Omar K. Matar

Electrically induced pattern formation in thin leaky dielectric films

The stability of the interface between two thin leaky dielectric liquid layers bounded between two flat electrodes is considered. A coupled system of evolution equations is derived for the interfacial location and charge density using lubrication theory. This system is parametrized by the dielectric constants of the two fluids in addition to ratios of their conductivities, viscosities, and thicknesses. A linear stability analysis is conducted and the behavior of the system in the nonlinear regime is also examined. The system is destabilized by electrical stresses that are resisted by capillarity and modified by viscous dissipation. Our results suggest that decreasing the thickness ratio is destabilizing, giving rise to periodic structures of decreasing wavelength. Decreasing the viscosity ratio was also found to lead to the formation of sharp-edged structures whose vertical extent is virtually equal to the gap width between the electrodes. Similar structures were also determined upon increasing the ratio ...

The spreading of surfactant solutions on thin liquid films

The spreading of a surfactant solution on a water film at first glance seems a trivial problem. However, in the last 30 years or so this has been shown to be anything like the case. There have been numerous studies which show that Marongoni driven fingering of the spreading surfactant front exists. In this paper this work has been reviewed and an attempt has been made to rationalise the results. The paper concludes with some recent observations of ours concerning the spreading of sodium dodecyl sulfate over relatively thick water films, 200 microm or less.

Pinchoff and satellite formation in surfactant covered viscous threads

The breakup of viscous liquid threads covered with insoluble surfactant is investigated here; partial differential equations governing the spatio-temporal evolution of the interface and surfactant concentrations are derived in the long wavelength approximation. These one-dimensional equations are solved numerically for various values of initial surfactant concentration, surfactant activity and the Schmidt number (a measure of the importance of momentum, i.e., kinematic viscosity, to surfactant diffusion). The presence of surfactant at the air–liquid interface gives rise to surface tension gradients and, in turn, to Marangoni stresses, that drastically affect the transient dynamics leading to jet breakup and satellite formation. Specifically, the size of the satellite formed during breakup decreases with increasing initial surfactant concentration and surfactant activity. The usual self-similar breakup dynamics found in the vicinity of the pinchoff location for jets without surfactant [Eggers, Phys. Rev. L...

Models for Marangoni drying

Marangoni drying is a new ultra-clean drying process, which relies on surface-tension gradient forces, so-called Marangoni stresses. This method is of particular use in the semiconductor industry wherein obtaining ultra-clean surfaces is of paramount importance. The present work provides a mathematical description of this novel process involving four coupled partial differential equations, derived in the thin-layer approximation, for the film thickness, the concentration of chemicals in the air, at the air–liquid interface and in the bulk of the liquid film. Numerical solution of these equations yields prediction of typical profiles that accompany the spreading and drying processes. Particular attention is aimed at the prediction of the minimum film thickness as a function of system parameters with a view to optimizing the drying process.

Linear stability analysis and numerical simulation of miscible two-layer channel flow

The stability of miscible two-fluid flow in a horizontal channel is examined. The flow dynamics are governed by the continuity and Navier–Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity. Our analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence in agreement with previous work. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion.

Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid

The linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. A pair of coupled Orr-Sommerfeld eigenvalue equations are derived and solved using an efficient spectral collocation method for cases in which unyielded regions are absent. An asymptotic analysis is also carried out in the long-wave limit, the results of which are in excellent agreement with the numerical predictions. Our analytical and numerical results indicate that increasing the dimensionless yield stress, prior to the formation of unyielded plugs below the interface, is destabilizing. Increasing the shear-thinning tendency of the lower fluid is stabilizing.

Fluoro- vs hydrocarbon surfactants: why do they differ in wetting performance?

Fluorosurfactants are the most effective compounds to lower the surface tension of aqueous solutions, but their wetting properties as related to low energy hydrocarbon solids are inferior to hydrocarbon trisiloxane surfactants, although the latter demonstrate higher surface tension in aqueous solutions. To explain this inconsistency available data on the adsorption of fluorosurfactants on liquid/vapour, solid/liquid and solid/vapour interfaces are discussed in comparison to those of hydrocarbon surfactants. The low free energy of adsorption of fluorosurfactants on hydrocarbon solid/water interface should be of a substantial importance for their wetting properties.

Self-excited hydrothermal waves in evaporating sessile drops

Pattern formation driven by the spontaneous evaporation of sessile drops of methanol, ethanol, and FC-72 using infrared thermography is observed and, in certain cases, interpreted in terms of hydrothermal waves. Both methanol and ethanol drops exhibit thermal wave trains, whose wave number depends strongly on the liquid volatililty and substrate thermal conductivity. The FC-72 drops develop cellular structures whose size is proportional to the local thickness. Prior to this work, hydrothermal waves have been observed in the absence of evaporation in shallow liquid layers subjected to an imposed temperature gradient. In contrast, here both the temperature gradients and the drop thickness vary spatially and temporally and are a natural consequence of the evaporation process.

On surfactant-enhanced spreading and superspreading of liquid drops on solid surfaces

07.1.14 KB. Ok to add published version to spiral, 12 months embargo has elapsed. CUP policy

On viscous beads flowing down a vertical fibre

The vertical flow of a fluid, under the influence of gravity, down the exterior of a rigid fibre is a flow accompanied by rich dynamics manifested via the formation of droplets, or beads, driven by a Rayleigh mechanism modulated by the presence of gravity. These droplets propagate down the fibre and undergo coalescence with preceding droplets. Different flow regimes are possible depending on system parameters such as the fibre radius, liquid flow rate and physical properties. We derive an evolution equation for the interface in the long-wavelength approximation, which captures the flow characteristics of the system; this model is similar to those previously used to investigate the dynamics of slender viscous threads in the absence of the fibre. Analytical and numerical solutions of the evolution equation yield information regarding the shape and propagation speeds of the droplets, which is in good agreement with available experimental data as well as those obtained as part of the present work. Connections with models already available in the literature are also established.