Convective drying at the pore scale is modelled using a two-component two-phase pseudopotential lattice Boltzmann model (LBM). Two lattice Boltzmann equations are solved, one for liquid water and its vapour and one for dry air. Water vapour is assumed to be well mixed with air forming wet air, while air can also be dissolved in liquid water at low concentration. The approach is shown to be able to model the binary diffusion of vapour and air in the gas phase following Fick’s law. Numerical stability is guaranteed using the lattice Boltzmann cascaded collision operator, which also provides flexibility to vary the mass fraction of water vapour from 2% up to 90% of the gas mixture. Contact angles can be chosen in a wide range extending a single-component approach to two-component systems. The model is validated based on microfluid drying experiments showing good agreement. The LBM model has been extended to non-isothermal conditions, where the heat transport including latent heat is modelled using a finite difference approach and coupled to LBM through the equation of state. Convective drying of a dual-porosity medium shows two drying regimes, a first drying period at a higher drying rate followed by a second drying period at reduced drying rate. The transition from the first to the second period is observed when capillary pumping from large pores to fine pores at the surface fades out. Based on the capillary pumping principle, we design layered porous media with different pore size and contact angle that guarantee capillary pumping to the surface until low degree of saturation, showing high drying rate and short drying period. Finally, the evaporative cooling effect of the wet porous medium during drying is assessed as a potential mechanism in cooling technologies.