Publications

Inertia-less viscoelastic channel flow displays a supercritical nonnormal mode elastic instability due to finite-size perturbations despite its linear stability. The nonnormal mode instability is determined mainly by a direct transition from laminar to chaotic flow, in contrast to normal mode bifurcation leading to a single fastest-growing mode. At higher velocities, transitions to elastic turbulence and further drag reduction flow regimes occur accompanied by elastic waves in three flow regimes. Here, we demonstrate experimentally that the elastic waves play a key role in amplifying wall-normal vorticity fluctuations by pumping energy, withdrawn from the mean flow, into wall-normal fluctuating vortices. Indeed, the flow resistance and rotational part of the wall-normal vorticity fluctuations depend linearly on the elastic wave energy in three chaotic flow regimes. The higher (lower) the elastic wave intensity, the larger (smaller) the flow resistance and rotational vorticity fluctuations. This mechanism was suggested earlier to explain elastically driven KelvinHelmholtz-like instability in viscoelastic channel flow. The suggested physical mechanism of vorticity amplification by the elastic waves above the elastic instability onset recalls the Landau damping in magnetized relativistic plasma. The latter occurs due to the resonant interaction of electromagnetic waves with fast electrons in the relativistic plasma when the electron velocity approaches light speed. Moreover, the suggested mechanism could be generally relevant to flows exhibiting both transverse waves and vortices, such as Alfven waves interacting with vortices in turbulent magnetized plasma, and TollmienSchlichting waves amplifying vorticity in both Newtonian and elasto-inertial fluids in shear flows.

We report frictional drag reduction and a complete flow relaminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that the intensity of the observed elastic waves and wall-normal vorticity correlate well with the measured drag above the onset of ET. Moreover, we find that the elastic wave frequency grows with the Weissenberg number, and at sufficiently high frequency it causes a decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving the interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and relaminarization phenomena at low Reynolds number.

We shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertialess flows with curved streamlines. Then we describe a theory of elastic turbulence and prediction of elastic waves Re≪1 and Wi ≫ 1, which speed depends on the elastic stress similar to the Alfvén waves in magneto-hydrodynamics and in a contrast to all other, which speed depends on medium elasticity. Since the established and testified mechanism of elastic instability of viscoelastic flows with curvilinear streamlines becomes ineffective at zero curvature, so parallel shear flows are proved linearly stable, similar to Newtonian parallel shear flows. However, the linear stability of parallel shear flows does not imply their global stability. Here we switch to the main subject, namely a recent development in inertialess parallel shear channel flow of polymer solutions. In such flow, we discover an elastically driven instability, elastic turbulence, elastic waves, and drag reduction down to relaminarization that contradict the linear stability prediction. In this regard, we discuss briefly normal versus non-normal bifurcations in such flows, flow resistance, velocity and pressure fluctuations, and coherent structures and spectral properties of a velocity field as a function of Wi at high elasticity number.

Polymer molecules in a flow undergo a coil-stretch phase transition on an increase of the velocity gradients. Model-independent identification and characterization of the transition in a random flow has been lacking so far. Here we suggest to use the entropy of the extension statistics as a proper measure due to strong fluctuations around the transition. We measure experimentally the entropy as a function of the local Weisenberg number and show that it has a maximum, which identifies and quantifies the transition. We compare the new approach with the traditional one based on the theory using either linear Oldroyd-B or nonlinear finite extensible nonlinear elastic polymer models.

Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the classical Ohm's law. The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where the constitutive pressure-speed relation is Stoke's law. Here we report evidence of such vortices observed in a viscous flow of Newtonian fluid in a microfluidic device consisting of a rectangular cavity-analogous to the electronic system. We extend our experimental observations to elliptic cavities of different eccentricities, and validate them by numerically solving bi-harmonic equation obtained for the viscous flow with no-slip boundary conditions. We verify the existence of a predicted threshold at which vortices appear. Strikingly, we find that a two-dimensional theoretical model captures the essential features of three-dimensional Stokes flow in experiments.

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at Re > 1. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatiotemporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with Wi and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e., Wi >> 1 and Re

We report detailed experimental studies of statistical, scaling, and spectral properties of elastic turbulence (ET) in a von Karman swirling flow between rotating and stationary disks of polymer solutions in a wide, from dilute to semidilute entangled, range of polymer concentrations phi. The main message of the investigation is that the variation of phi just weakly modifies statistical, scaling, and spectral properties of ET in a swirling flow. The qualitative difference between dilute and semidilute unentangled versus semidilute entangled polymer solutions is found in the dependence of the critical Weissenberg number Wi(c) of the elastic instability threshold on phi. The control parameter of the problem, the Weissenberg number Wi, is defined as the ratio of the nonlinear elastic stress to dissipation via linear stress relaxation and quantifies the degree of polymer stretching. The power-law scaling of the friction coefficient on Wi/Wi(c) characterizes the ET regime with the exponent independent of phi. The torque Gamma and pressure p power spectra show power-law decays with well-defined exponents, which has values independent of Wi and phi separately at 100

A microfluidic device for production of uniform size capsules with a prescribed membrane thickness is described. It is versatile, novel and suitable for various polymerization reactions. Parameters such as polymerization time and reagent concentrations can be precisely tuned to control the membrane properties. The device features a part which allows to overcome the diffusion barrier by initiating interfacial polymerization via chaotic mixing. It also allows the termination of the reaction and the collection of the resulting capsules. We observe different typical dynamical phenomena occurring in capsules during their flow along the microchannel, namely wrinkling of the membrane, parachute and bullet shapes and bursting of the capsules due to strong hydrodynamical flow. In addition to production, the monitoring of capsule dynamics in flow gave a possibility to estimate the elastic surface modulus E_S and the membrane thickness t. We found that E_S can be as low as 6 × 10⁻³ N m⁻¹ and that the thickness can be below 100 nm. This microfluidic device is therefore capable of producing uniform size capsule solutions with suitable membrane properties for the controlled release of drugs, and as a model system of red blood cells for microhydrodynamics experiments.

Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previous experiments and numerical simulations performed in similar ranges of the Wi and Re numbers, where the forward fork-bifurcation into a steady asymmetric flow due to the broken spatial inversion symmetry was reported. We discuss the plausible discrepancy between our findings and previous studies that could be attributed to the long recirculating cavity, where the length of the recirculating cavity plays a crucial role in the breaking of time translational invariance instead of the spatial inversion. The second transition is manifested via time aperiodic transverse fluctuations of the interface between the dyed and undyed fluid streams at the channel junction and advected downstream by the mean flow. Both instabilities are characterized by fluid discharge-rate and simultaneous imaging of the interface between the dyed and undyed fluid streams in the outflow channel.

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.

We report first experimental observations of dynamics of compound vesicles in linear flow realized in a microfluidic four-roll mill. We show that while a compound vesicle undergoes the same main tank-treading, trembling (TR), and tumbling regimes, its dynamics are far richer and more complex than that of unilamellar vesicles. A new swinging motion of the inner vesicle is found in TR in accord with simulations. The inner and outer vesicles can exist simultaneously in different dynamical regimes and can undergo either synchronized or unsynchronized motions depending on the filling factor. A compound vesicle can be used as a physical model to study white blood cell dynamics in flow similar to a unilamellar vesicle used successfully to model anucleate cells.

A polymer solution partially filling a rotating horizontal drum undergoes an elastically driven instability at low Reynolds numbers. This instability manifests itself through localized plumelike bursts, perturbing the free liquid surface. Here we present an expanded experimental account regarding the dynamics of individual plumes and the statistics pertaining to the complex collective interaction between plumes, which leads to plume coagulation. We also present a detailed description of an optical technique that enables the visualization and measurement of surface perturbations in coating flows within a rotating horizontal drum.

We report the experimental studies on interaction of two vesicles trapped in a microfluidic four-roll mill, where a plane linear flow is realized. We found that the dynamics of a vesicle in tank-treading motion is significantly altered by the presence of another vesicle at separation distances up to 3.2-3.7 times of the vesicle effective radius. This result is supported by measurement of a single vesicle back-reaction on the velocity field. Thus the experiment provides the upper bound for the volume fraction φ=0.08-0.13 of noninteracting vesicle suspensions.

Despite the recent upsurge of theoretical reduced models for vesicle shape dynamics, comparisons with experiments have not been accomplished. We review the implications of some of the recently proposed models for vesicle dynamics, especially the tumbling-trembling domain regions of the phase plane, and show that they all fail to capture the essential behavior of real vesicles for excess areas Δ greater than 0.4. We emphasize new observations of shape harmonics and the role of thermal fluctuations.

Strong non-Oberbeck-Boussinesq (OB) effects in turbulent convection were investigated experimentally in SF₆ in the vicinity of its gas-liquid critical point (CP). The temperature density dependencies of the thermodynamic kinetic properties of SF₆ near its CP at the average critical density lead to strong but symmetric vertical variations of the main physical propertieswhich enter into the control parameters of turbulent convection. This produces an up-down symmetry in the temperature drops across the upper lower half of the cellwhile the temperature in the middle of the cell remains equal to the average value. Thusin spite of the strong variations of the fluid properties across the cell heightthe up-down symmetry remains like in the OB case. The distinctive feature of the symmetric non-OB turbulent convection is that the heat transport scales with the Rayleigh number Ra like in the OB turbulent convection. At the same timeit shows a much stronger dependence on the Prtl number Pr. We singled out the influence of the non-OB effect on the heat transport found thatfor the same Pran eightfold larger non-OB effect does not alter either the value of the Nusselt numberNunor its scaling with respect to the Rayleigh numberNu^∝Ra^γ. The conclusion is that the strong symmetric non-OB effect by itself is not responsible for the strong Pr dependence of the heat transport near CP. The possible source of this Pr dependence is the strongly enhanced isothermal compressibility in the vicinity of CPwhich can affect the dynamics of plumes so the heat transport close to the CP manifests itself in a dependence of Nu on Pr much steeper than in the OB case.

An approach to quantitatively study vesicle dynamics as well as biologically-related micro-objects in a fluid flow, which is based on the combination of a dynamical trap and a control parameter, the ratio of the vorticity to the strain rate, is suggested. The flow is continuously varied between rotational, shearing, and elongational in a microfluidic 4-roll mill device, the dynamical trap, that allows scanning of the entire phase diagram of motions, i.e., tank-treading (TT), tumbling (TU), and trembling (TR), using a single vesicle even at λ = _in/η_out = 1, where η_in and η_out are the viscosities of the inner and outer fluids. This cannot be achieved in pure shear flow, where the transition between TT and either TU or TR is attained only at λ>1. As a result, it is found that the vesicle dynamical states in a general are presented by the phase diagram in a space of only 2 dimensionless control parameters. The findings are in semiquantitative accord with the recent theory made for a quasi-spherical vesicle, although vesicles with large deviations from spherical shape were studied experimentally. The physics of TR is also uncovered.

Injected power P and pressure p fluctuations in a swirling flow of polymer solutions in a wide range of polymer concentrations c in elastic turbulence regime show non-Gaussian statistics that strongly resemble statistical behavior of P and p in hydrodynamic turbulence. Together with this fact, weak dependence of the statistics of rescaled variables on c may suggest that there are universal mechanisms determining the intermittent statistics of P and p. We also show that the study of the statistics of p provides a way to study statistics of the elastic stresses in elastic turbulence otherwise currently unattainable.

We present results on the stretching of single tubular vesicles in an elongation flow toward dumbbell shapes, and on their relaxation. A critical strain rate ̇c exists; for strain rates ̇

We discuss the role of elastic stress in the statistical properties of elastic turbulence, realized by the flow of a polymer solution between two disks. The dynamics of the elastic stress are analogous to those of a small-scale fast dynamo in magnetohydrodynamics, and to those of the turbulent advection of a passive scalar in the Batchelor regime. Both systems are theoretically studied in the literature, and this analogy is exploited to explain the statistical properties, the flow structure, and the scaling observed experimentally. The following features of elastic turbulence are confirmed experimentally and presented in this paper: (i) The rms of the vorticity (and that of velocity gradients) saturates in the bulk of the elastic turbulent flow, leading to the saturation of the elastic stress. (ii) The rms of the velocity gradients (and thus the elastic stress) grows linearly with Wi in the boundary layer, near the driving disk. The rms of the velocity gradients in the boundary layer is one to two orders of magnitude larger than in the bulk. (iii) The PDFs of the injected power at either constant angular speed or torque show skewness and exponential tails, which both indicate intermittent statistical behavior. Also the PDFs of the normalized accelerations, which can be related to the statistics of velocity gradients via the Taylor hypothesis, exhibit well-pronounced exponential tails. (iv) A new length scale, i.e., the thickness of the boundary layer, as measured from the profile of the rms of the velocity gradient, is found to be relevant for the boundary layer of the elastic stresses. The velocity boundary layer just reflects some of the features of the boundary layer of the elastic stresses (rms of the velocity gradients). This measured length scale is much smaller than the vessel size. (v) The scaling of the structure functions of the vorticity, velocity gradients, and injected power is found to be the same as that of a passive scalar advected by an elastic turbulent velocity field.

The longest relaxation times of double- and single-stranded lambda DNA (ds λ-DNA, ss λ-DNA) were studied by viscosity measurements in an oscillatory flow and by stress relaxation measurements. The results for ds λ-DNA agreed well with chain retraction experiments of stretched single molecules; both were close to the relaxation time calculated from the Zimm model. The relaxation time of ss A-DNA is too small to be accurately measured by the stress relaxation experiments even in a very viscous solution. Such a small relaxation time makes it difficult to be studied in experiments of single molecule dynamics. For ds λ-DNA in the intermediate time scale, the stress relaxes in a power law manner toward the long time scale with an exponent of -0.95, which is in good agreement with the Brownian dynamics simulations.

We present experimental results on statistics of polymer orientation angles relative to the shear plane and tumbling times in shear flow with thermal noise. The strong deviation of the probability distribution functions (PDFs) of the orientation angles from Gaussian PDFs was observed in good accord with theory. A universal exponential PDF tail for the tumbling times and its predicted scaling with Wi (that is, the dimensionless shear rate normalized by the polymer relaxation time) are also tested experimentally against numerics. The scaling relations of PDF widths for both angles as a function of Wi are verified and compared with numerics.

By quantitative studies of statistics of polymer stretching in an elastic turbulence and the statistical properties of this random flow itself that are characterized by the average Lyapunov exponents of particle pair separations, (lambda) over bar, we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition. The experimental value of the onset of the coil-stretch transition, (lambda) over bar (cr) . tau = 0.77 +/- 0.20, where tau is the polymer relaxation time, is found to be rather close to the theoretically predicted one.

Chaotic flow was generated in a smooth microchannel of a uniform width at arbitrarily low Reynolds number with a polymer solution. The chaotic flow regime was characterized by randomly fluctuation three-dimensional velocity field and significant growth of the flow resistance. The chaotic flow leads to quite efficient mixing, which is almost diffusion independent. It is observed that for macromolecules, mixing time in this microscopic flow can be three to four orders of magnitude shorter than due to molecular diffusion.

By using high molecular weight fluorescent passive tracers with different diffusion coefficients and by changing the fluid velocity we study the dependence of a characteristic mixing length on the Peclet number, Pe, which controls the mixing efficiency. The mixing length is found to be related to Pe by a power law, L(mix)proportional toPe(0.26+/-0.01), and increases faster than expected for an unbounded chaotic flow. The role of the boundaries in the mixing length abnormal growth is clarified. The experimental findings are in good quantitative agreement with recent theoretical predictions.

The existence of internal viscoelastic waves below the elastic instability threshold in the circular Couette flow of a polymer solution is predicted. We present results of calculations of the dispersion relation of the waves. These weakly attenuating waves are sustained by a non-uniform elastic stress distribution and should occur in the region of stable stratification of the hoop elastic stresses in any viscoelastic fluid flow with curvilinear trajectories.

The synthesis and characterization of ultrahigh-molecular-weight fluorescent partially hydrolyzed polyacrylamide (HPAm) of the type P[Am*]_ξ[Am] ₈₅[AA]_15-ξ, where Am is an acrylamide unit, Am* is a fluorescent-labeled Am unit, and AA is an acrylic acid unit, are reported. The dansyl probe N-(8-aminooctanyl)-5-dimethylamino-1-naphthalene-sulfonamide [DNSNH(CH₂)₈NH₂], sensitive to conformational changes of the polymer, was covalently bound to the HPAm. The fluorescence of the dansyl-labeled polymer and the influence of various external stimuli, such as pH, NaCl and metal ions, are described. The dansyl probe acts as a hydrophobic pendant on the chain of HPAm. and shows a blue-shifted emission in comparison with the unattached dye. suggesting that the dansyl probe may cause a coiling effect toward a more compact structure of the polymer. Fluorescence emission studies reveal significant compaction of the polymer chain for pH in the range 4.7-9.8 and extension for pH below 3.7 or above 11.0. Increased fluorescence intensity. with respect to the fluorescence signal of the free dansyl probe in NaCl, is emitted by the dansyl-labeled polymer. Metal ions, such as Cd(II). Cu(II) and Co(II), modulate the fluorescence emission. Viscosity measurements yield further evidence of structural changes of HPAm, following the attachment of the dansyl probe. Fluorescence imaging of P[Am*]_ξ[Am]₈₅[AA]_15-ξ allows the observation of the dynamic behavior and the kinetics of conformational changes of the labeled polymer. Single polymer visualization is routinely achieved on DNA molecules, however, to our knowledge, nobody has so far extended this technique to synthetic polymers. It is shown by fluorescence microscopy that the dansyl-labeled polymer is stretched by a circular shear flow.

We report experimental studies of parametric excitation of second sound (SS) by first sound (FS) in super-fluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties of the instability, namely, the threshold, its temperature and geometrical dependencies, and the spectra of SS just above the onset were measured. They were found to be in good quantitative agreement with the theory. (ii) It was shown that the mechanism of SS amplitude saturation is due to the nonlinear attenuation of SS via three wave interactions between the SS waves. Strong low-frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with exponentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are discussed with respect to the nonlinear SS behavior. The first evidence of Gaussian statistics of the wave amplitudes for the parametrically generated wave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed several effects. Below the instability threshold, the SS phase conjugation as a result of three wave interactions between the FS and SS waves was observed. Above the threshold two interesting effects were found: a giant amplification of the SS wave intensity and strong resonance oscillations of the SS wave amplitude as a function of the FS amplitude. Qualitative explanations of these effects are suggested.

Mixing in fluids is a rapidly developing area in fluid mechanics, being an important industrial and environmental problem. The mixing of liquids at low Reynolds numbers is usually quite weak in simple flows, and it requires special devices to be efficient. Recently, the problem of mixing was solved analytically for a simple case of random flow, known as the Batchelor regime. Here we demonstrate experimentally that very viscous liquids containing a small amount of high-molecular-weight polymers can be mixed quite efficiently at very low Reynolds numbers, for a simple flow in a curved channel. A polymer concentration of only 0.001% suffices. The presence of the polymers leads to an elastic instability and to irregular flow, with velocity spectra corresponding to the Batchelor regime. Our detailed observations of the mixing in this regime enable us to confirm several important theoretical predictions: the probability distributions of the concentration exhibit exponential tails, moments of the distribution decay exponentially along the flow, and the spatial correlation function of concentration decays logarithmically.

Turbulence is a ubiquitous phenomenon that is not fully understood. It is known that the flow of a simple, newtonian fluid is likely to be turbulent when the Reynolds number is large (typically when the velocity is high, the viscosity is low and the size of the tank is large(1,2)). In contrast, viscoelastic fluids(3) such as solutions of flexible long-chain polymers have nonlinear mechanical properties and therefore may be expected to behave differently. Here we observe experimentally that the flow of a sufficiently elastic polymer solution can become irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales, and we observe an increase in the flow resistance by a factor of about twenty. Although the Reynolds number may be arbitrarily low, the observed flow has all the main features of developed turbulence. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 10(5) (refs 1, 2). The low Reynolds number or 'elastic' turbulence that we observe is accompanied by significant stretching of the polymer molecules, resulting in an increase in the elastic stresses of up to two orders of magnitude.

The interrelation between elastic and inertial effects in destabilizing the flow of a polymer solution is studied experimentally. To achieve this goal, solution elasticity is varied by three orders of magnitude and a diagram of the flow states in a Couette-Taylor system is obtained. The regions of purely elastic and purely inertial flow instabilities and a crossover region between them are characterized. The main feature of the elastic instability, constant Deborah number at the instability threshold, is verified. An analogy between inertial and elastic flow transitions and dynamics is found and the concept of viscoelastic similarity is introduced.

We report the experimental observation of the broadening of the frequency spectra of parametrically generated second sound waves by first sound in superfluid He⁴. The first experimental evidence of Gaussian statistics of amplitudes of parametrically generated waves is presented. Using the kinetic theory of parametric excitation we suggest that the broadening and exponential tails of spectra result from four-wave resonance interaction in a close analogy with similar evidence in parametrically generated spin waves. Universality of the exponential tails in the frequency spectra is suggested.

We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex pair (\u201cdiwhirl\u201d) in Couette flow with highly elastic polymer solutions. In contrast to the usual solitons the diwhirls are stationary. It is also a new object in fluid dynamicsa pair of vortices that build a single entity. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect.

It is shown that the Ginzburg-Landau model corrected for the normal component describes adequately the spin-up problem for the superfluid liquid helium. An analysis of the Eckhaus instability in an inhomogeneous rotationally invariant system is presented. It has been found that the number of vortices which can be nucleated at the threshold of instability scales with the radius of the container as (Formula presented). The effect of excitation of the vortex loops by thermal fluctuations is considered, and the barrier and the nucleation rate are evaluated.

We report experimental evidence that the velocity of a crack, in brittle materials, can be considered as a control parameter which determines several properties of the crack dynamics. Above a critical speed the crack develops an instability associated with a strong sound emission and a strong increase of the surface roughness. Both phenomena seem to be two efficient mechanisms which allow the crack to dissipate energy.

We present experimental results on phase separation of a binary mixture of isobutyric acid and water in a thin horizontal, extended layer at the critical concentration, x_c, and in the vicinity of the consolute temperature, T_c, subjected to a vertical temperature gradient spanning the critical temperature. For relatively small temperature gradients, spinodal decomposition-like patterns are stabilized. A bubble pattern appears for slightly larger temperature gradients, suprisingly always near the hotter boundary, even when T_hot > T_c. For still larger temperature gradients, polygon morphologies are observed. Their boundaries are probably formed by some kind of surface tension driven instability caused by the nonuniform surface tension along the bubble's interface. However, hydrodynamic instabilities alone have not been able to explain the novel morphologies. The average area of the cellular patterns varies strongly with T_c - T_cold and ΔT across the fluid layer, whereas the mean area of the bubble like patterns changes just slightly.

Rayleigh-Bénard convection^1-4, which occurs when a shallow fluid layer is heated from below, is commonly regarded as a paradigm for pattern formation under non-equilibrium conditions. The formation of hexagonal arrays of Bénard cells is well known, but more complex patterns such as targets⁵ and spirals^5-11 have also been reported. Similar patterns have been seen in electrohydrodynamical convection^12,13, oscillatory chemical reactions^14-19 and biological systems ^19,20. In general, the spiral and target states are found for different experimental conditions. Here we report the observation of a continuous transition between states containing many spirals and many targets, in a fluid undergoing Rayleigh-Bénard convection near the gas-liquid critical point. Whether spirals or targets are observed depends on the Prandtl number, the ratio between the thermal and viscous timescales in the fluid. Neither of these states seems to be predicted by the hydrodynamic equations that describe the fluid motions^{1-4, 21}. The fact that the transformation of one pattern into the other is continuous, and that under some conditions they can coexist, suggests that they may be generated by the same or a similar mechanism.

A detailed study of the Couette-Taylor system with axial flow in the range of Reynolds number Re up to 4.5, which is characterized by the propagating Taylor-vortices (PTV's) state, is presented. Two methods to measure the convective instability line are described. Comparative studies of the PTV's in the absolutely and convectively unstable regions are given. It was found that at Re1. The wave-number selection is also found to be different in both regions. As a result, we concluded that the PTV's in the convectively unstable region are noise-sustained structures (NSS's) which were recently considered theoretically and observed in numerical simulations. The selective spatial amplification of an external noise and the characteristic dependence of the healing length on the control parameters and on the aspect ratio confirm our suggestion that the mechanism of NSS generation is a selective spatial amplification of a permanent noise at the inlet. An interaction of the noise with the NSS's leads to a noise modulation of the PTV's velocity.

We present measurements of the critical temperature difference for the onset of thermal convection and the effective thermal conductivity in two³He-superfluid-⁴He mixtures. The mixtures were 6.8% and 9.8% by molar volume of³He in⁴He and the measurements were made from 0.65 K to just above the superfluid transition temperature for each mixture. The measurements were made as part of an effort to visualize convective flow patterns in helium mixtures using optical shadowgraph techniques. We discuss the implications of our results for this effort.

We present direct experimental measurements of the reflection coefficient r and of the group velocity s for traveling-wave convection in a binary fluid. We measure the dependence of r and s on the separation ratio. Theory predicts that, for small enough, r should vary as 1/2. This dependence was not found. Instead, the value of r is almost constant over the range -0.136

Experimental results on the mechanism of transition to defect-mediated turbulence which occurs in a narrow long strip of electroconvecting nematics are presented for the first time. The scenario consists of a secondary bifurcation from stationary convection of normal rolls (Williams domain (WD)) to tilted WD, with spontaneous parity breaking, and then a transition to spatio-temporally disordered state via defect nucléation. The central point of the mechanism presented here is the discovery of fluctuations of a soft longitudinal mode in tilted WD which together with finite transverse modes lead to the defect nucléation.

Couette-Taylor flow between cylinders with a superimposed axial flow is studied experimentally. The axial flow suppresses the basic stationary instability and leads to propagating Taylor vortices through a forward oscillatory bifurcation. While the throughflow velocity increases the propagating vortices are pushed downstream to the outlet so that at the velocity which corresponds to the absolute instability limit, the pattern is «blown» out of the system. The surprising coexistence of steady Ekman and propagating Taylor vortices close to the inlet and outlet boundaries was discovered. The wave number selection mechanism, similar to that existing in the front-propagating case, is also identified.

We report heat transport measurements and optical shadowgraph visualization of rotating Rayleigh-Bénard convection. For dimensionless rotation rates 140, 4300, the initial transition to convection, occurring at a Rayleigh number R much less than the linear-stability value for roll or vortex states, is a forward Hopf bifurcation to an azimuthally asymmetric state with mode number n. States with n=3, 4, 5, 6, and 7 exist at low to moderate R and precess with frequencies that depend on R and. At higher R there is a continuous transition to a state with noisy, time-dependent heat transport, a distinct array of vortices in the central region, and a modulation of the precession speed of the outer structures.

We present an experimental evidence of the existence of a large-scale global circulation flow in nonlinear traveling wave states in convecting binary mixtures. We covered three of the known TW patterns: linear counter-propagating waves (CPW), spatially and temporally modulated TW and spatially modulated TW. We found that the linear CPW that occur in transient regime do not carry mass while both nonlinear states do, and the mass-transport onset coincides with the transition to nonlinear TW. Using a photochromic technique we were able to show that in the spatially modulated TW state two types of particle trajectories exist: closed one which corresponds to mass transport with TW, and open one which represents mass transfer on average backwards. Good agreement with a simple model for the particle trajectories in TW was found. In spatially and temporally modulated TW state irregular behavior in mass transport probably indicates an existence of chaotic trajectories.

A novel time-dependent state in the form of traveling waves in electrohydrodynamic convection in a thin (15 m) cell of very large aspect ratio is experimentally studied. The transition leading to uniform waves is a continuous one bifurcating directly from the homogeneous state. The onset of spatiotemporal turbulence in this 2D system is characterized by the appearance of topological defects. The number of defects increases with the control parameter, and their statistical distribution is in very good quantitative agreement with a theoretical curve recently derived for "topological turbulence."

We investigate the transition from weakly nonlinear to nonlinear traveling-wave states. Pattern selection due to a transition from convective to absolute instability conditions is found, in good agreement with theory. While the linear properties depend on the (boundary-dependent) threshold of convection, the weakly nonlinear properties refer back to the threshold of an infinite system.

We present an experimental observation of convective transport in oscillatory convection of a binary mixture. The results show the existence of mass transfer in the direction of propagation of nonlinear traveling waves (TW) as well as that of a backflow. Good agreement with a simple model for particle trajectories in TW was found. We found that the two previously observed oscillatory states differ in mass transfer. In linear counterpropagating waves no mass transfer is detected, and the mass-transport onset coincides with the transition to nonlinear TW.

A novel localized structure of traveling waves (TWs) was observed at convection onset in ethanol-water mixtures. It is one of various possible flow patterns of TWs which were observed. We find that for almost-one-dimensional cell geometry unique dynamics of transient behavior (in the form of two counterpropagating TWs) can lead to various stable states.

The phase diagram of an externally modulated Rayleigh-Bénard system of binary mixtures near the codimension-two (CT) point is analyzed. The amplitude equation associated with this system is considered and the dynamical behavior is obtained by numerical integration of the equations of motion. We find that close to the CT point the system exhibits chaotic behavior, which in some region of the phase diagram coexists with the conductive state. It is suggested that these features may be observed experimentally even for small amplitude of the modulation as compared with the critical temperature difference Tc of the unmodulated system.

Digitally processed shadowgraph images revealed time-dependent flow patterns slightly above the convective onset in a cylindrical cell of aspect ratio LD2d=15.0 (D is diameter, d is height). This time dependence was monitored for up to 200 horizontal thermal diffusion times. At larger Rayleigh numbers, the system reached time-dependent states after much shorter transients.

We derive an amplitude equation for the convective instability of a binary fluid mixture in a porous medium near the nonequilibrium analog of a tricritical point. We find that the prefactor of the quintic term in this equation is always stabilizing in the vicinity of the "tricritical" point. Therefore, it seems posible to observe experimentally (e.g., via measurement of the Nusselt number) the crossover from classical-mean-field to tricritical behavior.