Origin of Rebound Suppression for Dilute Polymer Solution Droplets on Superhydrophobic Substrate.

Controlling droplet deposition with a minute amount of polymer additives is of profound practical importance in a wild range of applications. Previous work ascribed the relevant mechanisms to extensional viscosity, normal stress, wetting properties, etc., but the mechanism remains controversial. In this paper, we employ molecular dynamics simulations systematically for the first time to investigate the origin of rebound suppression for dilute polymer solution droplets on a flat superhydrophobic substrate. The results demonstrate that polymer-substrate interactions and impact velocities dominate the antirebound phenomenon. For low impact velocities, the dynamic characteristics of droplets are insensitive to polymer additives. However, large impact velocities will enhance the stretch behavior of polymer chains and make the chains closer to the substrate, increasing the probability of polymer molecules contacting the bottom substrate. With the cooperation of strong polymer-substrate interactions, polymer molecules can be absorbed easily by the bottom substrate, resisting the retraction process and leading to the onset of the antirebound behavior.

The piecewise parabolic method for elastic-plastic flow in solids.

A numerical technique of high-order piecewise parabolic method in combination of HLLD ("D" denotes Discontinuities) Riemann solver is developed for the numerical simulation of elastic-plastic flow. The introduction of the plastic effect is realized by decomposing the total deformation gradient tensor as the product of elastic and plastic deformation gradient tensors and adding plastic source term to the conservation law model equation with the variable of the elastic deformation gradient tensor. For the solution of the resulting inhomogeneous equation system, a temporal splitting strategy is adopted and a semi-implicit scheme is performed to solve the ODES in the plastic step, which is conducted to account for the contributions from plastic source terms. As seen from the results of test cases involving large deformation and high strain rate, the computational model used can reflect the characteristics of constitutive relation of material under strong impact action and our numerical method can realize the exact simulation of the elastic-plastic behavior of solid material, especially the accurate capture of the elastic-plastic waves. Further, it could also deal with high-speed impact problems with multi-material components, catching material interfaces correctly and keeping the interfaces sharp, when combined with interface tracking technique such as the level-set algorithm.

The piecewise parabolic method for Riemann problems in nonlinear elasticity.

We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD ("D" denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC ("C" denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid "stick" problem with the same material at the two sides of contact interface and the solid/solid "slip" problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

Stability analysis of Rayleigh-Bénard convection in a cylinder with internal heat generation.

The flow instabilities of Rayleigh-Bénard convection in a cylinder with effect of uniform internal heat source are investigated numerically. The instabilities of the static state and of axisymmetric flows are investigated by linear stability analysis. The convection threshold depends on the strength of internal heat source q and the aspect ratio of the cylinder Γ. The stability of axisymmetric flows is strongly affected by these two parameters, as well as the Prandtl number Pr. Depending on the value of q, three regimes are identified: weak internal heating, moderate internal heating, and strong internal heating regime. In a weak internal heating regime, the instability characteristics are similar to Rayleigh-Bénard convection. In a moderate internal heating regime, intense interaction of buoyancy instability and hydrodynamic instability result in complex instability curves. When q is large enough, the internal heating effect overwhelms the boundary heating effect. Specifically, the influence of Pr on instability is studied at a moderate internal heat strength q=6.4. An extremely multivalued stability curve is observed. At most five critical Rayleigh numbers can be determined for the axisymmetry-breaking instability at a certain Prandtl number. An axisymmetric unsteady instability mode is observed as well. By nonlinear simulation, the oscillatory flow patterns are obtained, and the axisymmetry-breaking bifurcation of the unsteady toroidal flow is studied.

Transient growth in Taylor-Couette flow of a Bingham fluid.

In this paper we investigate linear transient growth of perturbation energy in Taylor-Couette flow of a Bingham fluid. The effects of yield stress on transient growth and the structure of the optimal perturbation are mainly considered for both the wide-gap case and the narrow-gap case. For this purpose we complement the linear stability of this flow subjected to axisymmetric disturbances, presented by Landry et al. [M. P. Landry, I. A. Frigaard, and D. M. Martinez, J. Fluid Mech. 560, 321 (2006)], with the transient growth characteristics of both axisymmetric and nonaxisymmetric perturbations. We obtain the variations of the relative amplitude of optimal perturbation with yield stress, analyze the roles played by the Coriolis force and the additional stress in the evolution of meridional perturbations for the axisymmetric modes, and give the explanations for the possible change of the optimal azimuthal mode (featured by the maximum optimal energy growth G(opt)) with yield stress. These results might help us in the understanding of the effect of fluid rheology on transient growth mechanism in vortex flows.

Rayleigh-Bénard convection in a vertical annular container near the convection threshold.

The instabilities and transitions of flow in an annular container with a heated bottom, a cooled top, and insulated sidewalls are studied numerically. The instabilities of the static diffusive state and of axisymmetric flows are investigated by linear stability analysis. The onset of convection is independent of the Prandtl number but determined by the geometry of the annulus, i.e., the aspect ratio Γ (outer radius to height) and radius ratio δ (inner radius to outer radius). The stability curves for onset of convection are presented for 0.001≤δ≤0.8 at six fixed aspect ratios: Γ=1, 1.2, 1.6, 1.75, 2.5, and 3.2. The instability of convective flow (secondary instability), which depends on both the annular geometry and the Prandtl number, is studied for axisymmetric convection. Two pairs of geometric control parameters are chosen to perform the secondary instability analysis-Γ=1.2, δ=0.08 and Γ=1.6, δ=0.2-and the Prandtl number ranges from 0.02 to 6.7. The secondary instability exhibits some similarities to that for convection in a cylinder. A hysteresis stability loop is found for Γ=1.2, δ=0.08 and frequent changes of critical mode with Prandtl number are found for Γ=1.6, δ=0.2. The three-dimensional flows beyond the axisymmetry-breaking bifurcations are obtained by direct numerical simulation for Γ=1.2, δ=0.08.