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The dynamics of a viscous drop moving along a substrate under the influence of shear flow in a parallel-walled channel is investigated. A front tracking numerical method is used to simulate a drop with moving contact lines. A Navier slip boundary condition is applied to relax the contact line singularity. Steady state solutions are observed for small Reynolds and capillary number. Unsteady solutions are obtained with increasing Reynolds or capillary number. For large values of the parameters, the interface appears to rupture, but for intermediate parameter values, time periodic drop interface oscillations are possible as the drop is moving along the bottom channel wall. These different states are identified in the Reynolds number–capillary number plane for a specific range of physical parameters. The effects of density and viscosity ratio are also illustrated. [ABSTRACT FROM AUTHOR]

Experimental results are presented for the motion of a dry spot in a thin viscous film on a horizontal surface. These include global and spatial measurements of dry spot diameter, front velocities, static and dynamic contact angle, and the shape of the liquid-solid interface. Data are presented as a function of initial fluid depth for both an advancing fluid front of a collapsing dry spot and a receding fluid front of an opening dry spot. Results for both cases show that the final or static hole diameter increases as the initial fluid depth decreases. Also, insight is obtained into the relationship between the contact angle and the velocity for both advancing and receding fluid fronts. The experimental results are compared to a lubrication model, and good agreement is obtained. [ABSTRACT FROM AUTHOR]

Here we consider the gravity-driven dynamics of two superposed, incompressible, immiscible, viscous fluids flowing in a parallel-wall channel. The fluids are governed by the Navier-Stokes equations with surface tension along the interface. We use the front tracking numerical method to determine the solutions. Both stable and unstable solutions are obtained. The unstable solutions are characterized by a finger of lower fluid rising into the upper fluid. Our results are consistent with the predictions of linear stability theory. In addition, we attempt to characterize the growth of the unstable solutions as a function of the Reynolds and the Bond number. [ABSTRACT FROM AUTHOR]

The motion of a thin viscous layer of fluid on a horizontal solid surface bounded laterally by a dry spot and a vertical solid wall is considered. A lubrication model with contact line motion is studied. We find that for a container of fixed length the axisymmetric equilibrium solutions with small dry spots are unstable to axisymmetric disturbances. As the size of the dry spot increases, the equilibrium solutions become unstable to nonaxisymmetric disturbances. In addition, we present numerical solutions of the nonlinear evolution equations in the axisymmetric and nonaxisymmetric cases for different values of the parameters. The axisymmetric results show good agreement with existing experimental results. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped., (© 2016 The Author(s).)

Cryopreservation requires that stored materials be kept at extremely low temperatures and uses cryoprotectants that are toxic to cells at high concentrations. Lyopreservation is a potential alternative where stored materials can remain at room temperatures. That storage process involves desiccating cells filled with special glass-forming sugars. However, current desiccation techniques fail to produce viable cells, and researchers suspect that incomplete vitrification of the cells is to blame. To explore this hypothesis, a cell is modelled as a lipid vesicle to monitor the water content and membrane deformation during desiccation. The vesicle is represented as a moving, bending-resistant, inextensible interface and is tracked by a level set method. The vesicle is placed in a fluid containing a spatially varying sugar concentration field. The glass-forming nature is modelled through a concentration-dependent diffusivity and viscosity. It is found that there are optimal regimes for the values of the osmotic flow parameter and of the concentration dependence of the diffusivity to limit water trapping in the vesicle. Furthermore, it is found that the concentration dependencies of the diffusivity and viscosity can have profound effects on membrane deformations, which may have significant implications for vesicle damage during the desiccation process., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)

Recent experiments and calculations have highlighted the important role of surface-energy (gamma) anisotropy in governing island formation in the Ge/Si(001) system. To further elucidate the factors determining this anisotropy, we perform atomistic and continuum calculations of the orientation dependence of gamma for strained-Ge surfaces near (001), accounting for the presence of dimer-vacancy lines (DVLs). The net effect of DVLs is found to be a substantial reduction in the magnitude of the slope of gamma vs orientation angle, relative to the highly negative value derived for non-DVL, dimer-reconstructed, strained-Ge(001) surfaces. The present results thus point to an important role of DVLs in stabilizing the (001) surface orientation of a strained-Ge wetting layer.

Formation energies for Ge/Si(100) pyramidal islands are computed combining continuum calculations of strain energy with first-principles-computed strain-dependent surface energies. The strain dependence of surface energy is critically impacted by the presence of strain-induced changes in the Ge {100} surface reconstruction. The appreciable strain dependencies of rebonded-step {105} and dimer-vacancy-line-reconstructed {100} surface energies are estimated to give rise to a significant reduction in the surface contribution to island formation energies.