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This paper investigates particle deposition driven by fluid evaporation in a single pore channel representative of those found in porous membranes. A moving boundary problem for the 2D heat equation is coupled with an evolution equation for the pore radius, and describes the physical processes of fluid evaporation, diffusion of the particle concentration, and deposition on the pore channel wall. Furthermore, a stochastic differential equation (SDE) approach based on a Brownian motion particle-level description of diffusion is used as a similar phenomenological representation to the partial differential equation (PDE) model. Sensitivity analysis reveals trends in dominant model parameters such as evaporation rate, deposition rate, the volume scaling coefficient, and investigates the monotonicity of concentration. Evaluations of the asymptotically reduced model and the SDE model against the 2D PDE model are done in terms of the pore radius and solute concentration over time. For further exploration, we apply the model to a 2D droplet as well with both deterministic and stochastic approaches.