publication . Preprint . 2016

Simulating Surfactant Spreading: Impact of a Physically Motivated Equation of State

Sinclair, Dina; Levy, Rachel; Daniels, Karen E.;
Open Access English
  • Published: 16 Feb 2016
Abstract
For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant c...
Subjects
arXiv: Condensed Matter::Soft Condensed Matter
free text keywords: Physics - Fluid Dynamics, 35Q35, 76A20, 76M12, 76B45
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42 references, page 1 of 3

[1] Avanti Polar Lipids. www.avantilipids.com/index.php?option=com_content&view= article&id=1028&Itemid=220&catnumber=810131

[2] Angelini, T. E., Roper, M., Kolter, R., Weitz, D. A., and Brenner, M. P. Bacillus subtilis spreads by sur ng on waves of surfactant. Proceedings of the National Academy of Sciences 106, 43 (2009), 18109{18113.

[3] Barrett, J. W., Garcke, H., and Nurnberg, R. Finite element approximation of surfactant spreading on a thin lm. SIAM Journal on Numerical Analysis 41, 4 (2003), 1427{1464.

[4] Borgas, M. S., and Grotberg, J. B. Monolayer ow on a thin lm. Journal of Fluid Mechanics 193 (1988), 151{170.

[5] Braun, R. J. Dynamics of the tear lm. Annual Review of Fluid Mechanics 44 (2012), 267{297.

[6] Bull, J., and Grotberg, J. Surfactant spreading on thin viscous lms: lm thickness evolution and periodic wall stretch. Experiments in Fluids 34, 1 (2003), 1{15.

[7] J. Claridge, R. Levy, J. Wong https://github.com/claridge/implicit_solvers/ blob/master/ImplicitSolversPaper.pdf

[8] J. Claridge, R. Levy, J. Wong https://github.com/claridge/implicit_solvers/

[9] Conti, C., Autry, E. A., Kronmiller, G., and Levy, R. The e ects of spatial and temporal grids on simulations of thin lms with surfactant. SIURO 916 (2013), 81{93. [OpenAIRE]

[10] Craster, R., and Matar, O. Surfactant transport on mucus lms. Journal of Fluid Mechanics 425 (2000), 235{258. [OpenAIRE]

[11] Craster, R., and Matar, O. Dynamics and stability of thin liquid lms. Reviews of modern physics 81, 3 (2009), 1131. [OpenAIRE]

[12] De Wit, A., Gallez, D., and Christov, C. Nonlinear evolution equations for thin liquid lms with insoluble surfactants. Physics of Fluids 6, 10 (1994), 3256{3266. [OpenAIRE]

[13] Dow Chemical. http://www.dow.com/optim/optim-advantage/physical-properties/ viscosity.htm

[14] Dow Chemical. http://www.dow.com/optim/optim-advantage/physical-properties/ density.htm

[15] Espinosa, F., Shapiro, A., Fredberg, J., and Kamm, R. Spreading of exogenous surfactant in an airway. Journal of Applied Physiology 75, 5 (1993), 2028{2039. [OpenAIRE]

42 references, page 1 of 3
Abstract
For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant c...
Subjects
arXiv: Condensed Matter::Soft Condensed Matter
free text keywords: Physics - Fluid Dynamics, 35Q35, 76A20, 76M12, 76B45
Download from
42 references, page 1 of 3

[1] Avanti Polar Lipids. www.avantilipids.com/index.php?option=com_content&view= article&id=1028&Itemid=220&catnumber=810131

[2] Angelini, T. E., Roper, M., Kolter, R., Weitz, D. A., and Brenner, M. P. Bacillus subtilis spreads by sur ng on waves of surfactant. Proceedings of the National Academy of Sciences 106, 43 (2009), 18109{18113.

[3] Barrett, J. W., Garcke, H., and Nurnberg, R. Finite element approximation of surfactant spreading on a thin lm. SIAM Journal on Numerical Analysis 41, 4 (2003), 1427{1464.

[4] Borgas, M. S., and Grotberg, J. B. Monolayer ow on a thin lm. Journal of Fluid Mechanics 193 (1988), 151{170.

[5] Braun, R. J. Dynamics of the tear lm. Annual Review of Fluid Mechanics 44 (2012), 267{297.

[6] Bull, J., and Grotberg, J. Surfactant spreading on thin viscous lms: lm thickness evolution and periodic wall stretch. Experiments in Fluids 34, 1 (2003), 1{15.

[7] J. Claridge, R. Levy, J. Wong https://github.com/claridge/implicit_solvers/ blob/master/ImplicitSolversPaper.pdf

[8] J. Claridge, R. Levy, J. Wong https://github.com/claridge/implicit_solvers/

[9] Conti, C., Autry, E. A., Kronmiller, G., and Levy, R. The e ects of spatial and temporal grids on simulations of thin lms with surfactant. SIURO 916 (2013), 81{93. [OpenAIRE]

[10] Craster, R., and Matar, O. Surfactant transport on mucus lms. Journal of Fluid Mechanics 425 (2000), 235{258. [OpenAIRE]

[11] Craster, R., and Matar, O. Dynamics and stability of thin liquid lms. Reviews of modern physics 81, 3 (2009), 1131. [OpenAIRE]

[12] De Wit, A., Gallez, D., and Christov, C. Nonlinear evolution equations for thin liquid lms with insoluble surfactants. Physics of Fluids 6, 10 (1994), 3256{3266. [OpenAIRE]

[13] Dow Chemical. http://www.dow.com/optim/optim-advantage/physical-properties/ viscosity.htm

[14] Dow Chemical. http://www.dow.com/optim/optim-advantage/physical-properties/ density.htm

[15] Espinosa, F., Shapiro, A., Fredberg, J., and Kamm, R. Spreading of exogenous surfactant in an airway. Journal of Applied Physiology 75, 5 (1993), 2028{2039. [OpenAIRE]

42 references, page 1 of 3
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