https://doi.org/10.1140/epjs/s11734-025-01737-2
Regular Article
A robust lattice Boltzmann method for interface-bound transport of a passive scalar: application to surfactant-laden multiphase flows
Department of Mechanical Engineering, University of Colorado Denver, 1200 Larimer Street, 80204, Denver, CO, USA
a
kannan.premnath@ucdenver.edu
Received:
12
April
2025
Accepted:
4
June
2025
Published online:
21
June
2025
The transport of a passive scalar restricted on interfaces, which is advected by the fluid motions, has numerous applications in multiphase transport phenomena. A prototypical example is the advection–diffusion of the concentration field of an insoluble surfactant along interfaces. A sharp interface model of the surfactant transport on the interface (Stone, Phys Fluids A 111:1990) has been modified and further extended to a diffuse interface formulation based on a delta function regularization by Teigen et al. (Commun Math Sci 4:1009, 2009). However, the latter approach involves singular terms which can compromise its numerical implementation. Recently, Jain and Mani (Annual Research Briefs, Center for Turbulence Research, Stanford University, 2022) circumvented this issue by applying a variable transformation, which effectively leads to a generalized interface-bound scalar transport equation with an additional interfacial sharpening flux term that prevents lateral diffusion into the bulk phase regions. The resulting formulation has similarities with the conservative Allen–Cahn equation (CACE) used for tracking of interfaces. In this paper, we will discuss a novel robust central moment lattice Boltzmann (LB) method to simulate the interface-bound advection–diffusion transport equation of a scalar field proposed in Teigen et al. by applying Jain and Mani’s transformation. It is coupled with another LB scheme for the CACE to compute the evolving interfaces, and the resulting algorithm is validated against some benchmark problems available in the literature. As further extension, we have coupled it with our central moment LB flow solver for the two-fluid motions, which is modulated by the Marangoni stresses resulting from the variation of the surface tension with the local surfactant concentration modeled via the Langmuir isotherm. This is then validated by simulating insoluble surfactant-laden drop deformation and break-up in a shear flow at various capillary numbers.
Investigations on this research were presented at 32nd International Conference on Discrete Simulation of Fluid Dynamics (DSFD), Albuquerque, New Mexico, July 2023 and at American Physical Society (APS) 76th Annual Division of Fluid Dynamics (DFD) Meeting, Washington D.C., November 2023 (https://meetings.aps.org/Meeting/DFD23/Session/T16.6).
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
