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We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f^{''}+(βf^{'})^{2}+f=0, where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

Surface-energy minimization is used to study capillary effects that determine the stable configurations of (liquid or solid) particles atop tubes or wires. The results give allowable ranges for the volume (V_{c}) of the particles as a function of the inner and outer radii of the tubes, R_{I} and R_{o}, respectively. When R_{I}/R_{o}=0, the object is a nanowire. When R_{I}/R_{o}=1, it is a single-wall carbon nanotube. When 0

Heterostructured GaAs-AlGaAs core-shell nanowires with have attracted much attention because of their significant advantages and great potential for creating high performance nanophotonics and nanoelectronics. The spontaneous formation of Al-rich stripes along certain crystallographic directions and quantum dots near the apexes of the shell are observed in AlGaAs shells. Controlling the formation of these core-shell heterostructures remains challenging. A two-dimensional model valid on the wire cross section, that accounts for capillarity in the faceted surface limit and deposition has been developed for the evolution of the shell morphology and concentration in Al x Ga 1- x As alloys. The model includes a completely faceted shell-vapor interface. The objective is to understand the mechanisms of the formation of the radial heterostructures (Al-rich stripes and Al-poor quantum dots) in the nanowire shell. There are two issues that need to be understood. One is the mechanism responsible for the morphological evolution of the shells. Analysis and simulation results suggest that deposition introduces facets not present on the equilibrium Wulff shapes. A balance between diffusion and deposition yields the small facets with sizes varying slowly over time, which yield stripe structures, whereas deposition-dominated growth can lead to quantum-dot structures observed in experiments. There is no self-limiting facet size in this case. The other issue is the mechanism responsible for the segregation of Al atoms in the shells. It is found that the mobility difference of the atoms on the {112} and {110} facets together determine the non-uniform concentration of the atoms in the shell. In particular, even though the mobility of Al on {110} facets is smaller than that of Ga, Al-rich stripes are predicted to form along the {112} facets when the difference of the mobilities of Al and Ga atoms is sufficiently large on {112} facets. As the size of the shell increases, deposition becomes more important. The Al-poor dots are obtained at the apices of {112} facets, if the attachment rate of Al atoms is smaller there.

Recent reports that macroscopic vortex flows can discriminate between chiral molecules or their assemblies sparked considerable scientific interest both for their implications to separations technologies and for their relevance to the origins of biological homochirality. However, these earlier results are inconclusive due to questions arising from instrumental artifacts and/or insufficient experimental control. After a decade of controversy, the question remains unresolved-how do vortex flows interact with different stereoisomers? Here, we implement a model experimental system to show that chiral objects in a Taylor-Couette cell experience a chirality-specific lift force. This force is directed parallel to the shear plane in contrast to previous studies in which helices, bacteria and chiral cubes experience chirality-specific forces perpendicular to the shear plane. We present a quantitative hydrodynamic model that explains how chirality-specific motions arise in non-linear shear flows through the interplay between the shear-induced rotation of the particle and its orbital translation. The scaling laws derived here suggest that rotating flows can be used to achieve chiral separation at the micro- and nanoscales.

Understanding the spreading and solidification of liquids on cold solid surfaces is a problem of fundamental importance and general utility. The physics of nonisothermal spreading followed by phase change is still a mystery. The present work focuses on the dynamics and thermal characteristics of liquid drop spreading and their subsequent arrest due to freezing. The spreading of liquid is recorded, and the evolution of the liquid spreading diameter and liquid-solid contact angle is measured from the recordings of a high-speed digital camera. After the initiation of solidification, the liquid drops are pinned to the substrate, showing fixed footprints and contact angles. A physical hypothesis using scaling is provided to explain the relationship between the arrested base diameter (D*) and arrested contact angle (θ*) with respect to the Stefan number (Ste). The experimental observations of solidified drops on cold substrates corroborate the derived physical theory.

In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are negligible and the vesicle's shape is given approximately by the arc of a circle. Simple composite expansions of the vesicle's shape are derived that account for the shape of the membrane inside these corners.

Anomalous diffusion can be characterized by a mean-squared displacement 〈x(2)(t)〉 that is proportional to t(α) where α≠1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion (α<1). A novel numerical method is developed to handle the moving interface as well as the singular history kernel of subdiffusion. Two moving boundary problems are solved: the first involves a subdiffusion region to the one side of an interface and a classical diffusion region to the other. The interface will display non-monotone behaviour. The subdiffusion region will always initially advance until a given time, after which it will always recede. The second problem involves subdiffusion regions to both sides of an interface. The interface here also reverses direction after a given time, with the more subdiffusive region initially advancing and then receding.

We study the stability and rupture of thin liquid films on patterned substrates. It is shown that striped patterning on a length scale comparable to that of the spinodal instability leads to a resonance effect and an imperfect bifurcation of equilibrium film shapes. Weakly nonlinear analysis gives predictions for film shapes, stability, growth rates, and rupture times, which are confirmed by numerical solution of the thin-film equation. Film behavior is qualitatively different in the resonant patterning regime, but with sufficiently large domains rupture occurs on a spinodal length scale regardless of patterning. Instabilities transverse to the patterning are examined and shown to behave similarly as disturbances to films on uniform substrates. We explain some previously reported effects in terms of the imperfect bifurcation.