Heuristic Approach to Understanding the Accumulation Process in Hydrothermal Pores

One of the central questions of humankind is: which chemical and physical conditions arenecessary to make life possible? In this “origin-of-life” context, formamide plays an important role,because it has been demonstrated that prebiotic molecules can be synthesized from concentratedformamide solutions. Recently, it could be shown, using finite-element calculations combiningthermophoresis and convection processes in hydrothermal pores, that sufficiently high formamideconcentrations could be accumulated to form prebiotic molecules (Niether et al. (2016)). Depending onthe initial formamide concentration, the aspect ratio of the pores, and the ambient temperature,formamide concentrations up to 85 wt % could be reached. The stationary calculations show aneffective accumulation, only if the aspect ratio is above a certain threshold, and the correspondingtransient studies display a sudden increase of the accumulation after a certain time. Neither of theobservations were explained. In this work, we derive a simple heuristic model, which explainsboth phenomena. The physical idea of the approach is a comparison of the time to reach the top ofthe pore with the time to cross from the convective upstream towards the convective downstream.If the time to reach the top of the pore is shorter than the crossing time, the formamide moleculesare flushed out of the pore. If the time is long enough, the formamide molecules can reach thedownstream and accumulate at the bottom of the pore. Analysing the optimal aspect ratio as functionof concentration, we find that, at a weight fraction of w = 0.5, a minimal pore height is required foreffective accumulation. At the same concentration, the transient calculations show a maximum of theaccumulation rate