Session D20: Interfacial/Thin Film Instability II

Influence of Shear Stress Jumps in Self-Assembly and Growth of Nanopillars by Thermocapillary Forces

Recent theoretical and experimental studies have confirmed how thermocapillary forces can spontaneously generate periodic, 3D nanopillar arrays in viscous nanofilms exposed to a very large and uniform transverse thermal gradient [1,2]. These formations are quite sensitive to local growth conditions and exhibit variations in location, in-plane symmetry and growth rates. Here we explore the role of shear stress jumps in localizing and self-assembling pillar arrays for more rapid and regular formations. Finite element simulations and Fourier analysis of growing waveforms are used to quantify trends observed when a molten viscous nanofilm is held adjacent to a cold protrusion with sharp sidewalls. The sidewalls enforce a jump in the lateral thermal gradient along the free surface of the film which triggers formation of nanopillar trains. We investigate their number, height, spacing and growth rate as a function of the magnitude in shear stress jump and initial noise amplitude. We discuss why the characteristic wavenumber closely matches predictions from linear stability theory despite the large amplitude perturbation. \\[4pt] [1] M. Dietzel and S. M. Troian, Phys. Rev. Lett. 103, 074501 (2009); J. Appl. Phys. 108, 074308 (2010) \\[0pt] [2] E. McLeod, Y. Liu, and S. M. Troian, Phys. Rev. Lett. 106, 175501(2011)   

The Electrohydrodynamics of Superimposed Fluids Subjected to Nonuniform Electric Fields

The interaction of electric field with fluid interfaces has been a problem of long-standing interest; however, there is currently a resurgent of interest on the subject because of its potential applications in a host of novel microfluidic processes. A particularly attractive application is the electrolithography, where increasingly small structures can be formed in a polymeric liquid by application of a ``uniform'' electric field on a pair of patterned electrodes that enclose the liquid. Motivated by this and similar examples, here, we study the behavior of the interface separating two leaky dielectric fluids that are confined between two horizontal flat plates and are subjected to a nonuniform (sinusoidal) electric field. We perform Direct Numerical Simulation (DNS) using a front tracking/finite difference scheme and solve the governing electrohydrodynamics equations in the framework of Taylor's leaky dielectric theory. The equilibrium shapes of the interface are determined as a function of the controlling parameters of the problem such as the relative thicknesses of the two fluids.   

Thermocapillary Control of Thin Fluid Sheets

We consider the evolution and rupture dynamics of a thin viscous planar sheet subject to a symmetric initial long-wave disturbances in the thermal and velocity fields. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses, fluid inertia, van der Waals effects, capillarity, and heat transfer to the environment can be significant. From a linear stability analysis, we find that a stable thermal mode couples the velocity and interfacial dynamics. The phase difference between the initial temperature and velocity distributions is a key parameter in determining the time to rupture. Using phase modulation in the initial temperature along with amplitude modulation in the initial velocity allows the potential for control of the rupture patterns along the sheet. Self-similar rupture dynamics in the limit of zero van der Waals forces are also presented.   

Electrosprays generated by a DC electric field

The breakup of an electrified jet in a gas with an axially applied electric field is investigated theoretically. The jet fluid is taken to be a symmetric electrolyte and proper modelling of the cationic and anionic species is used by considering the Nernst-Planck equations in order to find the volume charge density that influences the electric field in the jet. The governing equations are investigated asymptotically in the long wave limit and the one dimensional model is solved numerically as a function of the hydrodynamic, electrical, and electrokinetic parameters. The electric field causes the jet to stretch and thin to a point where ion repulsion forces the jet to undergo Rayleigh fission. We measure the distance at which this point occurs by comparing the jet radius to the distance at which ion repulsion is important.   

Breakup of compound viscous threads with electrostatic and electrokinetic effects

The breakup of electrified viscous compound jets surrounded by a dielectric gas are investigated theoretically. The fluids are considered to be electrolytes and the core fluid viscosity is assumed to be much larger than that of the annular fluid. Axisymmetric configurations are considered with the three fluids bound by a cylindrical electrode that is held at a constant voltage potential. The model equations are investigated asymptotically in the long wave limit, yielding two cases corresponding to a negligible surface charge with electrokinetic effects and a leaky dielectric model. A linear stability analysis for both cases is performed and the electrical effects are found to have a stabilizing effect, which is consistent with previous investigations of single electrified jet breakup at small wave numbers. The one-dimensional equations are also solved numerically. The electric field is found to cause satellite formation in the core fluid, which does not occur in the purely hydrodynamic case, with the satellite size increasing with the strength of the electric field.   

Spreading, retraction, and sustained oscillations of surfactant-laden lenses

We examine the dynamics of surfactant laden-lenses spreading over liquid substrates. We use the lubrication theory in combination with models for the spreading process, the effects of surfactant at the contact line and the sorption kinetics above and below the critical micelle concentration. Our model is solved numerically using a finite-element formulation. We carry out a full parametric study and simulate a wide range interesting behaviour ranging from complete spreading of the lens, to spreading followed by retraction, to sustained pulsating oscillations.   

Convective rolls and hydrothermal waves in evaporating sessile drops

We examine the dynamics of a sessile droplet sitting on a uniformly heated solid, undergoing evaporation. We use a finite element formulation to solve the axisymmetric time-dependent problem and perform a linear stability analysis taking into account 3D perturbations around this base-state. Our numerical results show that the temperature gradients, which are a natural consequence of the evaporation process, give rise to instabilities including the presence of hydrothermal waves in close agreement with previous experimental observation. We discuss the mechanisms which give rise to these instabilities.   

Electrostatically-induced complex dynamics in viscous liquid film flows down the exterior of a cylinder

Annular flows on both the inner and outer walls of cylinders have a significant number of practical applications, from printing to fluid stabilisation to the augmentation of heat and mass transfer. It is important to understand the spatiotemporal dynamics of the interface in order to facilitate the possible control of the flow and efficiency of underlying processes. We investigate the evolution and stability of a viscous fluid layer wetting the surface of a cylinder and surrounded by a conductive gas. The inner cylinder is an electrode kept at constant voltage. A second concentric electrode, whose potential is allowed to vary as a function of both space and time, encloses the system. This induces electrostatic forces at the interface in competition to surface tension and viscous stresses. Asymptotic methods are used to derive several systems governing the interfacial position and charge accumulation. Two canonical sets of equations are derived, one valid for long-wave systems of moderate conductivity (a coupled Craster-Matar type system) and one valid for thin films of high conductivity (a Benney-type system). The resulting systems and their stabilities are investigated both analytically and numerically to compute travelling wave and transient simulations.   

An aerodynamic mechanism for the splashing-up of the ejecta sheet in high-velocity impacts

In this work, the deformation of a 2D liquid jet by aerodynamic stresses has been investigated by numerical simulations with the flow solver Gerris and a dynamic model was proposed to predict the shape of the jet. This is similar to the initial stages of the formation of the corolla upon impact of a drop on a solid. A self-similar behavior is observed in the simulations and the jet profile is in good agreement with the model prediction in exponential of the square root of time.   

Electric field induced instabilities at fluid-fluid interfaces in low conductivity, low frequency and small feature size limit

Electrohydrodynamic instabilities at fluid-fluid interfaces due to an externally applied electric field have become a popular field of research owing to their direct application in the field of lithography. With the advent of miniaturization, it has become critical to find new ways to reduce feature sizes to even smaller dimensions and in a cost-effective way. Researchers have been working on freezing the patterns formed when thin polymer films are subjected to electric fields, which give as low as 100 nm sized structures. Different fluids with lower surface tensions and higher conductivities are being pursued to reduce the dimensions of the pattern further. Simple linear models exist which can predict these dimensions while the final structure can be simulated. The present work addresses three cases where the linear models fail. The first case is when the thin film approximation which is a common assumption in the linear theory, becomes invalid. The second, when the charge relaxation time of the fluid is of the same order as the growth rate of the instability and the third, when the time period of the applied Alternating Current (AC) field is larger than the growth rate. In all these three cases, the regime in which the linear model fails is identified and an alternate linear model or non-linear analysis has been used to predict the observed experimental behavior.