Abstract
A Galerkin finite-element method is developed for solving the transport equation governing the evolution of the surface concentration of an insoluble surfactant over a stationary or evolving fluid interface. The numerical procedure is implemented on an unstructured three-dimensional surface grid consisting of six-node curved triangular elements. Numerical investigations show that the finite-element method is superior to a previously developed finite-volume method for both convection- and diffusion-dominated transport, and especially when the interfacial grid is coarse and steep gradients arise due to local accumulation. The numerical methods for surface transport are combined with a boundary-element method for Stokes flow, and dynamical simulations are performed to illustrate the possibly significant effect of the surface equation of state relating the surface tension to the surfactant concentration on the deformation of a viscous drop in simple shear flow.
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References
C. Pozrikidis, Effect of surfactants on film flow down a periodic wall. J. Fluid Mech. 496 (2004) 105-127.
M. Blyth and C. Pozrikidis, Effect of surfactants on the stability of two-layer channel flow. J. Fluid Mech. Accepted (2004).
C. Pozrikidis, Numerical investigation of the effect of surfactants on the stability and rheology of emulsions and foam. J. Eng. Math. 41 (2001) 237-258.
R.V. Craster, O.K. Matar and D.T. Papageorgiou, Pinchoff and satellite formation in surfactant covered viscous threads. Phys. Fluids 14 (2002) 1364-1376.
X. Li and C. Pozrikidis, The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow. J. Fluid Mech. 341 (1997) 165-194.
S. Yon and C. Pozrikidis, A finite-volume / boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop. Comp. Fluids 27 (1998) 879-902.
M. A. Drumright-Clarke and Y. Renardy, The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia. Phys. Fluids 16 (2004) 14-21.
S. Popinet and S. Zaleski, Bubble collapse near a solid boundary: a numerical study of the influence of viscosity. J. Fluid Mech. 464 (2002) 137-163.
G.E. Karniadakis and S.J. Sherwin, Spectral/hp Element Methods for CFD. New York: Oxford Univ. Press (1999) 390pp.
J. Donea and A. Huerta, Finite Element Methods for Flow Problems. Chichester: Wiley (2003) 350pp.
A.W. Adamson, Physical Chemistry of Surfaces. Fifth Edition. New York: Wiley (1990) 777pp.
N.R. Gupta and A. Borhan, Capsule motion and deformation in tube and channel flow. In: C. Pozrikidis Modeling and Simulation of Capsules and Biological Cells. Boca Raton: Chapman & Hall /CRC (2003) 333pp.
C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics. New York: Oxford Univ. Press (1997) 675pp.
C. Pozrikidis, Numerical Computation in Science and Engineering. New York: Oxford Univ. Press (1998) 627pp.
J.W. Demmel, Applied Numerical Linear Algebra. Philadelphia: SIAM (1997) 419pp.
C. Pozrikidis, A Practical Guide to Boundary-Element Methods with the Software Library BEMLIB. Boca Raton: Chapman & Hall /CRC (2002) 423pp.
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Pozrikidis, C. A finite-element method for interfacial surfactant transport, with application to the flow-induced deformation of a viscous drop. Journal of Engineering Mathematics 49, 163–180 (2004). https://doi.org/10.1023/B:ENGI.0000017493.02877.4f
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DOI: https://doi.org/10.1023/B:ENGI.0000017493.02877.4f