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Example: Adsorption and Heterogeneous Reactions

Example: Adsorption and Heterogeneous Reactions. Introduction. Small parallel plate reactor with an active surface is studied . These types of processes are found in heterogeneous reactors, biacores, etc.

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Example: Adsorption and Heterogeneous Reactions

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  1. Example: Adsorption and Heterogeneous Reactions

  2. Introduction • Small parallel plate reactor with an active surface is studied. These types of processes are found in heterogeneous reactors, biacores, etc. • The problem shows one of the most unique COMSOL Multiphysics features; coupling phenomena defined in different dimensions. In this case, a surface process is coupled to a process defined in a volume. • Mass balance is defined on the surface with surface diffusion and surface reaction rates using a “tangential PDE”. This, and the corresponding adsorbing and desorbing processes, can be coupled to the 2D problem through a (weak) boundary expression.

  3. Geometry • The flow channel is modeled with a geometry and PDE in 2D • The active surface is modeled with another PDE that ”lives” in 1D space only

  4. Coupling Scheme

  5. Weak Form • The surface equation needs to be defined in a 1D weak application mode, and it is coupled to the 2D PDE through a boundary condition: General Form: where: • “Tangential PDEs have derivatives in the direction of the tangent-plane to the surface only

  6. Weak Form (continued) Multiply by test function v and integrate: Perform integration by parts on left hand side: Rearranged: weak=Ds*(-csTx_test*csTx-csTy_test*csTy)+cs_test* (kads*c*(theta0-cs)-kdes*cs) In COMSOL Multiphysics: dweak=cs_test*cs_time

  7. Concentration in the Bulk and at the Surface Increase in lateral supply of reactant

  8. Surface Concentration as Function of Time at the Surface

  9. Time Evolution in Bulk

  10. Concluding Remarks • The model is highly relevant for heterogeneous reactions in the cases where the surface concentrations have to be accounted for. • Access to the weak form gives added flexibility. • Other uses for extended multiphysics can include: • Coupling process control to chemical/transport processes • Modelling phenomena on different scales, such as packed beds

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