Numerical simulation of bubble formation on orifice plates with a moving contact line

The formation of bubbles on an orifice plate involves a moving contact line, especially in case of poor wetting conditions. The dynamics of the moving contact line and contact angle have a significant impact on the bubble departure size. Therefore, for the numerical simulation, an appropriate contact line boundary condition is essential for a correct prediction of the bubble formation. Numerical tests have been performed on two kinds of contact line models, one is a contact line velocity dependent model (Model-A, a commonly used model) and the other is a stick-slip model (Model-B). The calculation results using Model-A depend greatly on the prescribed maximum contact line velocity. With Model-B a parameter-independent prediction can be obtained provided that the mesh is sufficiently fine. The dynamic advancing and receding contact angles, which are two required inputs to both models, have a significant influence on the predicted bubble departure diameter, if the contact line moves beyond the inner rim of the orifice. The effect of wettability on the bubble departure size is realized via the variation of the maximum contact diameter. When the contact line sticks to a small region near the inner rim of the orifice, such as the bubble formation on a thin-walled nozzle, the effects of the contact angle and contact line models are negligible.

[1]  Enrique Rame,et al.  On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation , 1991, Journal of Fluid Mechanics.

[2]  G. Son,et al.  Dynamics and Heat Transfer Associated With a Single Bubble During Nucleate Boiling on a Horizontal Surface , 1999 .

[3]  A. Bertozzi,et al.  Global models for moving contact lines. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  R. G. Cox.  The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow , 1986, Journal of Fluid Mechanics.

[5]  Catherine Colin,et al.  Dynamics of bubble growth and detachment in a viscous shear flow , 2006 .

[6]  S. Garoff,et al.  The effects of thin films on the hydrodynamics near moving contact lines , 1998 .

[7]  Mark E. Steinke,et al.  Contact angles and interface behavior during rapid evaporation of liquid on a heated surface , 2002 .

[8]  Wei Shyy,et al.  COMPUTATIONS OF DROP DYNAMICS WITH THE IMMERSED BOUNDARY METHOD, PART 2: DROP IMPACT AND HEAT TRANSFER , 2003 .

[9]  Brian Wetton,et al.  Computation of a Moving Drop/Bubble on a Solid Surface using a Front-Tracking Method , 2004 .

[10]  Abhijit Mukherjee,et al.  Numerical study of single bubbles with dynamic contact angle during nucleate pool boiling , 2007 .

[11]  Serafim Kalliadasis,et al.  Apparent dynamic contact angle of an advancing gas–liquid meniscus , 1994 .

[12]  Sandesh Somalinga,et al.  Numerical investigation of boundary conditions for moving contact line problems , 2000 .

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

[14]  J. Li,et al.  Numerical simulation of moving contact line problems using a volume-of-fluid method , 2001 .

[15]  Ilker S. Bayer,et al.  Contact angle dynamics in droplets impacting on flat surfaces with different wetting characteristics , 2006, Journal of Fluid Mechanics.

[16]  Y. Yang,et al.  Bubble Formation at an Orifice in Surfactant Solutions under Constant-Flow Conditions , 2000 .

[17]  O. Voinov.  Hydrodynamics of wetting , 1976 .

[18]  Peter Stephan,et al.  A new model for nucleate boiling heat transfer , 1994 .

[19]  Jaroslaw Drelich,et al.  The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough solid surfaces as observed with sessile-drop and captive-bubble techniques , 1996 .

[20]  S. Jakirlic,et al.  Dynamic contact angle of spreading droplets: Experiments and simulations , 2005 .

[21]  Dimos Poulikakos,et al.  Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling , 1995 .

[22]  M. Pasandideh-Fard,et al.  Capillary effects during droplet impact on a solid surface , 1996 .

[23]  Chi-Wang Shu,et al.  High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , 2001 .

[24]  Mark Sussman,et al.  An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow , 1999, SIAM J. Sci. Comput..

[25]  P. Spelt.  A level-set approach for simulations of flows with multiple moving contact lines with hysteresis , 2005 .

[26]  J. Liow,et al.  A model of bubble growth in wetting and non-wetting liquids , 1988 .

[27]  Y. Shikhmurzaev.  Moving contact lines in liquid/liquid/solid systems , 1997, Journal of Fluid Mechanics.

[28]  Michael K. Jensen,et al.  EVALUATION OF BUBBLE DEPARTURE DIAMETER CORRELATIONS , 1986 .

[29]  T. Blake,et al.  Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle , 1999 .

[30]  Abraham Marmur,et al.  A theoretical model for bubble formation at an orifice submerged in an inviscid liquid , 1976 .

[31]  Reginald B. H. Tan,et al.  An improved model for bubble formation using the boundary-integral method , 2005 .

[32]  Rainer Mertz,et al.  Numerical Study on the Formation of Taylor Bubbles in Capillary Tubes , 2009 .

[33]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[34]  Rajinder Kumar,et al.  Studies in bubble formation—I bubble formation under constant flow conditions , 1969 .

[35]  F. Durst,et al.  Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate , 2007 .

[36]  N. Chigarev,et al.  Variation of the contact angle in the quasistatic growth of a vapor bubble on a horizontal surface in a boiling liquid , 1986 .

[37]  Andrea Prosperetti,et al.  Dynamics of bubble growth and detachment from a needle , 1993, Journal of Fluid Mechanics.

[38]  Abraham Marmur,et al.  Equilibrium shapes and quasi-static formation of bubbles at submerged orifice , 1973 .

[39]  Takashi Nakamura,et al.  Influence of wetting conditions on bubble formation at orifice in an inviscid liquid. Transformation of bubble shape and size , 2003 .

[40]  George M. Homsy,et al.  Time-dependent free surface Stokes flow with a moving contact line. I. Flow over plane surfaces , 2004 .

[41]  Mohammad Jamialahmadi,et al.  Study of Bubble Formation Under Constant Flow Conditions , 2001 .

[42]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[43]  Hubert C. R. Schimann.  Force and Energy Measurement of Bubble-Particle Detachment , 2004 .