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Inorganic precipitate membranes play an important role in chemobrionics and origin of life research. They can involve a range of catalytic materials, affect crystal habits, and show complex permeabilities. Microfluidic flows are a powerful tool to drive reactions far from equilibrium and thus induce chemical selforganization. This dissertation documents results obtained from three different studies that utilize Y-shaped microfluidic devices to grow several types of complex inorganic membranes and explore their growth dynamics, catalysis, and reactivity as well as in situ and ex situ characterizations of their chemical compositions. We produce such membranes in a microfluidic device at the reactive interface between laminar streams of hydroxide and Co(II) solutions. The resulting linear membranes show striking color bands that over time expand in the direction of the Co(II) solution. The cumulative layer thicknesses (here up to 600 µm) obey square root laws indicating diffusion control. The effective diffusion coefficients are proportional to the hydroxide concentration but the membrane growth slows down with increasing concentrations of Co(II). Based on spatially resolved Raman spectra and other techniques, we present chemical assignments of the involved materials. Electron microscopy reveals that the important constituent alpha-Co(OH)2 crystallizes as thin hexagonal microplatelets. Under drying, the membrane curls into spirals revealing mechanical differences between the layers. The layered structures indicate steep chemical gradients at the interface. We also synthesize mineral membranes and test their ability to catalyze the formation of pyrophosphate from phosphate and acetyl phosphate across steep pH gradients in microfluidic devices. The mineral membranes involve iron(II), iron(III), and other divalent metal cations (calcium, manganese, cobalt, copper, zinc, and nickel). We then study the chemical compositions of the precipitate membranes (which included vivianite, goethite, and green rust) using in-situ and ex-situ micro-Raman spectroscopy. The yields of pyrophosphate are determined by aqueous 31P NMR spectroscopy. We found that Fe(II)+ and Ca(II) are the best catalysts for pyrophosphate synthesis among investigated ions; Fe(III) and mixed-valence iron membranes are also able to promote pyrophosphate formation. In addition, the pH gradients across the membranes affect the pyrophosphate yields and the smallest pH gradient results in the highest yield. Since pyrophosphate might have functioned as an energy storage/currency molecule on early Earth, essential for the emergence of life, These results suggest a possible route of substrate phosphorylation in prebiotic hydrothermal systems. Studies of membrane formation in microfluidic devices have been limited to non-redox and purely inorganic reactions. Here, we also investigate the formation of hybrid membranes at the interface of silver nitrate and 3,3',5,5'-tetramethylbenzidine solutions that are steadily co-injected into a microfluidic device. The membrane thickening occurs in both directions and reveals oscillatory dynamics. The hybrid membrane mainly consists of hair-like Ag microstructures, Ag nanowires, and unbranched TMB-TMB2+ microfibers. Branched dendrite-like fibers form on the TMB side when the flow is stopped. We characterize these components with techniques including micro-Raman and energy dispersive X-ray spectroscopy as well as scanning electron microscopy. We also study the effects of initial concentration ratios on the membrane thickening speed and its opaqueness. This dissertation focuses on the self-organization of purely inorganic membranes and organic-inorganic hybrid membranes at the interface of fluid flow in microfluidic devices and demonstrates an application to the origins-of-life research by forming simulated hydrothermal vent precipitates with steep gradients.