×

Electrified coating flows on vertical fibres: enhancement or suppression of interfacial dynamics. (English) Zbl 1294.76057

Summary: We investigate the evolution and stability of a wetting viscous fluid layer flowing down the surface of a cylinder, and surrounded by a conductive gas. The inner cylinder is an electrode kept at constant voltage, and a second, concentric electrode encloses the system whose potential is allowed to vary spatially. This induces electrostatic forces at the interface in competition with surface tension and viscous stresses. Asymptotic methods are used to derive a long-wave axisymmetric model governing the interfacial position and charge density. The resulting system of equations is investigated both analytically and numerically to determine its stability characteristics in the linear and nonlinear regimes.

MSC:

76A20 Thin fluid films
76W05 Magnetohydrodynamics and electrohydrodynamics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/j.ces.2008.05.003 · doi:10.1016/j.ces.2008.05.003
[2] DOI: 10.1063/1.2190248 · doi:10.1063/1.2190248
[3] DOI: 10.1016/j.electacta.2006.02.002 · doi:10.1016/j.electacta.2006.02.002
[4] DOI: 10.1017/S002211201000618X · Zbl 1225.76044 · doi:10.1017/S002211201000618X
[5] AIChE J. 38 pp 821– (2004)
[6] DOI: 10.1016/j.ces.2006.08.033 · doi:10.1016/j.ces.2006.08.033
[7] DOI: 10.1103/RevModPhys.81.1131 · doi:10.1103/RevModPhys.81.1131
[8] DOI: 10.1017/S0022112006008706 · Zbl 1087.76030 · doi:10.1017/S0022112006008706
[9] DOI: 10.1063/1.1693422 · Zbl 0216.52703 · doi:10.1063/1.1693422
[10] DOI: 10.1063/1.1852459 · Zbl 1187.76107 · doi:10.1063/1.1852459
[11] DOI: 10.1017/S0022112083002451 · Zbl 0571.76046 · doi:10.1017/S0022112083002451
[12] DOI: 10.1063/1.3548841 · Zbl 06421625 · doi:10.1063/1.3548841
[13] DOI: 10.1016/0021-9797(87)90027-0 · doi:10.1016/0021-9797(87)90027-0
[14] DOI: 10.1103/PhysRevE.83.066314 · doi:10.1103/PhysRevE.83.066314
[15] DOI: 10.1039/c1sm05183k · doi:10.1039/c1sm05183k
[16] DOI: 10.1103/PhysRevE.79.066305 · doi:10.1103/PhysRevE.79.066305
[17] DOI: 10.1103/RevModPhys.69.865 · Zbl 1205.37092 · doi:10.1103/RevModPhys.69.865
[18] DOI: 10.1103/PhysRevLett.79.217 · doi:10.1103/PhysRevLett.79.217
[19] DOI: 10.1103/PhysRevLett.98.244502 · doi:10.1103/PhysRevLett.98.244502
[20] DOI: 10.1063/1.1706737 · Zbl 0116.19102 · doi:10.1063/1.1706737
[21] DOI: 10.1017/S0022112057000373 · Zbl 0078.18003 · doi:10.1017/S0022112057000373
[22] DOI: 10.1038/39827 · doi:10.1038/39827
[23] DOI: 10.1093/imamat/hxs027 · Zbl 1314.76049 · doi:10.1093/imamat/hxs027
[24] DOI: 10.1016/j.jcis.2007.02.089 · doi:10.1016/j.jcis.2007.02.089
[25] DOI: 10.1115/1.521478 · doi:10.1115/1.521478
[26] DOI: 10.1017/jfm.2011.247 · Zbl 1241.76461 · doi:10.1017/jfm.2011.247
[27] DOI: 10.1115/1.1288932 · doi:10.1115/1.1288932
[28] DOI: 10.1063/1.3097888 · Zbl 1183.76559 · doi:10.1063/1.3097888
[29] DOI: 10.1103/RevModPhys.65.851 · Zbl 1371.37001 · doi:10.1103/RevModPhys.65.851
[30] DOI: 10.1021/la0472100 · doi:10.1021/la0472100
[31] DOI: 10.1016/j.physd.2010.07.011 · Zbl 1235.37030 · doi:10.1016/j.physd.2010.07.011
[32] DOI: 10.1017/S0022112006009712 · Zbl 1147.76574 · doi:10.1017/S0022112006009712
[33] DOI: 10.1016/S0032-3861(01)00540-7 · doi:10.1016/S0032-3861(01)00540-7
[34] DOI: 10.1016/j.jcis.2003.12.024 · doi:10.1016/j.jcis.2003.12.024
[35] DOI: 10.1146/annurev.fluid.29.1.27 · doi:10.1146/annurev.fluid.29.1.27
[36] Proc. Lond. Math. Soc. s1–10 pp 4– (1878)
[37] DOI: 10.1016/S0377-0257(01)00180-X · Zbl 1082.76518 · doi:10.1016/S0377-0257(01)00180-X
[38] DOI: 10.1103/RevModPhys.69.931 · doi:10.1103/RevModPhys.69.931
[39] DOI: 10.1063/1.3154586 · Zbl 1183.76389 · doi:10.1063/1.3154586
[40] DOI: 10.1016/0021-8502(94)90200-3 · doi:10.1016/0021-8502(94)90200-3
[41] Micro Total Analysis Systems, 98 pp 45– (1998)
[42] DOI: 10.1017/S0022112006008822 · Zbl 1151.76376 · doi:10.1017/S0022112006008822
[43] DOI: 10.1017/S0022112000003268 · Zbl 0969.76030 · doi:10.1017/S0022112000003268
[44] DOI: 10.1145/108556.108558 · Zbl 0900.65270 · doi:10.1145/108556.108558
[45] J. Phys. 32 pp 459– (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.