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.

Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

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.

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at seventy-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.

Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

Droplets of structured fluid on a flat substrate

We study the equilibrium morphology of droplets of symmetric AB diblock copolymer on a flat substrate. Using self-consistent field theory (SCFT), we provide the first predictions for the equilibrium droplet shape and its internal structure. When the sustrate affinity for the A component, $\eta_A$, is small, the droplet adopts a nearly spherical shape much like that of simple fluids. Inside the spherical droplet, however, concentric circular lamellar layers stack on top of each other; hence the thickness of the droplet is effectively quantized by a half-integer or integer number of layers. At larger $\eta_A$ and smaller contact angle, the area of the upper-most layer becomes relatively large, resulting in a nearly flat, faceted top surface, followed by a semi-spherical slope. This geometry is remarkably reminiscent of the droplet shapes observed with smetic liquid crystals.

Structural study of BSA/poly(ethylene glycol) lipid conjugate complexes

In this work we report the structural characteristics of bovine serum albumin/poly(ethylene glycol) lipid conjugate (BSA/PEG(2000)-PE) complexes under physiological conditions (37 degrees C and pH 7.4) for particular fractions of BSA to PEG-lipid concentration, CBSA/C-PEG2000-PE. Ultraviolet fluorescence spectroscopy (UV) results shown that PEG(2000)-PE is associated to BSA, leading to;protein unfolding for fixed C-BSA = 0.01 wt % and variable C-PEG2000-PE = 0.0015-0.6 wt %. Tryptophan groups on the BSA surface are in contact with the PEG-lipid at C-PEG2000-PE = 0.0015 wt %, while they are exposed to water at C-PEG2000-PE (>)0.0015 wt %. Dynamic and static light scattering (DLS and SLS) and small-angle neutron scattering (SANS) point out the existence of individual BSAIPEG-lipid complexes in the system for fixed C-BSA = 1 wt % and variable C-PEG2000-PE = 0.15-2 wt %. DLS shows that there is only one BSA molecule per protein/PEG-lipid complex, while SLS shows that the PEG-lipid associates to the BSA without promoting aggregation between adjacent protein/ polymer-lipid conjugate complexes. SANS was used to show that BSA/PEG(2000)-PE complexes adopt an oblate ellipsoidal shape. Partially unfolded BSA is contained in the core of the oblate ellipsoid, which is surrounded by an external shell containing the PEG(2000)-PE.

Dynamic modelling of a wind catcher/tower turret for natural ventilation

This paper discusses experimental and theoretical investigations and Computational Fluid Dynamics (CFD) modelling considerations to evaluate the performance of a square section wind catcher system connected to the top of a test room for the purpose of natural ventilation. The magnitude and distribution of pressure coefficients (C-p) around a wind catcher and the air flow into the test room were analysed. The modelling results indicated that air was supplied into the test room through the wind catcher's quadrants with positive external pressure coefficients and extracted out of the test room through quadrants with negative pressure coefficients. The air flow achieved through the wind catcher depends on the speed and direction of the wind. The results obtained using the explicit and AIDA implicit calculation procedures and CFX code correlate relatively well with the experimental results at lower wind speeds and with wind incidents at an angle of 0 degrees. Variation in the C-p and air flow results were observed particularly with a wind direction of 45 degrees. The explicit and implicit calculation procedures were found to be quick and easy to use in obtaining results whereas the wind tunnel tests were more expensive in terms of effort, cost and time. CFD codes are developing rapidly and are widely available especially with the decreasing prices of computer hardware. However, results obtained using CFD codes must be considered with care, particularly in the absence of empirical data.