Hydrogel could serve as a matrix material of new classes of solar cells and photoreactors with embedded microfluidic networks. These devices mimic the structure and function of plant leaves, which are a natural soft matter based microfluidic system. These unusual microfluidic-hydrogel devices with fluid-penetrable medium operate on the basis of convective-diffusive mechanism, where the liquid is transported between the non-connected channels via molecular permeation through the hydrogel. We define three key designs of such hydrogel devices, having linear, T-shaped, and branched channels and report results of numerical simulation of the process of their infusion with solute carried by the incoming fluid. The computational procedure takes into account both pressure-driven convection and concentration gradient-driven diffusion in the permeable gel matrix. We define the criteria for evaluation of the fluid infusion rate, uniformity, solute loss by outflow and overall performance. The T-shaped channel network was identified as the most efficient one and was improved further by investigating the effect of the channel-end secondary branches. Our parallel experimental data on the pattern of solute infusions are in excellent agreement with the simulation. These network designs can be applied to a broad range of novel microfluidic materials and soft matter devices with distributed microchannel networks.