9706847 Sussman This research concerns the analysis and development of numerical techniques for modeling solutions of the Navier-Stokes equations for two-phase incompressible flow. This methodology is specifically targeted at problems characterized by large density and viscosity jumps (e.g. air/water) and stiff, singular source terms, such as those due to the surface tension force. Problems with these features are extremely important in science and industry. Casting, mold filling, thin film processes, extrusion, spray deposition and jets are just a few examples. These problems present considerable challenges. Standard finite difference methods can either be too dissipative or too oscillatory near regions of large density variations. The resulting elliptic equation for enforcing the divergence free condition on the velocity field (projection step) has coefficients that exhibit a large jump at material interfaces. The resulting elliptic equation will also have a widely varying source term at material interfaces, since the divergence of the surface tension term will appear as a singular source term for the projection equation. In this research, the proposers plan to work in close collaboration with Dr. John Andrews of Xerox and David Wallace of Microfab technologies in developing numerical methods for modeling jetting devices. In an ink-jet device, it is important to study the characteristics of droplet formation. Because surface tension plays a large role in the droplet formation process, it is important for a numerical method to accurately model the surface tension effects during break-up of a droplet. It is also important for a numerical method to accurately predict the size of emitted droplets. Currently an adaptive level set method and a second order volume-of-fluid method have been developed for computing two-phase flows as characterized above. Objectives of the proposed research include improved numerical modeling of the interface between material boundaries and improved mo deling of surface tension, especially at points of droplet break-up. In the process of this study, the proposers will compare the behavior of the levelset method to that of the volume of fluid method which use a very similar formulation for the surface tension force. The proposers will also compare numerical solutions to solutions obtained via asymptotic methods and drop experiments conducted by Xerox. This research concerns the analysis and development of numerical techniques for modeling incompressible two-phase flow (such as air and water). Problems in two-phase flow are extremely important in science and industry. Casting, mold filling, thin film processes, extrusion, spray deposition and jets are just a few examples. In this research, the proposers plan to work in close collaboration with Dr. John Andrews of Xerox and David Wallace of Microfab technologies in developing numerical methods for modeling jetting devices. These companies develop jetting devices used in ink-jet printers, solder deposition and the fabrication of micro-optical elements. In a jetting device, it is important to study the characteristics of droplet formation. Because surface tension plays a large role in the droplet formation process, it is important for a numerical method to accurately model the surface tension effects during break-up of a droplet. It is also important for a numerical method to accurately predict the size of emitted droplets. Objectives of the proposed research include improved numerical modeling of the interface between material boundaries and improved modeling of surface tension, especially at points of droplet break-up. In the process of this study, the proposers will compare the behavior of the computational method with drop experiments conducted by Xerox.
