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Abstract Droplet microarray technology is of great interest in biology and chemistry as it allows for significant reactant savings and massive parallelization of experiments. Upon scaling down the footprint of each droplet in an array, it becomes increasingly challenging to produce the array drop‐by‐drop. Therefore, techniques for parallelized droplet production are developed, e.g., dip‐coating of biphilic substrates. However, it is in general difficult to tailor the characteristics of individual droplets, such as size and content, without updating the substrate. Here, the method of dip‐coating of uniformly patterned biphilic substrates in so‐called “acceleration‐mode” to produce droplet arrays featuring gradients in droplet height for fixed droplet footprint is developed. The results herein present this method applied to produce drops with base diameters varying over orders of magnitude, from as high as 6 mm to as small as 50 µm; importantly, the experimentally measured power‐law‐dependency of volume on capillary‐number matches analytical theory for droplet formation on heterogenous substrates though the precise quantitative values likely differ due to 2D substrate patterning. Gradient characteristics, including average droplet volume, steepness of the gradient, and its monotonicity, can all be tuned by changing the dip‐coating parameters, thus providing a robust method for high‐throughput screening applications and experiments. 

We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate $$Q$$ and the applied pressure drop $$\unicode[STIX]{x0394}p$$ , in apparent disagreement with Darcy’s law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy’s law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials.