We develop a dynamic model for suspensions of negatively buoyant particles on an incline. Our model includes settling due to gravity and resuspension of particles by shear-induced migration. We consider the case where the particles settle onto the solid substrate and two distinct fronts form: a faster liquid and a slower particle front. The resulting transport equations for the liquid and the particles are of hyperbolic type and we study the dilute limit for which we compute exact solutions. We also carry out systematic laboratory experiments, focusing on the motion of the two fronts. We show that the dynamic model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data.

The morphological path of droplets on a liquid substrate towards equilibrium is investigated experimentally and theoretically. The droplets emerge in the late stage of a dewetting process of short chained polystyrene (PS) dewetting from liquid polymethyl-methacrylate (PMMA). The three-dimensional droplet profiles are obtained experimentally by combining the in situ imaged PS/air interface during equilibration and the ex situ imaged PS/PMMA interface after removal of the PS by a selective solvent. Numerically the transient drop shapes are calculated by solving the thin-film equation in lubrication approximation using the experimentally determined input parameter like viscosity, film thickness and surface tensions. The numerically obtained droplet morphologies and time scales agree very well with the experimental drop shapes. An unexpected observation is that droplets with identical volumes synchronise their motion and become independent of the initial geometry long time before equilibrium is reached.

In this work we derive systems of coupled thin-film equations for immiscible liquid polymer layers on a solid substrate. We take into account slip between liquids and solids and also slip between both liquids. On the scale of tens of nanometres such two-layer systems are susceptible to instability and may rupture and dewet due to intermolecular forces. The stability of the two-layer system and its significant dependence on the order of magnitude of slip is investigated via these thin-film models. With weak slip at both the liquid-liquid and liquid-solid interface and polymer layers of comparable thickness, the dispersion relation typically shows two local maxima, one in the long-wave regime and the other at moderate wavenumbers. The former is associated with perturbations that mainly affect the gas-liquid interface and the latter with larger relative perturbation amplitudes at the liquid-liquid interface. Increasing the slip at the liquid-liquid interface generally favours the long-wave regime and can in fact revert the mode of the instability and thus significantly change the spinodal patterns. Moreover, the maxima shift to small wavenumbers for increasing slip.

We examine the semiclassical content of SU (3) Yang Mills theory on the lattice at finite temperature. Employing the cooling method, a set of classical fields is generated from a Monte Carlo ensemble. Various operators are used to inspect this set with respect to topological properties. We find pseudoparticle fields, so-called caloron solutions, possessing the remarkable features of (superpositions of) Kraan-van Baal solutions, i.e. extensions of Harrington-Shepard calorons to generic values of the holonomy.

Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.