A Similarity Parameter for Capillary Flows of Relevance to Micropropulsion

A similarity parameter for quasi-steady fluid flows advancing into horizontal capillary channels is presented. This parameter, which may be used to scale propellant feeding rates in microthrusters, can be interpreted as the ratio of the average fluid velocity in the capillary channel to a characteristic velocity of quasi-steady capillary flows. It allows collapsing a large data set of previously published and recent measurements spanning five orders of magnitude in the fluid velocity, fourteen different fluids, and four different geometries onto a single curve, and indicates the existence of a universal prescription for such flows. On time scales longer than the characteristic time it takes for the flow to become quasi-steady, the one-dimensional momentum equation leads to a non-dimensional relationship between the similarity parameter and the penetration depth that agrees well with most measurements. Departures from that prescription can be attributed to gravitational effects that are not accounted for in the one-dimensional theory.