{"uid":"cap_QP_rW_eLRJ3LGHOQKlecL","slug":"maxwell-stefan-multicomponent-molar-diffusion-velocity-solver-714ca9d0","name":"Maxwell-Stefan Multicomponent Molar Diffusion Velocity Solver","description":"Resolve coupled molar diffusion velocities from explicit pairwise molecular friction 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coupled molar diffusion velocities for a multicomponent mixture using explicit pairwise binary diffusivities and mole fraction gradients via the Maxwell-Stefan framework.","exampleAgentPrompt":"Solve the Maxwell-Stefan diffusion velocities for a 3-component mixture with mole amounts [0.3, 0.5, 0.2], mole fraction gradients [0.1, -0.05, -0.05], binary diffusivities matrix [[0,1.2,0.8],[1.2,0,0.6],[0.8,0.6,0]], and a total molar density of 40 mol/m³.","exampleUseCases":[{"title":"Ternary gas diffusion in membrane separation","prompt":"I have a 3-component gas mixture in a membrane separator with component amounts [0.4, 0.35, 0.25], mole fraction gradients [0.08, -0.03, -0.05], binary diffusivities [[0,2.1,1.5],[2.1,0,1.0],[1.5,1.0,0]], and a total molar density of 55 mol/m³ — can you compute the molar diffusion velocities for each species?"},{"title":"Multicomponent reformer gas transport modeling","prompt":"For a 4-component reformer gas with component amounts [0.2,0.4,0.25,0.15], mole fraction gradients [0.05,-0.02,-0.02,-0.01], binary diffusivities as a 4x4 matrix [[0,1.8,1.2,0.9],[1.8,0,1.5,1.1],[1.2,1.5,0,0.7],[0.9,1.1,0.7,0]], and total molar density of 80 mol/m³, please resolve the coupled Maxwell-Stefan molar diffusion velocities."},{"title":"Binary friction verification for two-component system","prompt":"I want to verify Maxwell-Stefan diffusion velocities for a simple 2-component system: component amounts [0.6, 0.4], mole fraction gradients [0.12, -0.12], binary diffusivities [[0, 2.5],[2.5, 0]], and total molar density of 30 mol/m³ — what are the resulting molar diffusion velocities?"}],"resultDescription":"Returns the resolved molar diffusion velocity vector for each component in the mixture, computed by inverting the coupled Maxwell-Stefan linear system built from the pairwise binary diffusivities, mole fraction gradients, component amounts, and total molar density.","failureModes":["Singular or ill-conditioned diffusivity matrix causing no unique solution","Sum of mole fraction gradients violating the constraint (non-zero sum) leading to rejection","Component count mismatch between component_amounts, mole_fraction_gradients, and binary_diffusivities arrays","Binary diffusivities matrix not square or not symmetric causing validation failure","Values out of allowed range (e.g. negative component amounts or diffusivities) causing schema rejection","Total molar density of zero or below minimum threshold causing division error"],"whenToPreferThis":"Use this endpoint when you need to solve the full coupled Maxwell-Stefan multicomponent diffusion system from explicit pairwise binary diffusivities rather than using simplified Fickian or effective diffusivity approximations. It is preferred for systems with 2–8 components where diffusion coupling between species is significant, such as in membrane separations, catalytic reactors, or gas absorption columns where cross-diffusion effects cannot be ignored.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:39:53.466Z","isFirstParty":false,"canonicalSlug":"maxwell-stefan-multicomponent-molar-diffusion-velocity-solver-714ca9d0"}