The effect of flow field & geometry on the dynamic contact angle

A number of recent experiments suggest that, at a given wetting speed, the dynamic contact angle formed by an advancing liquid-gas interface with a solid substrate depends on the flow field and geometry near the moving contact line. In the present work, this effect is investigated in the framework of an earlier developed theory that was based on the fact that dynamic wetting is, by its very name, a process of formation of a new liquid-solid interface (newly “wetted” solid surface) and hence should be considered not as a singular problem but as a particular case from a general class of flows with forming or/and disappearing interfaces. The results demonstrate that, in the flow configuration of curtain coating, where a liquid sheet (“curtain”) impinges onto a moving solid substrate, the actual dynamic contact angle indeed depends not only on the wetting speed and material constants of the contacting media, as in the so-called slip models, but also on the inlet velocity of the curtain, its height, and the angle between the falling curtain and the solid surface. In other words, for the same wetting speed the dynamic contact angle can be varied by manipulating the flow field and geometry near the moving contact line. The obtained results have important experimental implications: given that the dynamic contact angle is determined by the values of the surface tensions at the contact line and hence depends on the distributions of the surface parameters along the interfaces, which can be influenced by the flow field, one can use the overall flow conditions and the contact angle as a macroscopic multiparametric signal-response pair that probes the dynamics of the liquid-solid interface. This approach would allow one to investigate experimentally such properties of the interface as, for example, its equation of state and the rheological properties involved in the interface’s response to an external torque, and would help to measure its parameters, such as the coefficient of sliding friction, the surface-tension relaxation time, and so on.

Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Mineral and geochemical characterization of a leptic aluandic soil and a thapto aluandic-ferralsol developed on trachytes in Mount Bambouto (Cameroon volcanic line)

Mineral and geochemical investigations were carried out on soil samples and fresh rock (trachytes) from two selected soil profiles (TM profile on leptic aluandic soils and TL profile on thapto aluandic-ferralsols) from Mount Bambouto to better understand geochemical processes and mineral paragenesis involved in the development of soils in this environment. In TM profile, the hydrated halloysites and goethite occur in the weathered saprolite boulders of BC horizon while dehydrated halloysite, gibbsite and goethite dominate the soils matrices of BC and A horizons. In TL profile, the dehydrated halloysites and goethite are the most abundant secondary minerals in the weathered saprolites of C and BC horizons while gibbsite, hematite and kaolinite occur in the soil matrices of BC, B and A horizons. The highest gibbsite content is in the platy nodules of B horizon. In both soil profiles, organo-metal complexes (most likely of AI and Fe) are present in the surface A horizon. Geochemically, between the fresh rock and the weathered saprolites in both soils, SiO2, K2O, CaO, Na2O and MgO contents decrease strongly while Fe2O3 and Al2O3 tend to accumulate. The molar ratio of SiO2/Al2O3 (Ki) and the sum of Ca, Mg, K and Na ions (TRB) also decreases abruptly between fresh rocks and the weathered saprolites, but increases significantly at the soil surface. The TM profile shows intense Al enrichment whereas the TL profile highlights enrichment in both AI and Fe as the weathering progresses upwards. Both soil profiles are enriched in Ni, Cu, Ba and Co and depleted in U, Th, Ta, Hf, Y, Sr, Pb, Zr and Zn relative to fresh rock. They also show a relatively low fractionation of the rare earth elements (REE: La, Nd, Sm, Eu, Tb, Yb and Lu), except for Ce which tends to be enriched in soils compared to CI chondrite. All these results give evidence of intense hydrolysis at soil deep in Mount Bambouto resulting in the formation of halloysite which progressively transforms into gibbsite and/or dehydrated halloysite. At the soil surface, the prominent pedogenetic process refers to andosolization with formation of organo-metal complexes. In TL profile, the presence of kaolinite in soil matrices BC and B horizons is consistent with ferralitization at soil deep. In conclusion, soil forming processes in Mount Bambouto are strongly influenced by local climate: (i) in the upper mountain (>2000 m), the fresh, misty and humid climate favors andosolization; whereas (ii) in the middle lands (1700-2000 m) with a relatively dry climate, both andosolization at the soil surface and ferralitization at soil deep act together. (C) 2009 Elsevier B.V. All rights reserved.