Jill Klentzman

The effect of evaporation on fingering instabilities

We investigate the flow of evaporating thin films of viscous liquid on inclined solid substrates under the influence of gravity. A lubrication-type approach is used to develop a three-dimensional model of the flow including physical effects such as capillarity, gravity, Marangoni stresses, disjoining pressure, and evaporation. Numerical simulations are then carried out based on the model. The effect of evaporation on the so-called fingering instability that develops along the contact line in the transverse direction of the flow is studied. It is found that evaporation acts to suppress the instability if the evaporation number, a nondimensional measure of the mass flow rate across the interface, is above a critical value. The critical value decreases as the inclination angle is decreased. For the values of evaporation number below the critical one, the fingers grow initially but then saturate at a length that depends on the evaporation conditions. It is also shown that thermocapillarity acts to enhance the...

Projection of the solution of the linearized navier-stokes equations in reacting high speed boundary layers onto discrete modes

The problem of multimode decomposition of small perturbations in high-speed boundary layers in chemical nonequilibrium is addressed using the discretized adjoint approach. The solution of the linearized Navier-Stokes equations is considered in the quasi-parallel flow approximation using the normal mode analysis, and the ordinary differential equations for the amplitude functions are discretized using fourth-order finite differences. The discretization leads to a system of linear algebraic equations in the form of the generalized eigenvalue problem. It is straightforward to define the left eigenvectors (eigenvectors of the adjoint problem) and to formulate the biorthogonality condition for the discrete modes. Assuming that there is a complete system of eigenfunctions of the discrete and continuous spectra, the biorthogonality condition allows for the finding of the projection of a solution onto the discrete modes. The biorthogonality condition is also utilized for solving the receptivity problem with perturbations introduced at the wall.

Stability of Boundary Layers in Binary Mixtures of Oxygen and Nitrogen

An inviscid stability analysis of binary mixtures of oxygen and nitrogen in thermal equilibrium is presented. The boundary-layer equations for a chemically reacting gas are solved using second-order finite differences in the streamwise and wall normal directions. The linearized stability equations in the inviscid limit are solved using the fourth-order Runge-Kutta method with a constant step size. Examples of flows with an equilibrium state at the boundary layer edge and considering either an adiabatic, non-catalytic wall or a cold wall are reported for free stream conditions corresponding to Mach number 5. In the considered examples, the real gas effects have a stabilizing effect on the first mode and destabilizing effect on the second mode.

Stability and receptivity of high speed boundary layers in oxygen

The stability and receptivity of high speed boundary layers in binary mixtures of oxygen are investigated including chemical non-equilibrium effects. The analysis is conducted for two-dimensional perturbations for both an inviscid and a viscous model and the results are compared to examine the impact of viscous effects. It is found that the viscosity effects stabilize the flow, and the main impact on temperature and mass fraction perturbations occurs in the viscous sublayer and in the critical layer. The biorthogonal eigenfunction system is used to study the receptivity of the boundary layers including real gas effects. The results demonstrate that the receptivity coefficients have two maxima associated with the branching points in the discrete spectrum. The maxima become stronger when the wall temperature is low.

Mathematical modeling of moving contact lines in heat transfer applications

We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.

Laser-Induced Melting and Phase Explosion in Liquid Metal Films

We develop a mathematical model of liquid flow and phase change phenomena during fabrication of micro- and nanochannels by laser-induced melting and evaporation of thin metal films deposited on glass substrates. Channels of cross-sectional sizes between several hundred nanometers and a few micrometers can be manufactured by wet etching or contact photolithography after the desired pattern is created by the laser in the metal film. Interaction of the laser beam with the metal film is a complicated process, characterized by high temperature gradients. In this work we investigate the regime where phase explosion takes place in a small region of the metal film surrounded by a pool of molten metal. In the melt region, both evaporation from the surface and viscous flow induced by thermocapillary stresses take place; all these processes are incorporated into the model. Evolution of the surface of the molten film is investigated, and the impact of phase explosion on the flow is discussed.© 2008 ASME