Solvent-pumped evaporation-driven concentration of an initial distribution of solutes on a porous substrate is considered in one and two dimensions. Approximate analytic solutions to the isotropic advection-dispersion equations are first found for a Gaussian kernel and an infinite domain, following the smoothed particle approximation. Analytic solutions for more general initial distributions are then found as sums of Gaussians, and comparison is made with numerical solutions. In each case, initial distributions are advected toward the stagnation point and concentrated. Two-dimensional analysis is then extended to describe anisotropy in permeability and diffusion, and hydrodynamic dispersion. Radial-flow experiments are performed using filter papers and water-soluble dyes. Diffusion coefficients, temperature and humidity profiles, and the evolution of spot distributions are measured. The results confirm minor anisotropy in permeability and diffusion, limited hydrodynamic dispersion, and largely uniform evaporation. Péclet numbers over 2500 are demonstrated. Evaporation-driven concentration provides a mechanism for solute transport over long timescales. Potential applications lie in the design of paper spray microanalytical devices operating by solvent pumping rather than capillary flow.
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