(648c) Interfacial Reaction-Diffusion Dynamics with Large Partition Coefficients

Interfacial reactions at liquid–liquid, liquid–solid, and solid–solid boundaries are central to many natural and engineered processes. In liquid–liquid systems, these reactions drive polymer synthesis, catalysis, and extraction methods. At liquid–solid interfaces, they play a critical role in heterogeneous catalysis, battery operation, and corrosion. Similarly, in solid–solid systems, interfacial reactions influence material properties in ceramics, alloys, and semiconductors. In all cases, the coupling of mass transport across boundaries with reaction kinetics poses significant challenges for predictive modeling, particularly when a reactant strongly partitions into an adjacent phase.

In this work, we develop an analytical framework for interfacial reaction–diffusion dynamics in systems characterized by large partition coefficients. We begin by formulating coupled partial differential equations that describe the diffusion of a reactant in Phase 1, the equilibrium partitioning at the interface (quantified by a partition coefficient K), and the reaction–diffusion processes in Phase 2. By nondimensionalizing concentration, length, and time scales, we identify two key dimensionless groups: a normalized reaction time, η = k′t, where k′ is a lumped first‑order rate constant, and a partition–diffusion parameter, κ = K√(D₂/D₁), which couples equilibrium partitioning with the diffusivities in the two phases.

We derive analytic expressions that quantify the key scales for the reaction rate, interfacial flux, interfacial concentration, and cumulative product formation in short-, intermediate-, and long-time regimes. At early times (η ≪ 1), the reaction is dominated by diffusion in Phase 2, and the interfacial rate grows as η¹ᐟ², reflecting the development of a reaction–diffusion boundary layer. At intermediate times (η ∼ 1), reactant consumption is balanced by diffusive replenishment from Phase 1, resulting in a plateau of the normalized reaction rate. At late times (η ≫ κ⁻²), depletion of the reactant in Phase 1 and increased transport resistance lead to a decay of the reaction rate proportional to η⁻¹ᐟ². By providing rigorous bounds and asymptotic expressions for interfacial reaction rates and fluxes, our framework offers a predictive tool for the rational design of processes across chemical engineering and materials science.