Tiezheng Qian

Pancake bouncing on superhydrophobic surfaces

Engineering surfaces that promote rapid drop detachment1,2 is of importance to a wide range of applications including anti-icing3–5, dropwise condensation6, and self-cleaning7–9. Here we show how superhydrophobic surfaces patterned with lattices of submillimetre-scale posts decorated with nano-textures can generate a counter-intuitive bouncing regime: drops spread on impact and then leave the surface in a flattened, pancake shape without retracting. This allows for a four-fold reduction in contact time compared to conventional complete rebound1,10–13. We demonstrate that the pancake bouncing results from the rectification of capillary energy stored in the penetrated liquid into upward motion adequate to lift the drop. Moreover, the timescales for lateral drop spreading over the surface and for vertical motion must be comparable. In particular, by designing surfaces with tapered micro/nanotextures which behave as harmonic springs, the timescales become independent of the impact velocity, allowing the occurrence of pancake bouncing and rapid drop detachment over a wide range of impact velocities.

Molecular scale contact line hydrodynamics of immiscible flows.

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy. Our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular-scale vicinity of the contact line. In particular, the behavior at high capillary numbers, leading to the breakup of the fluid-fluid interface, is accurately predicted.

A variational approach to moving contact line hydrodynamics

In immiscible two-phase flows, the contact line denotes the intersection of the fluid-fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial-slip regime, extending to mesoscopic length scales. The sharp (fluid-fluid) interface limit of the hydrodynamic model, together with some general implications of slip versus no slip, are discussed.

Power-Law Slip Profile of the Moving Contact Line in Two-Phase Immiscible Flows

Large-scale molecular dynamics (MD) simulations on two-phase immiscible flows show that, associated with the moving contact line, there is a very large 1/x partial-slip region where x denotes the distance from the contact line. This power-law partial-slip region is verified in large-scale adaptive continuum calculations based on a local, continuum hydrodynamic formulation, which has proved successful in reproducing MD results at the nanoscale. Both MD simulations and numerical solutions of continuum equations indicate the existence of a universal slip profile in the Stokes-flow regime.

Dynamic flow and switching bistability in twisted nematic liquid crystal cells

We investigate the switching bistability based on the interaction between dynamic flow and director rotation in twisted nematic liquid crystal cells. Numerical calculation shows that there exists a general type of bistable twisted director configuration. Two specific cases are verified experimentally.

Moving contact line on chemically patterned surfaces

We simulate the moving contact line in two-dimensional chemically patterned channels using a diffuse-interface model with the generalized Navier boundary condition. The motion of the fluid–fluid interface in confined immiscible two-phase flows is modulated by the chemical pattern on the top and bottom surfaces, leading to a stick–slip behaviour of the contact line. The extra dissipation induced by this oscillatory contact-line motion is significant and increases rapidly with the wettability contrast of the pattern. A critical value of the wettability contrast is identified above which the effect of diffusion becomes important, leading to the interesting behaviour of fluid–fluid interface breaking, with the transport of the non-wetting fluid being assisted and mediated by rapid diffusion through the wetting fluid. Near the critical value, the time-averaged extra dissipation scales as U , the displacement velocity. By decreasing the period of the pattern, we show the solid surface to be characterized by an effective contact angle whose value depends on the material characteristics and composition of the patterned surfaces.

Hydrodynamic slip boundary condition at chemically patterned surfaces: a continuum deduction from molecular dynamics.

We investigate the slip boundary condition for flows past a chemically patterned surface. Molecular dynamics simulations show that fluid forces and stresses vary laterally along the patterned surface. A subtraction scheme is developed to verify the validity of the Navier slip boundary condition, locally, for the patterned surface. A continuum hydrodynamic model is formulated using the Navier-Stokes equation and the Navier boundary condition, with a slip length varying along the patterned surface. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from molecular simulations.

Superconducting characteristics of 4-Å carbon nanotube–zeolite composite

We have fabricated nanocomposites consisting of 4-Å carbon nanotubes embedded in the 0.7-nm pores of aluminophosphate-five (AFI) zeolite that display a superconducting specific heat transition at 15 K. MicroRaman spectra of the samples show strong and spatially uniform radial breathing mode (RBM) signals at 510 cm−1 and 550 cm−1, characteristic of the (4, 2) and (5, 0) nanotubes, respectively. The specific heat transition is suppressed at >2 T, with a temperature dependence characteristic of finite-size effects. Comparison with theory shows the behavior to be consistent with that of a type II BCS superconductor, characterized by a coherence length of 14 ± 2 nm and a magnetic penetration length of 1.5 ± 0.7 μm. Four probe and differential resistance measurements have also indicated a superconducting transition initiating at 15 K, but the magnetoresistance data indicate the superconducting network to be inhomogeneous, with a component being susceptible to magnetic fields below 3 T and other parts capable of withstanding a magnetic field of 5 T or beyond.

Driven cavity flow: From molecular dynamics to continuum hydrodynamics

Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition (NBC) and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the...

The exact solution for the generalized time-dependent harmonic oscillator and its adiabatic limit

Abstract In this paper, we find the exact solution for the generalized time-dependent harmonic oscillator by making use of the Lewis-Riesenfeld theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berrys phase for the oscillator obtained. We proceed to use the exact solution to construct the coherent state and calculate the corresponding classical Hannays angle.