Roman O. Grigoriev

Chaotic mixing in thermocapillary-driven microdroplets

Liquid microdroplets represent a convenient system for studies of mixing by chaotic advection in discrete microscopic volumes. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Thorough mixing via chaotic advection requires destruction of all such invariant surfaces. To illustrate this idea, we demonstrate that quick and thorough mixing inside a spherical microdroplet suspended in a layer of substrate fluid can be obtained by moving the droplet along a two-dimensional path using temperature-induced surface tension gradients. The use of flow invariants also provides a convenient way to analyze the mixing properties of flows in many other experimental implementations.

Control of evaporatively driven instabilities of thin liquid films

In the process of drying, thin volatile liquid films often undergo a long-wavelength instability leading to nonuniformities or formation of dry spots, with the strength of the instability increasing with the volatility and temperature of the liquid. Perhaps counterintuitively, this evaporative instability can be actively suppressed by an appropriate heating procedure. We use linear stability analysis of the lubrication approximation to show that spatially nonuniform time-dependent radiative heating can indeed have a stabilizing effect. Evaporation is shown to introduce several fundamentally new aspects into the control problem for heated liquid films, compared to the relatively well-studied case of thermal convection. The control problem becomes especially interesting and nontrivial for mixtures and solutions with negative Marangoni numbers due to a peculiar cancellation effect rendering the system insensitive to temperature control at a certain wavelength. It is shown that taking the time dependence of the mean thickness of the film into account is necessary to circumvent this insensitivity.

Contact line instability and pattern selection in thermally driven liquid films

Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a non-normal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the non-normality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the ev...

Thermocapillary migration of interfacial droplets

We study the thermocapillary driven motion of a droplet suspended at an interface of two fluid layers subjected to an imposed temperature gradient parallel to the interface. We compute the temperature and velocity fields inside and outside of the droplet using a boundary collocation numerical scheme in the limit of small capillary and thermal Peclet numbers and compare the results with the classical problem of thermocapillary migration of a droplet in the bulk. In particular, we find that, for typical values of parameters, interfacial droplets migrate in the direction opposite to the temperature gradient, while in the classical problem migration is always in the direction of the gradient. Furthermore, we find that a rich variety of flow structures can emerge inside interfacial droplets. We also confirm that for parameters matching a recent experimental study of mixing inside interfacial microdroplets [R. O. Grigoriev, V. Sharma, and M. F. Schatz, Lab Chip 6, 1369 (2006)] the interior flow can be approxima...

Experimental study of the effect of noncondensables on buoyancy-thermocapillary convection in a volatile low-viscosity silicone oil

The convective flow in a layer of volatile silicone oil with a kinematic viscosity of 0.65 cSt confined to a sealed cavity with a transverse aspect ratio of 3.2 was visualized using particle pathlines and quantified by particle-image velocimetry at dynamic Bond numbers estimated to be of order unity and laboratory Marangoni numbers as great as 3600. The effect of noncondensables (i.e., air) was studied by comparing convection in the liquid layer below a vapor space at pressures ranging from 4.8 kPa to 101 kPa, corresponding to air molar fractions ranging from 14% to 96%, respectively, and silicone-oil vapor, under otherwise identical conditions. The results for convection at 101 kPa are in qualitative agreement with previous studies, and clarify the time-dependent flow observed at high Marangoni numbers. The results show that decreasing the relative air concentration increases the critical Marangoni numbers for transition between different flow states, even though the air concentration does not appear to ...

Mixing properties of steady flow in thermocapillary driven droplets

We consider mixing via chaotic advection in microdroplets suspended at the free surface of a liquid substrate and driven along a straight line using the thermocapillary effect. With the help of a model derived by Grigoriev [Phys. Fluids 17, 033601 (2005)] we show that the mixing properties of the flow inside the droplet can vary dramatically as a function of the physical properties of the fluids and the imposed temperature profile. Proper characterization of the mixing quality requires introduction of two different metrics. The first metric determines the relative volumes of the domain of chaotic streamlines and the domain of regular streamlines. The second metric describes the time for homogenization inside the chaotic domain. We compute both metrics using perturbation theory in the limit of weak temperature dependence of the surface tension coefficient at the free surface of the substrate.

Velocity profile in a two-layer Kolmogorov-like flow

In this article, we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, which assumes a horizontal flow whose direction is independent of the vertical coordinate, we derive a generalized two-dimensional vorticity equation describing the evolution of the horizontal flow. Also, we derive an expression for the vertical profile of the horizontal velocity field. Measuring the horizontal velocity fields at the electrolyte-air and electrolyte-dielectric interfaces using particle image velocimetry, we validate the theoretical predictions of the horizontal velocity and its vertical profile for steady as well as for freely decaying Kolmogorov-like flows. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow in the electrolyt...

CONVECTION, EVAPORATION, AND CONDENSATION OF SIMPLE AND BINARY FLUIDS IN CONFINED GEOMETRIES

Rayleigh-Benard and Marangoni convection in a layer of a homogeneous fluid with a free surface in the absence of phase change is a classic (and extensively studied) problem of fluid mechanics. Phase change has a major effect on the convection problem. Most notably, significant latent heat generated at the free surface as a result of phase change can dramatically alter the interfacial temperature, and hence, the thermocapillary stresses. Furthermore, differential evaporation in binary fluids can lead to considerable variation in the concentration field, producing solutocapillarity stresses, which can compete with thermocapillarity and buoyancy.This talk describes numerical studies of convection in alcohol and alcohol-water mixtures due to a horizontal temperature gradient in the presence of phase change. We illustrate how the composition of the liquid and the presence of non-condensable gases (e.g., air) can be used to alter the balance of the dominant forces. In particular, by adding or removing air from the test cell, the direction of the flow can be reversed by emphasizing either the thermocapillary or the solutocapillary stresses.© 2012 ASME

Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols.

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.