Formation mechanism of thermally controlled pH gradients

Spatial proton gradients create energy in biological systems and are likely a driving force for prebiotic systems. Due to the fast diffusion of protons, they are however difficult to create as steady state, unless driven by other non-equilibria such as thermal gradients. Here, we quantitatively predict the heat-flux driven formation of pH gradients for the case of a simple acid-base reaction system. To this end, we (i) establish a theoretical framework that describes the spatial interplay of chemical reactions with thermal convection, thermophoresis, and electrostatic forces by a separation of timescales, and (ii) report quantitative measurements in a purpose-built microfluidic device. We show experimentally that the slope of such pH gradients undergoes pronounced amplitude changes in a concentration-dependent manner and can even be inverted. The predictions of the theoretical framework fully reflect these features and establish an understanding of how naturally occurring non-equilibrium environmental conditions can drive pH gradients.