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.

Epithelial tissue, in which cells adhere tightly to each other and to the underlying substrate, is one of the four major tissue types in adult organisms. In embryos, epithelial sheets serve as versatile substrates during the formation of developing organs. Some aspects of epithelial morphogenesis can be adequately described using vertex models, in which the two-dimensional arrangement of epithelial cells is approximated by a polygonal lattice with an energy that has contributions reflecting the properties of individual cells and their interactions. Previous studies with such models have largely focused on dynamics confined to two spatial dimensions and analyzed them numerically. We show how these models can be extended to account for three-dimensional deformations and studied analytically. Starting from the extended model, we derive a continuum plate description of cell sheets, in which the effective tissue properties, such as bending rigidity, are related explicitly to the parameters of the vertex model. To derive the continuum plate model, we duly take into account a microscopic shift between the two sublattices of the hexagonal network, which has been ignored in previous work. As an application of the continuum model, we analyze tissue buckling by a line tension applied along a circular contour, a simplified set-up relevant to several situations in the developmental contexts. The buckling thresholds predicted by the continuum description are in good agreement with the results of stability calculations based on the vertex model. Our results establish a direct connection between discrete and continuum descriptions of cell sheets and can be used to probe a wide range of morphogenetic processes in epithelial tissues.

No abstract

We report on instabilities during the spreading of volatile liquids, with emphasis on the novel instability observed when isopropyl alcohol is deposited on a monocrystalline Si wafer. This instability is characterized by emission of drops ahead of the expanding front, with each drop followed by smaller, satellite droplets, forming the structures which we nickname "octopi" due to their appearance. A less volatile liquid, or a substrate of larger heat conductivity, suppresses this instability. We formulate a theoretical model that reproduces the main features of the experiment.

We consider evaporation of pure liquid drops on a thermally conductive substrate. Two commonly used evaporative models are considered: one that concentrates on the liquid phase in determining the evaporative flux and the other one that centers on the gas-vapor phase. A single governing equation for the evolution of drop thickness, including both models, is developed. We show how the derived governing equation can be used to predict which evaporation model is appropriate for different considered experimental conditions.