A numerical method for the calculation of drag and lift of a deformable droplet in shear flow

Journal of Computational Physics

Volumn 241, Issue , 2013, Pages 35-57

  Suh, Youngho ^a   Lee, Changhoon ^a  

^a Yonsei University   (South Korea)

Author keywords

Droplet deformation; Feedback force; Level set method; Shear flow

Indexed keywords

DRAG; DROP BREAKUP; FEEDBACK; NUMERICAL METHODS; OSCILLATING FLOW;

ACTING FORCE; DROPLET DEFORMATION; FEEDBACK FORCES; FORCING FUNCTION; LEVEL SET METHOD; LINEAR SHEAR FLOW; PARTICLE POSITION; SHEAR FLOW FIELDS; STABILITY ANALYZE; STABILITY BOUNDARIES;

SHEAR FLOW;

EID: 84874475599     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2013.01.034     Document Type: Article

References (30)

1. Oliver D.L.R., Chung J.N. Flow about a fluid sphere at low to moderate Reynolds numbers. J. Fluid Mech. 1987, 177:1-18.
2. Rivkind V.Y., Ryskin G.M. Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers. Fluid Dyn. 1976, 11:5-12.
3. Dandy D.S., Leal L.G. Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate reynolds numbers. J. Fluid Mech. 1989, 208:161-192.
4. Haywood R.J., Renksizbulut M., Raithby G.D. Numerical solution of deforming evaporating droplets at intermediate Reynolds numbers. Numer. Heat Transfer A 1994, 26:253-272.
5. Haywood R.J., Renksizbulut M., Raithby G.D. Transient deformation and evaporation of droplets at intermediate Reynolds numbers. Int. J. Heat Mass Transfer 1994, 37:1401-1409.
6. Helenbrook B.T., Edwards C.F. Quasi-steady deformation and drag of uncontaminated liquid drops. Int. J. Multiphase Flow 2002, 28:1631-1657.
7. Feng J.Q. A deformable liquid drop falling through a quiescent gas at terminal velocity. J. Fluid Mech. 2010, 658:438-462.
8. Chaffey C.E., Brenner H. A second-order theory for shear deformation of drops. J. Colloid Interface Sci. 1967, 24:258-269.
9. Guido S., Greco F. Drop shape under slow steady shear flow and during relaxation. Experimental results and comparison with theory. Rheol. Acta 2001, 40:176-184.
10. Renardy Y. The effects of confinement and inertia on the production of droplets. Rheol. Acta 2007, 46:521-529.
11. Shaffman P.G. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 1965, 22:385-400.
12. Dandy D.S., Dwyer H.A. A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J. Fluid Mech. 1990, 216:381-410.
13. Kurose R., Komori S. Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 1999, 384:183-206.
14. Sugioka K.I., Komori S. Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow. J. Fluid Mech. 2007, 570:155-175.
15. Son G. A level set method for incompressible two-fluid flows with immersed solid boundaries. Numer. Heat Transfer B 2005, 47:473-489.
16. Suh Y., Son G. A level-set method for simulation of a thermal inkjet process. Numer. Heat Transfer B 2008, 54:138-156.
17. Sussman M., Smereka P., Osher S. A level set approach for computing solution to incompressible two-phase flow. J. Comput. Phys. 1994, 114:146-159.
18. Takewaki H., Yabe T. The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations. J. Comput. Phys. 1987, 70:355-372.
19. Yabe T., Ishikawa T., Wang P.Y., Aoki T., Kadota Y., Ikeda F. A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers. Comput. Phys. Commun. 1991, 66:233-242.
20. Bell J.B., Colella P., Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 1989, 85:257-283.
21. Oshima S., Park M.K., Makiharam K., Yamane R. Position control of magnetic droplet by means of magnetic field. Trans. JSME 1995, 61:186-193.
22. Potts H.E., Barrett R.K., Diver D.A. Dynamics of freely-suspended drops. J. Phys. D 2001, 34:2529.
23. Ishikawa T., Paradis P.F., Koike N., Watanabe Y. Effects of the positioning force of electrostatic levitators on viscosity measurements. Rev. Sci. Instrum. 2009, 80:013906.
24. Lee C. Stability characteristics of the virtual boundary method in three-dimensional applications. J. Comput. Phys. 2003, 184:559-591.
25. Loth E. Quasi-steady shape and drag of deformable bubbles and drops - a review. Int. J. Multiphase Flow 2008, 34:523-546.
26. Clift R., Grace J.R., Weber M.E. Bubbles, Drops, and Particles 1978, Academic Press.
27. Beard K.V., Ochs H.T., Kubesh R.J. Natural oscillations of small raindrops. Nature 1989, 342:408-410.
28. Gunn R., Kinzer G.D. The terminal velocity of fall for water droplets in stagnant air. J. Meteor. 1949, 6:243-248.
29. Rayleigh J.W.S. On the capillary phenomena of jets. Proc. R. Soc. London 1879, 19:71-97.
30. Feng J.Q., Beard K.V. A perturbation model of raindrop oscillation characteristics with aerodynamic effects. J. Atmos. Sci. 1991, 48:1856-1868.