Pattern competition in temporally modulated Rayleigh-Bénard convection

Momentum transport of morphological instability in fluid displacement with changes in viscosity

Saffman-Taylor instability exhibits a stepwise unstable morphology from a stable interface to viscous fingering, eventually leading to tip splitting. The nonlinear dynamics of the destabilized interface depends on various flow properties. However, the physicochemical mechanism that determines the transition point of the flow state is unclear. We studied the interfacial instability transition in miscible displacement from a thermodynamic perspective by calculating the momentum transport and entropy production. Using numerical analysis based on Darcy's law coupled with the convection-diffusion equation, the observed flux-dependent flow state transitions were attributed to the selection of the flow state with a higher entropy production.

Viscoelastic Thermovibrational Flow Driven by Sinusoidal and Pulse (Square) Waves

The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.

Thermodynamic Analysis of Bistability in Rayleigh-Bénard Convection

Bistability is often encountered in association with dissipative systems far from equilibrium, such as biological, physical, and chemical phenomena. There have been various attempts to theoretically analyze the bistabilities of dissipative systems. However, there is no universal theoretical approach to determine the development of a bistable system far from equilibrium. This study shows that thermodynamic analysis based on entropy production can be used to predict the transition point in the bistable region during Rayleigh–Bénard convection using the experimental relationship between the thermodynamic flux and driving force. The bistable region is characterized by two distinct features: the flux of the second state is higher than that of the first state, and the entropy production of the second state is lower than that of the first state. This thermodynamic interpretation provides new insights that can be used to predict bistable behaviors in various dissipative systems.

Confinement induced splay-to-bend transition of colloidal rods

We study the nematic phase of rodlike f d-virus particles confined to channels with wedge-structured walls. Using laser scanning confocal microscopy we observe a splay-to-bend transition at the single particle level as a function of the wedge opening angle. Lattice Boltzmann simulations reveal the underlying origin of the transition and its dependence on nematic elasticity and wedge geometry. Our combined work provides a simple method to estimate the splay-to-bend elasticity ratios of the virus and offers a way to control the position of defects through the confining boundary conditions.

Dynamics of traveling waves under spatiotemporal forcing

We study dynamics of traveling waves under spatiotemporal forcing in nonequilibrium systems. Based on the model equations where phase separation and chemical reactions take place simultaneously so that traveling waves are formed in a self-organized manner, we apply a space-time dependent external force. Entrainment and modulation of traveling waves are investigated numerically in one dimension. We develop a theoretical analysis to understand the dynamics obtained.

Influence of excitation wave forms and frequencies on the fundamental time symmetry of the system dynamics, studied in nematic electroconvection

The dynamics of periodically driven nematic electroconvection, a classical dissipative pattern forming system, is studied experimentally and theoretically. We demonstrate that for certain excitation wave forms, the system's dynamic response can be periodic with the excitation or subharmonic, depending on the periodicity of the excitation as control parameter, while for some classes of wave forms, a subharmonic response seems to be principally excluded. In particular, we describe influences of frequency and time symmetry of triangular excitation wave forms. Two intrinsically different routes for the transition to subharmonic dynamics are observed. The time characteristics of the system variables are determined by numerical solution of appropriate model equations and a Floquet analysis. Experimental data are compared to calculations of the model system of two coupled linear differential equations. Results of experiment and model are in excellent agreement.

Pattern formation induced by nonequilibrium global alternation of dynamics

We recently proposed a mechanism for pattern formation based on the alternation of two dynamics, neither of which exhibits patterns. Here we analyze the mechanism in detail, showing by means of numerical simulations and theoretical calculations how the nonequilibrium process of switching between dynamics, either randomly or periodically, may induce both stationary and oscillatory spatial structures. Our theoretical analysis by means of mode amplitude equations shows that all features of the model can be understood in terms of the nonlinear interactions of a small number of Fourier modes.

Traveling concentric-roll patterns in Rayleigh-Bénard convection with modulated rotation

We present experimental results for pattern formation in Rayleigh-Bénard convection with modulated rotation about a vertical axis. The dimensionless rotation rate Omega was varied as Omega(m)=Omega[1+delta cos(phi Omega t)] (time is scaled by the vertical viscous diffusion time of the cell). We used a cylindrical cell of aspect ratio (radius/height) Gamma=11.8 and varied Omega, delta, phi, and epsilon identical with R/R(c)(Omega)-1 (R is the Rayleigh number). The fluid was water with a Prandtl number of 4.5. Sufficiently far above onset even a small delta greater than approximately 0.02 stabilized a concentric-roll (target) pattern. Multiarmed spirals were observed close to onset. The rolls of the target patterns traveled radially inward independent of the sense of rotation. The radial speed v was nearly independent of epsilon for fixed Omega, delta, and phi. However, v increased with any one of Omega, delta, and phi when all the other parameters were held fixed.

Stationary and oscillatory spatial patterns induced by global periodic switching

We propose a new mechanism for pattern formation based on the global alternation of two dynamics, neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state associated with that dynamics. However, when the two dynamics are globally alternated sufficiently rapidly, the system exhibits stationary spatial patterns. Somewhat slower switching leads to oscillatory patterns. We support our findings by numerical simulations and discuss the results in terms of the symmetries of the system and the ratio of two relevant characteristic times, the switching period and the relaxation time to a homogeneous state in each separate dynamics.

Envelope Equations Near the Onset of a Hexagonal Pattern

We present the amplitude equation including slow spatial modulations for the hexagonal patterns observed near the onset of the Bénard instability in the presence of non-Boussinesq effects. In contrast to the onset of convection in Boussinesq approximation for rigid-rigid boundary conditions, we do not find a generalized thermodynamic potential. The same conclusion is found to hold for surface tension driven Marangoni convection and for temporally modulated convection. We also point out the applicability of our approach to other systems such as the Rosenzweig instability in ferrofluids as well as to the baroclinic instability and to the buckling of plates and shells, for which an envelope equation, which is second order in time, results.