Interaction forces between a deformable air bubble and a spherical particle of tuneable hydrophobicity and surface charge in aqueous solutions.

Interaction forces between an air bubble and a spherical particle of moderate and tuneable surface charge density and hydrophobicity in aqueous solutions were measured using atomic force microscopy. Bitumen coated silica spheres were used as model particles of tuneable charge density and hydrophobicity due to pH-dependent ionisation of carboxylic acids at bitumen-water interfaces. The measured force profiles showed a long-range repulsion prior to jump into contact, indicating the rupture of intervening liquid film between the bitumen and bubble surfaces. The long-range repulsive force increased with increasing pH. The measured force profiles were analysed by adopting the model originally developed by White and co-workers to account for deformation and change in shape of bubbles before rupture of the intervening liquid film. Satisfactory agreement between the theory and measured force profiles was obtained, showing the suitability of the model to describe the measured interaction forces. The model was then used to study the physical parameters on the particle-bubble interaction forces prior to three phase contact line (TPCL) formation. The hydrophobic decay length, surface potential and size of bubble and probe particles, and ionic strength of the medium (KCl concentration) were found to have a strong influence on the predicted force profiles.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel.

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.

Streaming potential and electroosmotic flow in heterogeneous circular microchannels with nonuniform zeta potentials: requirements of flow rate and current continuities.

Real surfaces are typically heterogeneous, and microchannels with heterogeneous surfaces are commonly found due to fabrication defects, material impurities, and chemical adsorption from solution. Such surface heterogeneity causes a nonuniform surface potential along the microchannel. Other than surface heterogeneity, one could also pattern the various surface potentials along the microchannels. To understand how such variations affect electrokinetic flow, we proposed a model to describe its behavior in circular microchannels with nonuniform surface potentials. Unlike other models, we considered the continuities of flow rate and electric current simultaneously. These requirements cause a nonuniform electric field distribution and pressure gradient along the channel for both pressure-driven flow (streaming potential) and electric-field-driven flow (electroosmosis). The induced nonuniform pressure and electric field influence the electrokinetic flow in terms of the velocity profile, the flow rate, and the streaming potential.

Oscillating laminar electrokinetic flow in infinitely extended circular microchannels.

This article addresses the problem of oscillating laminar electrokinetic liquid flow in an infinitely extended circular microchannel. Based on the Debye-Huckel approximation for low surface potential at the channel wall, a complex variable approach is used to obtain an analytical solution for the flow. The complex counterparts of the flow rate and the current are linearly dependent on the pressure gradient and the external electric field. This property is used to show that Onsager's principle of reciprocity continues to be valid (involving the complex quantities) for the stated problem. During oscillating pressure-driven flow, the electroviscous effect for a given value of the normalized reciprocal electrical double-layer (EDL) thickness is observed to attain a maximum at a certain normalized frequency. In general, an increasing normalized frequency results in a reduction of EDL effects, leading to (i). a volumetric flow rate in the case of streaming potential approaching that predicted by the theory without EDL effects, and (ii). a reduction in the volumetric flow rate in the case of electroosmosis.

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels.

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.

Dynamic and static interactions between bitumen droplets in water.

In the commercial bitumen extraction operation, dynamic and static interaction forces between bitumen drops in water determine the likelihood of desirable bitumen coalescence at different process stages. These dynamic and static forces were measured using colloidal particle scattering and hydrodynamic force balance techniques, respectively. In the former technique, dynamic interactions are studied through droplet-droplet collision trajectory measurement. In the latter technique, the static attractive forces between droplets are determined when a doublet is separated with a known and adjustable hydrodynamic force. The dynamic force measurement implies the presence of rigid chains on bitumen surfaces. The mean chain lengths for deasphalted bitumen at pH 7, whole bitumen at pH 7, and whole bitumen at pH 8.5 are 50, 78, and 41 nm, respectively. However, the static force measurement indicates much shorter mean chain lengths (<9 nm) in these three bitumen systems. Shorter chain length indicates weaker repulsive force. This finding of a much weaker repulsion between bitumen droplets under static conditions has important implications on the commercial bitumen extraction operation.