The minimum or natural rate of flow and droplet size ejected by Taylor cone–jets: physical symmetries and scaling laws

We aim to establish the scaling laws for both the minimum rate of flow attainable in the steady cone–jet mode of electrospray, and the size of the resulting droplets in that limit. Use is made of a small body of literature on Taylor cone–jets reporting precise measurements of the transported electric current and droplet size as a function of the liquid properties and flow rate. The projection of the data onto an appropriate non-dimensional parameter space maps a region bounded by the minimum rate of flow attainable in the steady state. To explain these experimental results, we propose a theoretical model based on the generalized concept of physical symmetry, stemming from the system time invariance (steadiness). A group of symmetries rising at the coneto-jet geometrical transition determines the scaling for the minimum flow rate and related variables. If the flow rate is decreased below that minimum value, those symmetries break down, which leads to dripping. We find that the system exhibits two instability mechanisms depending on the nature of the forces arising against the flow: one dominated by viscosity and the other by the liquid polarity. In the former case, full charge relaxation is guaranteed down to the minimum flow rate, while in the latter the instability condition becomes equivalent to 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercialShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 15 (2013) 033035 1367-2630/13/033035+13$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft