Unconditional jetting

TL;DR

This paper investigates conditions under which capillary jets can be made arbitrarily thin or flow rates arbitrarily small, identifying parameter regions where the jet remains supercritical and does not transition to dripping.

Contribution

It introduces a new understanding of jet stability regions where the jet remains supercritical regardless of flow rate, supported by analytical studies and experimental validation.

Findings

Jets can be made arbitrarily thin in certain parameter regions.

Supercritical jet flow persists independently of flow rate in these regions.

Analytical models match experimental observations.

Abstract

Capillary jetting of a fluid dispersed into another immiscible phase is usually limited by a critical Capillary number, a function of the Reynolds number and the fluid properties ratios. Critical conditions are set when the minimum spreading velocity of small perturbations $v^*_-$ along the jet (marginal stability velocity) is zero. Here we identify and describe parametrical regions of high technological relevance, where $v^*_- > 0$ and the jet flow is always supercritical independently of the dispersed liquid flow rate: within these relatively broad regions, the jet does not undergo the usual dripping-jetting transition, so that either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or the issued flow rate can be made arbitrarily small. In this work, we provide illustrative analytical studies of asymptotic cases for both negligible and dominant inertia forces. In this latter case, requiring a non-zero jet surface velocity, axisymmetric perturbation waves ``surf'' downstream for all given wave numbers while the liquid bulk can remain static. In the former case (implying small Reynolds flow) we found that the jet profile small slope is limited by a critical value; different published experiments support our predictions.