Flow characteristics at the interface during droplet formation in a flow-focusing microfluidic channel—numerical analysis of dripping and jetting regimes

This work has the purpose to elucidate in deeper detail the conjugated physical phenomena at the interface between two immiscible fluids in microfluidic devices. The two typical regimes—dripping and jetting—emerging in flow-focusing devices are considered for the analysis. Dynamic (time-dependent analysis of fixed or Lagrangian-tracked points) and local (lines along the interface, at a fixed time instance) analyses have been conducted from a parallel numerical simulation on a fine numerical grid. The results comprise various pressures and tangential stresses and their balance during the droplet formation process with special attention paid to the moments and locations of the droplet release. It was found that the dripping regime is characterized by the local balance of the pressure drop due to surface tension \({ {\Delta p}}_{\upsigma } \text{and}\) ${\mathrm{\Delta }p}_{\mathrm{\sigma }}\text{and}$ the Laplace pressure \({ {\Delta p}}_{\text{Lapl}}\) ${\mathrm{\Delta }p}_{\text{Lapl}}$ across the interface. Only at the last moments before the droplet pinch-off does the former pressure dominate. In contrast, in the jetting regime, there is a clear domination of the pressure due to tension during the whole process of droplet formation. Shear stresses, presented by the von Mises criterion, are several times (jetting regime) or even an order of magnitude (dripping regime) lower than the surface tension pressure and the Laplace pressure. In both regimes, when the interface curvature κ changes locally its sign, the pressure at the centerline axis shows a clear local maximum. For the jetting regime, the downstream derivative of this centerline pressure is the first parameter that changes along the jet axis—thus indicating the onset of instabilities for this regime—and it is then followed by a wavelike change of the radius of the jet.