Ordering of small particles in one-dimensional coherent structures by time-periodic flows.

Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional dynamic coherent structures. This effect may take place for particles so small that often they would be expected to behave as passive tracers and be used in PIV measurement technique. We link the particle tendency to form one-dimensional structures to the nonlinear phenomenon of phase locking. We propose that this general mechanism is, in particular, responsible for the enigmatic formation of the "particle accumulation structures" discovered experimentally in thermocapillary flows more than a decade ago and unexplained until now.

New flow regimes generated by mode coupling in buoyant-thermocapillary convection.

We report on a new nonlinear dynamics occurring in a confined cylindrical column filled with fluid (liquid bridge) and heated from above. We demonstrate and analyze the novel oscillatory flow state created by the interaction of two hydrothermal waves of different origins: one propagates vertically from the cold towards the hot side (m=0) and another is traveling in the azimuthal direction (m=1). Their interaction leads to an exotic flow structure: during a part of the oscillation period the resulting wave propagates in a given azimuthal direction, whereas during the rest of the period it moves in the opposite direction. A new bimodal flow regime is found to exist over a parameter range where these modes have comparable influence. The phase diagrams, obtained by three-dimensional nonlinear simulations, are reported. They shed light on the instability mechanism and criteria of the existence of novel states.

Impact of conditions at start-up on thermovibrational convective flow.

The development of thermovibrational convection in a cubic cell filled with high Prandtl number liquid (isopropanol) is studied. Direct nonlinear simulations are performed by solving three-dimensional Navier-Stokes equations in the Boussinesq approximation. The cell is subjected to high frequency periodic oscillations perpendicular to the applied temperature gradient under zero gravity. Two types of vibrations are imposed: either as a sine or cosine function of time. It is shown that the initial vibrational phase plays a significant role in the transient behavior of thermovibrational convective flow. Such knowledge is important to interpret correctly short-duration experimental results performed in microgravity, among which the most accessible are drop towers ( approximately 5s) and parabolic flights ( approximately 20s) . It is obtained that under sine vibrations, the flow reaches steady state within less than one thermal time. Under cosine acceleration, this time is 2 times longer. For cosine excitations, the Nusselt number is approximately 10 times smaller in comparison with the sine case. Besides, in the case of cosine, the Nusselt number oscillates with double frequency. However, at the steady state, time-averaged and oscillatory characteristics of the flow are independent of the vibrational start-up. The only feature that always differs the two cases is the phase difference between the velocity, temperature, and accelerations. We have found that due to nonlinear response of the system to the imposed vibrations, the phase shift between velocity and temperature is never equal exactly to pi2 , at least in weightlessness. Thus, heat transport always exists from the beginning of vibrations, although it might be weak.

Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment.

We report experimental evidence of convection caused by translational vibration of nonuniformly heated fluid in low gravity. The theory of vibrational convection in weightlessness is well developed but direct experimental proof has been missing. An innovative point of the experiment is the observation of a temperature field in the front and side views of the cubic cell. In addition, particle tracing is employed. The evolution of this field is studied systematically in a wide range of frequencies and amplitudes. The flow structures reported in previous numerical studies are confirmed. The transition from four-vortex flow to the pattern with three vortices is observed in the transient state.

Onset of convection in Soret-driven instability.

It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. The most obvious case is the isothermal Rayleigh-Taylor instability when a heavy fluid is placed on top of a light one. In the nonisothermal case, while heating from above, the density stratification is stable in a pure liquid. However, unstable density stratification might be established in a binary mixture with a negative Soret effect in the case of heating from above: the heavier liquid is accumulated on the top of the lighter one. Due to the large differences between viscous, thermal, and diffusion times the system has a tendency to fingering buoyant instabilities. At some moment the flow may be initiated. Near the onset of convection the flow pattern has a columnar convective structure: for a relatively low applied temperature difference Delta T the lighter and colder liquid is drawn up in the central part of the cell and the heavier liquid flows down along the walls. For finite size systems the situation is reversed at higher Delta T. Here we present results of three-dimensional direct numerical simulations of heat and mass transfer in a system with a negative Soret effect. While the development of Soret-induced convection is similar for a wide class of liquids: water based mixtures, colloidal, and polymer solutions, the parameters of the chosen system correspond to a realistic binary mixture of water (90%) and isopropanol (10%) enabling comparison of theoretical predictions with planned experimental studies.

Multistability of oscillatory thermocapillary convection in a liquid bridge.

A parametric investigation of the onset of chaos in a liquid bridge was numerically carried out for a medium Prandtl number liquid, Pr = 4, and unit aspect ratio under zero-gravity conditions. Spatiotemporal patterns of thermocapillary flow were successively studied beginning from the onset of instability up to the appearance of the nonperiodic flow and further on. Well-tested numerical code is used for solving the three-dimensional time-dependent Navier-Stokes equations in cylindrical coordinate system. Two-dimensional steady flow becomes oscillatory with azimuthal wave number m=2 as a result of Hopf bifurcation at Re(cr)(1)=630. A second independent solution with wave number m=3 was found to appear at Reynolds number Re(cr)(2) approximately 810. Two branches of three-dimensional periodic orbits, traveling waves with m=2 and m=3, coexist for Re>Re(cr)(2). Additional stable branches do not connect them. The different flow organizations reveal different behaviors in the supercritical area. The m=2 traveling wave always remains periodic, but the mode m=3 starts exhibiting chaotic features at Re approximately 4200. The onset of temporal nonperiodicity was shown to be associated with development of broadband noise in spectra and preceded by a quasiperiodicity. The flow stabilizes back to periodic with single frequency when Re exceeds a value Re approximately 5100. The window of periodicity exists up to at least Re=6000, the largest investigated value of the Reynolds number.