Measurement and modeling on hydrodynamic forces and deformation of an air bubble approaching a solid sphere in liquids

The interaction between bubbles and solid surfaces is central to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. A main challenge is to accurately and reliably control the relative motion over a wide range of hydrodynamic conditions and at the same time to determine the interaction forces, bubble–solid separation and bubble deformation. Existing experimental methods are able to focus only on one of the aspects of this problem, mostly for bubbles and particles with characteristic dimensions either below 100 μm or above 1 cm. As a result, either the interfacial deformations are measured directly with the forces being inferred from a model, or the forces are measured directly with the deformations to be deduced from the theory. The recently developed integrated thin film drainage apparatus (ITFDA) filled the gap of intermediate bubble/particle size ranges that are commonly encountered in mineral and oil recovery applications. Equipped with side-view digital cameras along with a bimorph cantilever as force sensor and speaker diaphragm as the driver for bubble to approach a solid sphere, the ITFDA has the capacity to measure simultaneously and independently the forces and interfacial deformations as a bubble approaches a solid sphere in a liquid. Coupled with the thin liquid film drainage modeling, the ITFDA measurement allows the critical role of surface tension, fluid viscosity and bubble approach speed in determining bubble deformation (profile) and hydrodynamic forces to be elucidated. Here we compare the available methods of studying bubble–solid interactions and demonstrate unique features and advantages of the ITFDA for measuring both forces and bubble deformations in systems of Reynolds numbers as high as 10. The consistency and accuracy of such measurement are tested against the well established Stokes–Reynolds–Young–Laplace model. The potential to use the design principles of the ITFDA for fundamental and developmental research is demonstrated.     

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.     

Flow through isotropic granular porous media

A generalization of the Navier-Stokes equation is developed to include laminar flow through a rigid isotropic granular porous medium of spatially varying permeability. The model is based on a theory of interspersed continua and the mean geometrical properties of an idealized granular porous microstructure. The derived momentum transport equations are applicable to granular porous media over the entire porosity range from zero through unity. No restriction with respect to flow velocity is imposed, except for the assumption of laminar flow within the pores. The results provide useful and versatile equations and substantiate many of the empirical equations currently in use. One of the major advantages of the generalized momentum equation is its adaptability to numerical simulation.     

Shear-induced coalescence of emulsified oil drops

Crude oil droplets, when suspended in water, possess negative surface charges which give rise to double-layer repulsive forces between the drops. According to conventional DLVO theory, the magnitude of this repulsion (based on the measured zeta potential) is more than sufficient to prevent coalescence of the droplets. Indeed, when two such droplets were brought together on direct (i.e., "head-on") approach, coalescence was rarely observed. Upon oblique approach, however, the same droplets were seen to coalesce readily. An oblique encounter must necessarily give rise to lateral relative motion-or shearing-between the droplet surfaces. It is speculated that, if the charge distributions at the droplet surfaces were heterogeneous, lateral shearing would facilitate many encounters between surface patches of different zeta potentials across the intervening water film. If the repulsion across any local region were sufficiently weak to allow formation of an oil bridge across the water film, coalescence of the drops would follow inevitably. With the hypothesis of surface heterogeneity, it is not necessary to invoke any additional colloidal interactions (such as "hydrophobic forces") to account for the observed droplet-droplet coalescence. This finding may have important implications for the underlying mechanisms of emulsion stability in general and the commercial extraction of bitumen from oil sands in particular.     

Particle deposition onto charge heterogeneous surfaces: convection-diffusion-migration model

The role of surface charge heterogeneity of planar collectors on particle deposition and distribution was investigated in the vicinity of a heterogeneous surface for a radial impinging jet flow geometry. The charge heterogeneity was modeled as concentric circular stripes bearing different surface charges. Particle deposition was studied employing the Eulerian approach (convection-diffusion-migration equation). It was observed that when the collector was completely unfavorable, the presence of small amounts of charge heterogeneity in the form of a small fraction of favorably charged stripes enhanced the deposition rate substantially. In contrast, when the collector was completely favorable, the presence of small amounts of charge heterogeneity in the form of a small fraction of unfavorably charged stripes did not affect the particle deposition rate significantly.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

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.     

Sandwich structures at oil-water interfaces under alkaline conditions

Equilibrium liquid crystal (LC) layer on an interface between crude oils and water was observed at high pH. This layer is composed mainly of sodium naphthenates produced in situ at the water/oil interface. Transient LC layer was also evolved at the interface of aqueous phase of sodium hydroxide solutions and oleic phase of naphthenic acid (NA) solutions as result of a chemical reaction between NaOH and NA. This chemical reaction causes transport process resulting in a disturbance of the interface. Optical observation of this interface disturbance reviled that the interface covered with LC shows considerably lower flexibility as compared to LC free interface. The LC layer eventually dissolves in the water phase at low oil-to-water ratio, while at high oil-to-water ratio it can form an equilibrium phase, which spreads spontaneously at the oil-water interface.     

The behaviour of micro-bitumen drops in aqueous clay environments

This study summarises the rheological behaviour of emulsion bitumen drops in the presence of aqueous solutions of de-ionised or process water (DIW or PW) containing montmorillonite clays (M) and/or calcium ions (Ca++). The presence of calcium ions and montmorillonite clays resulted in the plastic behaviour of bitumen drops. In a DIW+M+Ca++ system, increasing temperature and calcium ion concentration resulted in an increase in the number and degree of plastic bitumen drops. In the presence of considerable amounts of Ca++ ions and/or at higher experimental temperature, bitumen drops in a PW+M system exhibited no significant overall plasticity of their surfaces. Both calcium and sodium ions contained in process water compete with each other to occupy the montmorillonite clay surface. At the pH value of process water (pH congruent with8), increasing the temperature did not change the value of bitumen droplet zeta potential. Stability of bitumen-in-water emulsions at 22 degrees C showed that bitumen droplets coalesced upon contact in the DIW+M system. The addition of calcium ions (Ca++) led to the inhibition of coagulation and coalescence of bitumen droplets, which may indicate the formation of CaM aggregates at the bitumen-water interface.