Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed. Received 20 August 1998     

Transport and sedimentation of solid particles in Bénard hexagonal cells

The motion of particles moving under gravity in the velocity field of a liquid in a Bénard hexagonal cell is studied experimentally and numerically for Stokes flow conditions. We then explain the settlement of particles in the centers of cells to form a regular quincunx. It is found that sedimentation also occurs preferentially along the lines connecting the centers of adjacent cells to form a triangle deposition tessellation. Finally, it is explained why particles occupy the central part of each convective cell while the peripheral part of the cell quickly becomes limpid. Numerical results are in agreement with the experimental observations of Bénard and those of the present study.     

A study of the spatial and temporal evolution of auto-ignition kernels using time-resolved tomographic OH-LIF

In this paper, the spatial and temporal evolution of auto-ignition kernels from methane jets propagating into a NO_x-vitiated, high-turbulence, hot air co-flow was studied by means of time-resolved tomographic laser-induced fluorescence of OH (Tomo OH-LIF). Measurements were performed using a burst dye laser system at 10 kHz for volumetric laser illumination and a multi-camera arrangement (8-views) for detection of the fluorescence signal. Auto-ignition kernels were detected three-dimensionally and tracked using a robust algorithm based on the intensity gradient of the volumetrically reconstructed signals. The size and location of the detected kernels were evaluated for operating conditions with different Reynolds numbers of the fuel jet. Results showed that auto-ignition randomly occurred with high probability in a well defined fairly axisymmetric radial region with strong fluctuations in the main direction of the flow. The increase of the Reynolds number of the fuel jet resulted in a radial spread of the location of auto-ignition events. The statistical evaluation of the orientation and growth of auto-ignition kernels with respect to the mean flow field showed that the kernels were oriented tangentially to the flow and temporally evolve towards this preferential direction as the ignition events progressed.     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998     

Processes limiting the rate of response in photorefractive composites

The processes limiting the rate of response of highly diffractive, reorientationally enhanced photorefractive polymer composite materials are identified from a series of degenerate four wave mixing and Mach–Zehnder interferometric measurements. In the regime of low intensity writing beams charge generation limits the rate of holographic grating formation, but at higher intensities charge transport or reorientation of dye molecules can restrict the rate of grating formation more strongly. A grating risetime of 540 ms is observed in a composite of high dye content with high reorientational mobility of the dye molecules. In this case it is proposed that the charge carrier mobility of the doped poly(N-vinylcarbazole):2,4,7-trinitro-9-fluorenone (PVK:TNF) matrix is the principal limiting factor in grating response rates.     

Group and phase velocities in the free-surface visco-potential flow: New kind of boundary layer induced instability

Water wave propagation can be attenuated by various physical mechanisms. One of the main sources of wave energy dissipation lies in boundary layers. The present work is entirely devoted to thorough analysis of the dispersion relation of the novel visco-potential formulation. Namely, in this study we relax all assumptions of the weak dependence of the wave frequency on time. As a result, we have to deal with complex integro-differential equations that describe transient behaviour of the phase and group velocities. Using numerical computations, we show several snapshots of these important quantities at different times as functions of the wave number. Good qualitative agreement with previous study [D. Dutykh, Eur. J. Mech. B/Fluids 28 (2009) 430] is obtained. Thus, we validate in some sense approximations made anteriorly. There is an unexpected conclusion of this study. According to our computations, the bottom boundary layer creates disintegrating modes in the group velocity. In the same time, the imaginary part of the phase velocity remains negative for all times. This result can be interpreted as a new kind of instability which is induced by the bottom boundary layer effect.     

Diffusion in fluids with large mean free paths: Non-classical behavior between Knudsen and Fickian limits

Diffusion in fluids is analyzed at non-classical conditions, intermediate between the Knudsen and Fickian limits. The fluid is considered in the framework of the Einstein’s diffusion evolution equation involving expansions of the density distribution in powers of displacement and time. The standard truncation of these expansions results in the classical model of diffusion; however, higher-order terms lead to a departure from classical behavior. This has not been studied or discussed adequately in the literature previously.Here, we present an exact solution of the Einstein’s diffusion evolution equation without truncation of the density expansions. This solution illustrates limitations in the classical truncations and demonstrates non-classical effects due to large mean free paths, λ. In particular, this new solution shows that, at large λ, there are significant quantitative deviations from classical diffusion profiles. In addition, this solution demonstrates a dramatic change in the diffusion mechanism from the state where the molecular motions are predominantly ballistic to one of molecular chaos. This has implications for fundamentals of fluids between the Knudsen and Fickian limits, and for a variety of fields where evolution of a system includes random, multi-scale displacement of particles, such as nanotechnology, vacuum techniques, turbulence, and astrophysics.