Two-phase viscoelastic jetting

Two-Phase Viscoelastic Jetting Jiun-Der Yu ∗ Epson Research and Development, Inc. 3145 Porter Drive, Suite 104 Palo Alto, CA 94304 Shinri Sakai Seiko Epson Corporation Technology Platform Research Center 281 Fujimi, Fujimi-machi, Suwa-gun Nagano-ken, 399-0293, Japan J.A. Sethian † Department of Mathematics University of California, Berkeley Berkeley, CA 94720 Abstract A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage. The corresponding author. This author was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Re- search, U.S. Department of Energy, under Contract Number DE-AC03-76SF00098, and the Division of Mathematical Sciences of the National Science Foundation.

[1]  John B. Bell,et al.  A projection method for viscous incom-pressible flow on quadrilateral grids , 1961 .

[2]  M. Gerritsma.  Time dependent numerical simulations of a viscoelastic fluid on a staggered grid , 1996 .

[3]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[4]  J. Sethian,et al.  A coupled level set projection method applied to ink jet simulation , 2003 .

[5]  P. Colella,et al.  A stable and convergent scheme for viscoelastic flow in contraction channels , 2005 .

[6]  S. Sakai,et al.  Dynamics of Piezoelectric Inkjet Printing Systems. , 2000 .

[7]  Peter Smereka,et al.  Axisymmetric free boundary problems , 1997, Journal of Fluid Mechanics.

[8]  Raz Kupferman,et al.  Simulation of Viscoelastic Fluids , 1998 .

[9]  James A. Sethian,et al.  Numerical Methods for Propagating Fronts , 1987 .

[10]  James A. Sethian,et al.  A coupled quadrilateral grid level set projection method applied to ink jet simulation , 2005 .

[11]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[12]  J. Bell,et al.  A Second-Order Projection Method for Variable- Density Flows* , 1992 .

[13]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[14]  P. Colella.  Multidimensional upwind methods for hyperbolic conservation laws , 1990 .

[15]  John B. Bell,et al.  A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection , 1996, SIAM J. Sci. Comput..

[16]  M. Denn.  ISSUES IN VISCOELASTIC FLUID MECHANICS , 1990 .

[17]  Mark Sussman,et al.  FORMATION OF DROPLETS IN MICROSCALE JETTING DEVICES , 2007 .

[18]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[19]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[20]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[21]  J. Sethian,et al.  Projection methods coupled to level set interface techniques , 1992 .

[22]  J. Sethian.  AN ANALYSIS OF FLAME PROPAGATION , 1982 .

[23]  A. Chorin.  Numerical Solution of the Navier-Stokes Equations* , 1989 .

[24]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[25]  J. Sethian.  Curvature and the evolution of fronts , 1985 .

[26]  R. Kupferman.  Simulation of Viscoelastic Fluids : Couette – Taylor Flow , 1998 .

[27]  Ann S. Almgren,et al.  An adaptive level set approach for incompressible two-phase flows , 1997 .

[28]  Michael Griebel,et al.  Numerical Simulation in Fluid Dynamics: A Practical Introduction , 1997 .

[29]  P. Concus,et al.  Variational Methods for Free Surface Interfaces , 1987 .

[30]  John B. Bell,et al.  Approximate Projection Methods: Part I. Inviscid Analysis , 2000, SIAM J. Sci. Comput..