Commun. Comput. Phys., 9 (2011), pp. 1362-1374.

Mass Transport/Diffusion and Surface Reaction Process with Lattice Boltzmann

Giuseppe De Prisco 1*, Xiaowen Shan 2

1 Exa Corporation, 55 Network Drive, Burlington, Massachusetts 01773, USA; and Ingrain Inc, 3733 Westheimer Road, Houston, Texas 77027, USA.
2 Exa Corporation, 55 Network Drive, Burlington, Massachusetts 01773, USA.

Received 2 October 2009; Accepted (in revised version) 24 December 2010
Available online 18 February 2011


Multi-component flow with chemical reactions is a common problem in different industrial applications: the mixing chamber of a reaction injection molding (RIM) machine; the dynamics of diesel soot particles interacting with a porous-ceramic particulate filter; reactive transport in porous media; bio-chemical processes involving enzyme-catalyzed kinetics. In all these cases, mass diffusion/convection and wall or volume chemical interactions among components play an important role. In the present paper we underline the importance of diffusion/convection/reaction mechanisms in bio-chemical processes using the Lattice Boltzmann (LB) technique. The bio-application where we studied diffusion/convection/reaction mechanisms is the quorum-sensing pathway for the bio-synthesis of the AI-2, a molecule that allows the bacteria to launch a coordinated attack on a host immune system (see [9, 10] for more details of the bio-application). The overall goal is to create a micro-device to screen potential drugs that inhibit AI-2 bio-synthesis. The Michaelis-Menten saturation kinetic model is implemented at the reactive surface and the results are shown in terms of two dimensionless numbers: Damkohler (Da) and Peclet (Pe) number. For high Pe number a small conversion of reactants into products is obtained at the reactive surface, but the overall flux of products is high; moreover, a fast saturation of the conversion of reactants to products is obtained for high Da numbers. The trade-off for setting the Pe and Da numbers depends on the specific application and the technologies used in the micro-device (e.g., sensitivity of the detector, cost of reactants).

AMS subject classifications: 76P05, 76R05, 76R50, 74F25, 92C45
PACS: 05.10.-a, 05.20.Dd, 47.11.Qr,
Key words: Lattice Boltzmann, multi-component, diffusion-reaction.

*Corresponding author.
Email: (G. De Prisco), (X. Shan)

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