References
1. Malekjafarian, M. and Sadrnezhaad, S.K. \Eect of
SiC on microstructural features and compressive properties
of aluminum foam", Scientia Iranica, 21(4), pp.
1325-1329 (2014).
2. Latizadeh, H. \An analytical method to analysis
of foam drainage problem", International Journal of
Mathematical Sciences, 7(1), (2013).
3. Feng, J.J. and Bertelo, C.A. \Prediction of bubble
growth and size distribution in polymer foaming based
on a new heterogeneous nucleation model", J. Rheol.,
48, pp. 439-462 (2004).
1310 E. Amiri Rad/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 1303{1311
4. Hilgenfeldt, S., Koehler, S.A., and Stone, H.A. \Dynamics
of coarsening foams: Accelerated and selflimiting
drainage", Phys. Rev. Lett., 86(20), pp. 4704-
4707 (2001).
5. Sandler, J., Wollecke, F., Altstadt, V., Wettstein, E.,
and Rakutt, D. \Principal correlation of pvc melt
elongational properties with foam cell morphology",
Cellular Polym., 19, pp. 371-388 (2000).
6. Sha, M.A. and Flumerfelt, R.W. \Initial bubble
growth in polymer foam processes", Chem. Eng. Sci.,
52, pp. 627-633 (1997).
7. Ramesh, N.S., Rasmussen, D.H., and Campbell, G.A.
\The heterogeneous nucleation of microcellular foams
assisted by the survival of microvoids in polymers
containing low glass transition particles. Part i: mathematical
modeling and numerical simulation", Polym.
Eng. Sci., 34, pp. 1685-1696 (1994).
8. Arefmanesh, A., Advani, S.G., and Michaelides, E.E.
\A numerical study of bubble growth during low
pressure structural foam molding process", Polymer
Eng. Sci., 30, pp. 1330-1337 (1990).
9. Paulsen, J.D., Carmigniani, R., Kannan, A., Burton,
J.C., and Nagel, S.R. \Coalescence of bubbles and
drops in an outer
uid", Nat. Commun., 5(3182)
(2014). Doi: 10.1038/ncomms4182.
10. Paulsen, J.D. \Approach and coalescence of liquid
drops in air", Phys. Rev. E., 88, 063010 (2013).
11. Paulsen, J.D., Burton, J.C., Nagel, S.R., Appathurai,
S., Harris, M.T., and Basaran, O.A. \The inexorable
resistance of inertia determines the initial regime of
drop coalescence", Proc. Natl. Acad. Sci. USA., 109,
pp. 6857-6861 (2012).
12. Paulsen, J.D., Burton J.C., and Nagel, S.R. \Viscous
to inertial crossover in liquid drop coalescence", Phys.
Rev. Lett., 106, 114501 (2011).
13. Baroudi, L., Kawaji, M., and Lee T. \Eects of initial
conditions on the simulation of inertial coalescence
of two drops", Comp. Math. Appl., 67, pp. 282-289
(2013).
14. Sprittles, J.E. and Shikhmurzaev, Y.D. \Coalescence
of liquid drops: Dierent models versus experiment",
Phys. Fluids, 24, 122105 (2012).
15. Czerski, H. \A candidate mechanism for exciting sound
during bubble coalescence", J. Acoust. Soc. Am., 129,
EL83-EL88 (2011).
16. Case, S.C. \Coalescence of low-viscosity
uids in air",
Phys. Rev. E., 79, 026307 (2009).
17. Case, S.C. and Nagel, S.R. \Coalescence in lowviscosity
liquids", Phys. Rev. Lett., 100, 084503
(2008).
18. Fezzaa, K., and Wang, Y. \Ultrafast x-ray phasecontrast
imaging of the initial coalescence phase of two
water droplets.", Phys. Rev. Lett., 100, 104501 (2008).
19. Giribabu, K. and Ghosh, P. \Binary coalescence of
air bubbles in viscous liquids in presence of non-ionic
surfactant", Can. J. Chem. Eng., 86, pp. 643-650
(2008).
20. Gilet, T., Mulleners, K., Lecomte, J.P., Vandewalle,
N., and Dorbolo, S. \Critical parameters for the partial
coalescence of a droplet", Phys. Rev. E., 75, 036303
(2007).
21. Aarts, D.G.A.L., Lekkerkerker, H.N.W., Guo, H.,
Wegdam, G.H., and Bonn, D. \Hydrodynamics of
droplet coalescence", Phys. Rev. Lett., 95, 164503
(2005).
22. Thoroddsen, S.T., Takehara, K., and Etoh, T.G. \The
coalescence speed of a pendent and a sessile drop", J.
Fluid Mech., 527, pp. 85-114 (2005).
23. Wu, M., Cubaud T., and Ho, C.M. \Scaling law in
liquid drop coalescence driven by surface tension",
Phys. Fluids, 16, L51-L54 (2004).
24. Duchemin, L., Eggers, J., and Josserand, C. \Inviscid
coalescence of drops", J. Fluid Mech., 487, pp. 167-178
(2003).
25. Ghosh, P. and Juve kar, V.A. \Analysis of the drop
rest phenomenon", Chem. Eng. Res. Design, 80(7),
pp. 715-728 (2002).
26. Eggers, J., Lister, J.R., and Stone, H.A. \Coalescence
of liquid drops", J. Fluid Mech., 401, pp. 293-310
(1999).
27. Amaya-Bower, L. and Lee, T. \Single bubble rising
dynamics for moderate Reynolds number using lattice
Boltzmann method", Computers & Fluids, 39(7), pp.
1191-1207 (2010).
28. Stover, L.R., Tobias, C.W., and Denn, M.M. \Bubble
coalescence dynamics", AIChE Journal, 43, pp. 2385-
2392 (1997).
29. Egan, E.W. and Tobias, C.W. \Measurement of interfacial
re-equilibration during hydrogen bubble coalescence",
J. Electrochem. Soc., 141, pp. 1118-1126
(1994).
30. Chaudhari, R.V. and Hofmann, H. \Coalescence of gas
bubbles in liquids", Rev. Chem. Eng., 10, pp. 131-191
(1994).
31. Oolman, T.O. and Blanch, H.W. \Bubble coalescence
in stagnant liquids", Chem. Eng. Commun., 43, pp.
237-261 (1986).
32. Hirt, C.W. and Nichols, B.D. \Volume of
uid (VOF)
method for the dynamics of free boundaries", J. Comp.
Phys., 39, pp. 201-225 (1982).
33. Bhaga, D. and Weber, M.E. \In-line interaction of a
pair of bubbles in a viscous liquid", Chem. Eng. Sci.,
35, pp. 2467-2474 (1980).
34. Narayanan, S., Goossens, H.J. and Kossen, N.W.F.
\Coalescence of two bubbles rising in line at low
Reynolds numbers", Chem. Eng. Sci., 29, pp. 2071-
2082 (1974).
35. Amiri Rad, E. \Evaluation the radius dependency of
surface tension in nano-droplets by a diuse-interface
lattice boltzmann", Progress in Computational Fluid
Dynamics An International Journal, 17(4), pp. 232-
238 (2017).
E. Amiri Rad/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 1303{1311 1311
36. Amiri Rad, E. and Salimi, M. \Investigating the eects
of shear rate on the collapse time in a gas-liquid system
by lattice Boltzmann", Meccanica, 52(4-5), pp. 915-
924 (2016)
37. Amiri Rad, E. \Control of droplet collapse during
coarsening process by imposing shear
ow: A lattice
Boltzmann simulation", Meccanica, 50(4), pp. 995-
1001 (2015).
38. Amiri Rad, E. \Investigation the eects of shear rate
on stationary droplets coalescence by lattice Boltzmann",
Meccanica, 49(6), pp. 1457-1467 (2014).
39. Amiri Rad, E. \Coalescence of two at-rest equal-sized
drops in static vapor of the same material: A lattice
Boltzmann approach", J. Mech. Sci. Technol., 28(9),
pp. 3597-3603 (2014).
40. Dupuis, A. and Yeomans, J.M. \Modeling droplets
on superhydrophobic surfaces: equilibrium states and
transitions", Langmuir., 21, pp. 2624-2629 (2005).
41. Briant, A.J., Wagner, A.J., and Yeomans, J.M. \Lattice
Boltzmann simulations of contact line motion. I.
Liquid-gas systems", Phys. Rev. E., 69, 031602 (2004).
42. Swift, M.R., Osborn, W.R., and Yeomans, J.M. \Lattice
Boltzmann simulation of nonideal
uids", Phys.
Rev. Lett., 75, pp. 830-833 (1995).
43. Swift, M.R., Orlandini, E., Osborn, W.R., and Yeomans,
J.M. \Lattice Boltzmann simulations of liquidgas
and binary
uid systems.", Phys. Rev. E., 54, pp.
5041-5052 (1996).
44. Hou, S., Zou, Q., Chen, S., Doolen, G. and Cogley,
A.C. \Simulation of cavity
ow by the lattice Boltzmann
method", J. Comput. Phys., 118, pp. 329-347
(1995).
45. Shan, X. and Chen, H. \Simulation of nonideal gases
and liquid-gas phase transitions by the lattice Boltzmann
equation", Phys. Rev. E., 49, pp. 2941-2948
(1994).
46. Succi, S. \The Lattice Boltzmann Equation for Fluid
Dynamics and Beyond", Oxford University Press
(2001).
47. Holdych, D.J., Rovas, D., Georgiadis, J.G. and Buckius,
R.O. \An improved hydrodynamics formulation
for multiphase
flow lattice-Boltzmann models", Int. J.
Mod. Phys., C9, pp. 1393-1404 (1998).
48. Evans, R. \The nature of the liquid-vapour interface
and other topics in the statistical mechanics of nonuniform,
classical
uids", Adv. Phys., 28, pp. 143-200
(1979).
49. Landau, L.D. and Lifshitz, E.M. Statistical Physics,
Pergamon Press (1958).
50. Jamet, D., Torres, D. and Brackbill, J.U. \On the
theory and computation of surface tension: The elimination
of parasitic currents through energy conservation
in the second-gradient method", Journal of
Computational Physics, 182, pp. 262-276 (2002).