Heuristic Approach to Understanding the Accumulation Process in Hydrothermal Pores

One of the central questions of humankind is: which chemical and physical conditions are necessary 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 concentrated formamide solutions. Recently, it could be shown, using finite-element calculations combining thermophoresis and convection processes in hydrothermal pores, that sufficiently high formamide concentrations could be accumulated to form prebiotic molecules (Niether et al. (2016)). Depending on the 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 an effective accumulation, only if the aspect ratio is above a certain threshold, and the corresponding transient studies display a sudden increase of the accumulation after a certain time. Neither of the observations were explained. In this work, we derive a simple heuristic model, which explains both phenomena. The physical idea of the approach is a comparison of the time to reach the top of the 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 molecules are flushed out of the pore. If the time is long enough, the formamide molecules can reach the downstream and accumulate at the bottom of the pore. Analysing the optimal aspect ratio as function of concentration, we find that, at a weight fraction of $w=0.5$ , a minimal pore height is required for effective accumulation. At the same concentration, the transient calculations show a maximum of the accumulation rate.