water emulsions Part 1. Partitioning of clay particles and preparation of emulsions

Kaolinite clay particles treated with asphaltenes were used to study the partitioning of the clay particles between an oil-in-water emulsion and an aqueous phase. It was found that the interaction energy of the adsorbed particles and the equilibrium ratio of the clay concentration at the oil droplet surface to that in the bulk water were strong functions of the clay contact angle θ, for θ > 65°. For a given initial clay concentration in the bulk water and emulsification conditions, the variation of the oil droplet diameter with θ exhibited a minimum at θ ≈ 65°. Under similar emulsification conditions, a higher initial clay concentration in the bulk water resulted in the formation of smaller oil droplets and a larger volume of creamed emulsion.

Numerical study of steady flow past spheroids

Numerical methods have been used to investigate the steady incompressible flow past oblate and prolate spheroids for Reynolds numbers up to 100. The ratio of minor to major axis of the spheroids investigated were 0·9, 0·5 and 0·2, together with 1·0, which represents the limiting case of a sphere. The pressure distribution and the skin and form drag coefficients were numerically evaluated for the various Reynolds numbers. Streamlines, equi-vorticity lines and equivelocity lines are presented and show in detail the flow characteristics.