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      On diffuse interface modeling and simulation of surfactants in two-phase fluid flow

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          Abstract

          An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

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          Most cited references47

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          Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling

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            Time‐Dependence of Boundary Tensions of Solutions I. The Role of Diffusion in Time‐Effects

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              A simple derivation of the time‐dependent convective‐diffusion equation for surfactant transport along a deforming interface

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                Author and article information

                Journal
                2011-06-30
                2012-10-05
                Article
                10.4208/cicp.120712.281212a
                1106.6233
                eec3f11c-f4f8-42b0-9a2b-316421734633

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                76T30, 65M60, 65Z05
                Commun. Comput. Phys. 14(4):879--915, 2013
                math.NA math.AP physics.flu-dyn

                Analysis,Numerical & Computational mathematics,Thermal physics & Statistical mechanics

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