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.

Liquid flow over a substrate structured by seeded nanoparticles

Recent experiments have demonstrated that nanoparticles which sparsely distributed over a solid substrate can substantially change the flow conditions at the solid surface in the presence of slip. Inspired by these observations, the flow past tiny particles seeded on a solid substrate is investigated theoretically in the framework of an interface formation model. It has been shown, that even a single seeded nanoparticle can reduce significantly the measurable tangential component of hydrodynamic velocity at the substrate and affect the amount of the observed apparent slippage of the liquid. The effect from the particle manifests in a form of a long relaxation tail defined by the characteristic time of the interface formation process. A comparison with experiments has demonstrated a good agreement between theoretically predicted and experimentally observed values of the relaxation tail length scale.

Cyclic extrusion of a lava dome based on a stick-slip mechanism

Lava dome eruptions are sometimes characterised by large periodic fluctuations in extrusion rate over periods of hours that may be accompanied by Vulcanian explosions and pyroclastic flows. We consider a simple system of nonlinear equations describing a 1D flow of lava extrusion through a deep elastic dyke feeding a shallower cylindrical conduit in order to simulate this short-period cyclicity. Stick-slip conditions depending on a critical shear stress are assumed at the wall boundary of the cylindrical conduit. By analogy with the behaviour of industrial polymers in a plastic extruder, the elastic dyke acts like a barrel and the shallower cylindrical portion of the conduit as a die for the flow of magma acting as a polymer. When we applied the model to the Soufrière Hills Volcano, Montserrat, for which the key parameters have been evaluated from previous studies, cyclic extrusions with periods from 3 to 30 h were readily simulated, matching observations. The model also reproduces the reduced period of cycles observed when a major unloading event occurs due to lava dome collapse.