%0 Book Section %1 citeulike:13975759 %A Bothe, Dieter %A Prüss, Jan %A Simonett, Gieri %B Nonlinear Elliptic and Parabolic Problems %C Basel %D 2005 %E Brezis, Haim %E Chipot, Michel %E Escher, Joachim %I Birkhäuser %K surfactant-transport-equation 35q30-navier-stokes-equations 76d45-capillarity-in-viscous-fluids 76t10-liquid-gas-two-phase-flows-bubbly-flows 35r35-free-boundary-problems %P 37--61 %R 10.1007/3-7643-7385-7\_3 %T Well-posedness of a Two-phase Flow with Soluble Surfactant %U http://dx.doi.org/10.1007/3-7643-7385-7\_3 %V 64 %X The presence of surfactants, ubiquitous at most fluid/liquid interfaces, has a pronounced effect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momentum along the interface — so-called Marangoni effects. The mathematical model governing the dynamics of such systems is studied for the case in which the surfactant is soluble in one of the adjacent bulk phases. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phase. Within the model, the motions of the surfactant and of the adjacent bulk fluids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing L p -maximal regularity we obtain well-posedness of this model for a certain initial configuration. The proof is based on recent L p -theory for two-phase flows without surfactant. %@ 978-3-7643-7266-8

@incollection{citeulike:13975759, abstract = {{The presence of surfactants, ubiquitous at most fluid/liquid interfaces, has a pronounced effect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momentum along the interface — so-called Marangoni effects. The mathematical model governing the dynamics of such systems is studied for the case in which the surfactant is soluble in one of the adjacent bulk phases. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phase. Within the model, the motions of the surfactant and of the adjacent bulk fluids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing L p -maximal regularity we obtain well-posedness of this model for a certain initial configuration. The proof is based on recent L p -theory for two-phase flows without surfactant.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Basel}, author = {Bothe, Dieter and Pr\"{u}ss, Jan and Simonett, Gieri}, biburl = {https://www.bibsonomy.org/bibtex/29f9a45d74b0047b422ed1a56b5bcbeb5/gdmcbain}, booktitle = {Nonlinear Elliptic and Parabolic Problems}, citeulike-article-id = {13975759}, citeulike-attachment-1 = {bothe_05_well.pdf; /pdf/user/gdmcbain/article/13975759/1058154/bothe_05_well.pdf; f34d33e75a0524a77db62215a8232d06174b7380}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/3-7643-7385-7\_3}, citeulike-linkout-1 = {http://link.springer.com/chapter/10.1007/3-7643-7385-7\_3}, doi = {10.1007/3-7643-7385-7\_3}, editor = {Brezis, Haim and Chipot, Michel and Escher, Joachim}, file = {bothe_05_well.pdf}, interhash = {ad9fd1d2a7b151e5b6df1aed7188b05b}, intrahash = {9f9a45d74b0047b422ed1a56b5bcbeb5}, isbn = {978-3-7643-7266-8}, keywords = {surfactant-transport-equation 35q30-navier-stokes-equations 76d45-capillarity-in-viscous-fluids 76t10-liquid-gas-two-phase-flows-bubbly-flows 35r35-free-boundary-problems}, pages = {37--61}, posted-at = {2016-03-11 04:08:28}, priority = {2}, publisher = {Birkh\"{a}user}, series = {Progress in Nonlinear Differential Equations and Their Applications}, timestamp = {2019-11-19T01:43:36.000+0100}, title = {{Well-posedness of a Two-phase Flow with Soluble Surfactant}}, url = {http://dx.doi.org/10.1007/3-7643-7385-7\_3}, volume = 64, year = 2005 }