Dip coating in the presence of a substrate-liquid interaction potential

In this work we investigate theoretically the Landau-Levich problem of dip coating in the presence of a strong interaction potential normal to the substrate. This study is motivated by dip coating at very low capillary numbers when the deposited film thickness is less than 1 µm and such interaction forces become important. The objective of this work is to demonstrate that in the presence of an extra body force the solution procedure differs significantly from the classical one and leads to substantial deviations from the Landau-Levich law for the entrained film thickness. In particular, attractive potentials produce film thickening and the resulting film thickness is independent of speed to lowest order. Repulsive potentials bring about more complicated behavior and lead either to films whose thickness is also independent of speed, or to a modification of the leading order constant in the classical Ca^(2/3) law. Demonstration of these effects is given for a model potential. The analysis is generally applicable to many physical situations when there is an interaction between a coating liquid and a substrate, e.g., dip coating of ferromagnetic liquids on magnetic substrates, or dip coating of liquids carrying charges

Surfactant effects in the Landau–Levich problem

In this work we study the classical Landau–Levich problem of dip-coating. While in the clean interface case and in the limit of low capillary numbers it admits an asymptotic solution, its full study has not been conducted. With the help of an efficient numerical algorithm, based on a boundary-integral formulation and the appropriate set of interfacial and inflow boundary conditions, we first study the film thickness behaviour for a clean interface problem. Next, the same algorithm allows us to investigate the response of this system to the presence of soluble surface active matter, which leads to clarification of its role in the flow dynamics. The main conclusion is that pure hydrodynamical modelling of surfactant effects predicts film thinning and therefore is not sufficient to explain the film thickening observed in many experiments

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses (as accounted by the conventional interfacial boundary conditions) lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law

Thermocapillary flows and their stability: Effects of surface layers and combination

The theoretical analysis of the fluid mechanics and heat transfer of motions driven by surface tension gradients (Marangoni convection) was researched. Convection accompanying the process of growing high quality single crystals from the melt in a micro-g environment was examined. The geometries considered include two dimensional liquid filled slots and axisymmetric float-zone configurations

Thermocapillary flows and their stability: Effects of surface layers and contamination

The fluid mechanics and heat transfer of motions driven by surface tension gradients (Marangoni convection) were analyzed theoretically to obtain an understanding of the convection accompanying the process of growing high quality single crystals from the melt in a mu-g environment. The geometries considered include two dimensional liquid filled slots and axisymmetric float zone configurations

Problems in Microgravity Fluid Mechanics: G-Jitter Convection

This is the final report on our NASA grant, Problems in Microgravity Fluid Mechanics NAG3-2513: 12/14/2000 - 11/30/2003, extended through 11/30/2004. This grant was made to Stanford University and then transferred to the University of California at Santa Barbara when the PI relocated there in January 2001. Our main activity has been to conduct both experimental and theoretical studies of instabilities in fluids that are relevant to the microgravity environment, i.e. those that do not involve the action of buoyancy due to a steady gravitational field. Full details of the work accomplished under this grant are given below. Our work has focused on: (i) Theoretical and computational studies of the effect of g-jitter on instabilities of convective states where the convection is driven by forces other than buoyancy (ii) Experimental studies of instabilities during displacements of miscible fluid pairs in tubes, with a focus on the degree to which these mimic those found in immiscible fluids. (iii) Theoretical and experimental studies of the effect of time dependent electrohydrodynamic forces on chaotic advection in drops immersed in a second dielectric liquid. Our objectives are to acquire insight and understanding into microgravity fluid mechanics problems that bear on either fundamental issues or applications in fluid physics. We are interested in the response of fluids to either a fluctuating acceleration environment or to forces other than gravity that cause fluid mixing and convection. We have been active in several general areas

Moisture Content and Migration Dynamics in Unsaturated Porous Media

Fundamental studies of fluid mechanics and transport in partially saturated soils are presented. Solution of transient diffusion problems in support of the development of probes for the in-situ measurement of moisture content is given. Numerical and analytical methods are used to study the fundamental problem of meniscus and saturation front propagation in geometric models of porous media

Confinement induced instability of thin elastic film

A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical peel geometry, undulations appear along the contact line below a critical film thickness or below a critical curvature of the plate. Perturbation analysis of the stress equilibrium equations shows that for a critically confined film the total excess energy indeed attains a minima for a finite amplitude of the perturbations which grow with further increase in the confinement.Comment: 11 pages, 6 figure

Stability of time-modulated electroosmotic flow

We present a linear stability analysis of parallel electroosmotic flow in a slot geometry. A spatially uniform time harmonic electric field is applied to a dilute electrolyte solution contained between two infinite parallel plates. The base state ion concentrations and electric potential are determined using the Poisson–Boltzmann equation in the Debye–Hückel approximation. The base velocity field is found to be time harmonic and parallel. It is shown that the original system can be replaced by an equivalent one consisting of an electrically neutral fluid enclosed between oscillating parallel plates, whose speed and frequency of oscillation depend on the modulated electric field. Further, the system of linearized disturbance equations can be decoupled into two stability problems: The first, called the electrokinetic problem, describes the evolution of disturbance ion concentrations and electric potential and is independent of the disturbance velocity components. The second, called the Stokes layer problem describes an oscillatory Stokes layer forced by an electrical body force. The stability of each system is determined by Floquet analysis of a dynamical system obtained from a truncated Galerkin expansion of the perturbation quantities. Our calculations show the system to be linearly stable over a wide range of parameters, with damping rates that become quite small for certain combinations of Stokes and Reynolds numbers. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69805/2/PHFLE6-16-7-2349-1.pd

Migration of droplets driven by thermocapillary effects

Se estudia el desplazamiento de gotas, en dos dimensiones y bajo condiciones de mojabilidad parcial, ubicadas sobre un sustrato calentado en forma no uniforme. Se resuelve la ecuación que gobierna el perfil de altura de la gota, bajo las hipótesis de lubricación. El modelado incluye el efecto de la mojabilidad parcial (ángulo de contacto no nulo) mediante un termino que representa las fuerzas intermoleculares entre el sustrato y el líquido. En vez de asumir una forma fija para la forma de la gota, como en trabajos previos, aquí se resuelve la evolución temporal del perfil de altura. Hemos identificado dos regímenes de flujo y una zona de transición.We study the thermocapillary migration of two dimensional droplets of partially wetting liquids on a nonuniform heated substrate. An equation for the thickness profile of the droplet is solved under the hypothesis of the lubrication theory. The model includes the effect of a non-zero contact angle introduced through a disjoiningconjoining pressure term. Instead of assuming a fixed shape for the droplet, as in previous works, here we allow the droplet to change its profile with time. We identify and describe two different regimes and a transition zone.Fil: Gomba, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Instituto de Física Arroyo Seco; ArgentinaFil: Homsy, G. M.. University of California; Estados Unido