Ooshida Takeshi

Position control of desiccation cracks by memory effect and Faraday waves.

Pattern formation of desiccation cracks on a layer of a calcium carbonate paste is studied experimentally. This paste is known to exhibit a memory effect, which means that a short-time application of horizontal vibration to the fresh paste predetermines the direction of the cracks that are formed after the paste is dried. While the position of the cracks (as opposed to their direction) is still stochastic in the case of horizontal vibration, the present work reports that their positioning is also controllable, at least to some extent, by applying vertical vibration to the paste and imprinting the pattern of Faraday waves, thus breaking the translational symmetry of the system. The experiments show that the cracks tend to appear in the node zones of the Faraday waves: in the case of stripe-patterned Faraday waves, the cracks are formed twice more frequently in the node zones than in the anti-node zones, presumably due to the localized horizontal motion. As a result of this preference of the cracks to the node zones, the memory of the square lattice pattern of Faraday waves makes the cracks run in the oblique direction differing by 45 degrees from the intuitive lattice direction of the Faraday waves.Graphical abstract

Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number

Waves on a thin liquid layer falling down a solid wall, either vertical or inclined, are studied by means of a reduced equation. This equation is developed by the regularized long-wave expansion method, which is a combination of the Pade approximation and the long-wave expansion. Its numerical solutions are compared with the calculations of the full Navier–Stokes equation, simplified Navier–Stokes equation (the “boundary-layer” equation), and the traditional long-wave equations, as well as with experimental measurements. When the Reynolds number R is as small as unity, the present equation agrees with the Navier–Stokes equation and also with the traditional long-wave equations. For larger values of R, the traditional long-wave equations lose their validity and make a false prediction, while the present equation agrees with the Navier–Stokes equation, as long as the rescaled Reynolds number δ*=R/W1/3 does not exceed unity in the case of vertical films. Unlike the “boundary-layer” equation developed by prev...

Internal Stress in a Model Elastoplastic Fluid

Plastic materials can carry memory of past mechanical treatment in the form of internal stress. We introduce a natural definition of the vorticity of internal stress in a simple two-dimensional model of elastoplastic fluids, which generates the internal stress. We demonstrate how the internal stress is induced under external loading, and how the presence of the internal stress modifies the plastic behavior.

Continuum theory of memory effect in crack patterns of drying pastes.

A possible clarification of memory effect observed in crack patterns of drying pastes [A. Nakahara and Y. Matsuo, J. Phys. Soc. Japan 74, 1362 (2005)] is presented in terms of a macroscopic elastoplastic model of isotropic pastes. We study flows driven by steady gravitational force instead of external oscillation. The model predicts creation of residual tension in favor of cracks perpendicular to the flow direction, thus causing the same type of memory effect as that reported by Nakahara and Matsuo for oscillated CaCO_3 pastes.

Analytical calculation of four-point correlations for a simple model of cages involving numerous particles.

Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.

Formation and propagation of a shock wave due to evaporation processes at imperfect interfaces

Transient motions of a vapor due to evaporation processes from its plane condensed phase at imperfect conditions have been considered numerically based not only on the Boltzmann equation of BGK type but also on the formulation of fluid dynamic level, i.e., the Navier-Stokes equations subject to the boundary conditions appropriate for evaporation and condensation derived earlier from the kinetic theory analysis. The imperfectness of the interface of the condensed phase has been taken into account in terms of an adjustable parameter αc first introduced by Wortberg and his co-workers. The parameter, variously called the condensation coefficient or condensation parameter or evaporation coefficient, may presumably be associated with some kind of imperfectness of the interface but has nothing to do with the condensation coefficient commonly defined at the level of kinetic theory. The results based on both of these systems of equations agree quite well, describing even the process of establishment of the flow field as well as its established state. Some of the results obtained are compared with the experimental results available for Helium II by Furukawa and Murakami. The comparison between the present results and the experimental ones shows that the incorporation of the adjustable parameter seems to work fairly well in some cases but not in other cases. No decisive conclusion can yet be drawn. However, this parameter is simple and may serve to incorporate to some extent ambiguous nature associated with the imperfectness of the interface.Transient motions of a vapor due to evaporation processes from its plane condensed phase at imperfect conditions have been considered numerically based not only on the Boltzmann equation of BGK type but also on the formulation of fluid dynamic level, i.e., the Navier-Stokes equations subject to the boundary conditions appropriate for evaporation and condensation derived earlier from the kinetic theory analysis. The imperfectness of the interface of the condensed phase has been taken into account in terms of an adjustable parameter αc first introduced by Wortberg and his co-workers. The parameter, variously called the condensation coefficient or condensation parameter or evaporation coefficient, may presumably be associated with some kind of imperfectness of the interface but has nothing to do with the condensation coefficient commonly defined at the level of kinetic theory. The results based on both of these systems of equations agree quite well, describing even the process of establishment of the flow fi...

Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise

For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. We verify numerically for the shell-model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.

Transient to steady evaporation and condensation of a vapor between the cylindrical phases—Navier-Stokes and Boltzmann solutions—

Motions of a vapor, transient to steady, due to evaporation and condensation processes occurring at the cylindrical condensed phases have been considered numerically based not only on the Boltzmann equation of BGK type but also on the formulation for phase-change problems at ordinary fluid dynamic level, in other words, the Navier-Stokes equations with the boundary conditions at the interface for evaporation and condensation derived earlier from a general asymptotic analysis of the weakly nonlinear version of the Boltzmann equation of BGK type. The results based on both of these systems of governing equations agree quite well, describing even the early processes of establishment of the flow fields as well as their transient and final states. The production of the waves, shock waves and contact regions, their propagation and interaction with the condensed phases are clearly seen on both systems of equations. From this fact, the usefulness of the fluid dynamic formulation can be recognized and it can be use...

On a small structure in velocity field within a contact region

In a contact region (contact surface in Euler terms) connecting the two uniform regions in a flow field such as caused by the sudden break of a membrane in a shock-tube, there exists a small structure in velocity field, which has been reported earlier by the calculation based on the Boltzmann equation of the BGK type. Probably, the accepted view would be that the velocity within this region is uniform. Here this velocity structure is investigated thoroughly based on not only the Boltzmann equation but also the Navier–Stokes equations. Actually the velocity field has a hump or a pit, the width of which is found to be the same as the thickness of the region. The magnitude of the hump or the pit decreases with time, inversely proportional to the square root of time. At the so-called tailoring condition at which the contact region has so far been thought not to manifest itself, actually it does exist; the velocity structure does not appear of course but the temperature and, hence, the density still have struc...

Flows of a Vapor due to Phase Change Processes at the Condensed Phases with Temperature Fields as their Internal Structures

Transient to steady motions of a vapor caused by the evaporation and condensation processes occurring at the condensed phases placed in parallel have been studied based on the Boltzmann equation of BGK type. As the internal structures of the condensed phases, the temperature fields are taken into account. Because of this, the temperatures of the interfaces become unknown parameters and, therefore, the condition of the continuity of energy flow across the interface has to be imposed simultaneously with the conditions so far used for the cases with no internal structures. This extra condition gives great difficulty in the numerical simulations but this has been surmounted by a simple method developed earlier in our laboratory. The present analysis has also incorporated a certain kind of imperfectness of the interface in the boundary conditions by the introduction of a simple parameter, called the imperfectness parameter here, first proposed by Wortberg and his colleague. The results obtained describe approp...