Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D9: Instability: Interfacial and Thin-Film II |
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Chair: Demetrios Papageorgiou, Imperial College London Room: 333 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D9.00001: Influence of surfactant concentration on satellite formation from the rupture of viscous liquid filaments Emilia Nowak, Mark Simmons, Richard Craster, Omar Matar Drop formation from the rupture of liquid filaments are critically affected by the presence of liquid soluble surfactants, particularly above the critical micelle concentration (CMC). In this paper, we apply the long wave approximation to elucidate the interfacial topology leading to the formation of droplets and satellites from the rupture of a cylindrical fluid filament. The numerical results are compared with experiments performed using aqueous filaments in a continuous phase of silicone oil, using an aqueous phase soluble surfactant (SLES) over a range of concentrations above and below the CMC. Comparisons are made as a function of the capillary number and viscosity of the continuous phase, focusing on the temporal variation in minimum filament radius, contact angle and the number and size of the droplets formed. Similarities and differences between the experiments and the model are noted. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D9.00002: Surfactant-driven dynamics of immiscible jets under microfluidic confinement Joao Cabral, Junfeng Yang, Omar Matar We examine the dynamics of three water jets in oil (PDMS) under microfluidic confinement in the presence of surfactant (sodium dodecyl sulphate). Our experimental results demonstrate the occurrence of two flow regimes, ``jetting'' and ``dripping,'' depending on the choice of system parameters; the latter are the flow-rates of water and oil, the viscosity ratio, and the surfactant concentration. In the dripping regime, the average diameter of the water droplets decreases with increasing oil flow-rate until a transition to jetting occurs. In the jetting regime, and at high oil and water flow-rates, and high oil viscosity, our results demonstrate that each jet exhibit sinusoidal deformations that appear to be either in- or out-of-phase with those of their neighbours'. Numerical simulations of the system studied experimentally are also carried out using a volume-of-fluid approach, which account for the presence of insoluble surfactant. The results of these simulations capture the trends observed in the experiments. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D9.00003: The influence of evaporation on instabilities of liquid layer with insoluble surfactant Alexander Mikishev, Alexander Nepomnyashchy A horizontally infinite layer of an evaporating incompressible Newtonian liquid with insoluble surfactant on the free deformable surface is studied theoretically. The layer is subjected to a transverse temperature gradient. The evaporation process is described by 2D one-side model based on the assumptions of density, viscosity and thermal conductivity of the gaseous phase being small compared to the same properties of the liquid phase. Surface tension of the liquid-vapor surface linearly depends on temperature and concentration of surfactant. On the basis of experiments we assume that thermal resistance to the evaporation at the interface is a linear function of surfactant concentration. The evaporation mass flux depends on the interface temperature and vapor pressure. Using the long-wave approximation and assumption of slow time evolution the system of nonlinear equations is obtained. The equations retain all relevant physical effects which take place in the system. Linear stability analysis of the base state in the case of non-equilibrium evaporation is performed. The results are compared to those of the non-evaporating case. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D9.00004: The stabilizing mechanism of surfactants in falling films Vasilis Bontozoglou, George Karapetsas We investigate the stabilizing effect of surfactants in gravity-driven liquid films flowing down inclined surfaces. To this end, we consider the Navier-Stokes equations along with advection-diffusion equations and chemical kinetic fluxes for the surfactant transport and derive an analytical solution by expanding in the limit of long-wave disturbances. We present a physical mechanism for the role of a surfactant of arbitrary solubility. The stabilizing effect is due to an interfacial concentration gradient which is in-phase with the interfacial deformation inducing Marangoni stresses driving liquid from the crest to the trough. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation, and leads to the attenuation of Marangoni stresses. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D9.00005: Nonlinear phenomena in two-fluid shear flows in the presence of surfactants Anna Kalogirou, Demetrios Papageorgiou The flow of two superposed fluids in a channel in the presence of an insoluble surfactant is studied. The surfactant is present at the interface in a dilute concentration. Asymptotic analysis in the limit of a thin lower layer is performed and a system of coupled weakly nonlinear evolution equations is derived. The system describes the evolution of the film thickness and the local surfactant concentration. A novel feature is the presence of a nonlocal term due to multiphase coupling. The system of nonlinear evolution equations is solved numerically and the effect of surfactants on the dynamics is investigated. Numerical experiments for zero and for finite Reynolds numbers indicate that the solutions are mostly nonlinear travelling waves of permanent form or time-periodic travelling waves. As the length of the system increases, the dynamics of the system become more complex and include quasi-periodic and chaotic solutions. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D9.00006: Numerical Study of a Hydrodynamic Instability Driven by Evaporation Sergio Hernandez-Zapata, Julio Cesar Ruben Romo-Cruz, Erick Javier Lopez-Sanchez, Gerardo Ruiz-Chavarria The study of hydrodynamic instabilities in liquid layers produced by evaporation has several applications on industry and technology. In this work we study numerically the conditions under which a liquid layer becomes unstable when evaporation in the vapor-liquid interphase is present. The evaporation process follows the Hertz-Knudsen law (the evaporation rate is proportional to the difference between the saturated vapor pressure at the liquid layer temperature and the vapor partial pressure in the environment). Additionally to the usual boundary conditions on solid walls (for example, the non-slip condition for the velocity), we analyze the boundary conditions in the vapor-liquid interphase where the momentum and energy balances have to be taken into account and where the evaporation plays a crucial role. To solve this problem the linear theory of stability is used; that is, a small perturbation around the basic solution is applied (flow at rest and a temperature stationary field). The equations are solved using the Chebyshev pseudo-spectral method. The results are compared with the more usual Rayleigh-B\'{e}nard and Marangoni mechanisms as well as with some experiments carried out by our team. [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D9.00007: Long-wave Marangoni convection in a heated liquid layer with insoluble surfactant Matvey Morozov, Alex Oron, Alexander Nepomnyashchy Recently, long-wave Marangoni convection in a heated binary-liquid layer was considered by Podolny \textit{et al.} (Phys. Fluids \textbf{18}, 054104, 2006) revealing rich dynamics stemming from oscillatory instability. These results were obtained in the absence of surfactants. In the present work we investigate an opposite limit: a liquid layer with insoluble surfactant. We consider a liquid layer lying on a solid horizontal substrate with insoluble surfactant adsorbed at the deformable free surface. Convection is triggered by a given transverse temperature gradient. Long-wave linear stability analysis of the quiescent state of the layer reveals a competition between monotonic and oscillatory modes of instability. We derive nonlinear evolution equations governing the large-scale dynamics of the layer. Linear stability analysis of these equations indicates their applicability only in the case of oscillatory instability. We then carry out weakly nonlinear analysis in the vicinity of the oscillatory-instability threshold for the case of a 2D layer, and study corresponding pattern selection. Finally, we compare the analytical results with the numerical solutions of our nonlinear evolution equations. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D9.00008: Completely Stabilizing the Interface in a Rayleigh-Taylor Problem by Heating Ranga Narayanan, Lewis Johns The interface in a Rayleigh-Taylor problem can be stabilized to perturbations of any wavelength by merely heating. We present a simple formula for estimating the temperature difference required to do this. We assume that the fluid resides in a porous medium so as to simplify the algebraic manipulations and to avoid surface tension gradients. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D9.00009: Nonlinear dynamics of a binary liquid layer heated from above Alexander Nepomnyashchy, Sergey Shklyaev It is well known [Pearson, JFM, 1958] that for the Marangoni convection the critical wavenumber $k_c$ scales as $B^{1/4}$ as the Biot number $B$ characterizing the heat flux from the free surface tends to zero. In a layer of binary mixture [Podolny et al., Phys. Fluids, 2005], for heating from above another longwave mode, with $k_c=O(\sqrt{B})$, is important. In this work we study the nonlinear evolution of the latter mode. It is shown that the amplitude of steady convection is governed by a solvability condition for a certain linear nonhomogeneous problem. This makes possible an analytical study of finite-amplitude regimes of convection, with perturbations of the temperature and solute concentration of order unity. It is shown that up-hexagons and squares are selected on hexagonal and square lattices, respectively. On the superlattice combining both square and hexagonal lattices multistability takes place: at the Marangoni number larger than a certain critical value both squares and up-hexagons are stable. [Preview Abstract] |
Sunday, November 24, 2013 4:12PM - 4:25PM |
D9.00010: Vibration impact on Marangoni instability in a thin film Sergey Shklyaev, Alexey Alabuzhev, Mikhail Khenner We study the influence of a vertical vibration on Marangoni instability in a thin film heated from below. Using a multi-scale expansion the film dynamics is considered in a wide range of the vibration frequency $\omega$: from $\omega t_v\gg 1$ to $\omega t_g=O(1)$, where $t_v$ is the time of viscous relaxation across the layer and $t_g$ is the typical time of the longwave surface dynamics. We have shown that for $\omega t_g \gg 1$ there is no interaction between the Faraday instability and the Marangoni convection because of the large differences in the characteristic time- and length scales (see also [Thiele et al. , JFM (2006)]). Therefore, the averaging technique is applied to derive the equation governing the film dynamics in slow time (in comparison with $1/\omega$). We show that the vibration suppresses the Marangoni instability in a confined cavity; however, the branching remains subcritical. This amplitude equation becomes invalid for the ultra-low frequency, $\omega t_g=O(1)$. In this case the standard amplitude equation [Oron et al., Rev. Mod. Phys. (1997)] is obtained, but with the modulated gravity. The vibration does not change the stability threshold; the subcritical excitation leads to the emergence of a limit cycle instead of a film rupture. [Preview Abstract] |
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