Phoretic interactions in two-medium wedge geometries

We investigate the diffusiophoretic motion of a chemically isotropic active colloid in a three-dimensional wedge formed by two distinct fluid media, in the limit of vanishing Péclet and Reynolds numbers. The concentration field is obtained using the Fourier–Kontorovich–Lebedev transform, yielding an exact representation for arbitrary wedge opening angles and interfacial contrasts. We introduce the interfacial parameter Γ =(1-λ )/(1+λ ) Γ = ( 1 - λ ℓ ) / ( 1 + λ ℓ ) , where λ λ denotes the diffusivity contrast and ℓ the solute partition coefficient. For Γ =± 1 Γ = ± 1 and commensurate wedge angles, the solution reduces to finite image constructions, with distinct structures for even and odd commensurability. The general solution also recovers the planar-interface and semi-infinite-interface limits. The leading-order translational phoretic velocity is derived from the concentration field, revealing a strong interplay between wedge geometry and interfacial properties that governs both the magnitude and direction of particle motion. This work provides a framework for understanding and controlling phoretic transport in confined multiphase environments and offer a basis for extensions to finite-size geometries and mixed fluid–fluid and solid boundary conditions. Our results may find applications in the control of active-particle transport in confined multiphase environments, where interfacial properties and geometry can be exploited to tune phoretic motion.