Digital Sub-millimeter Bubble-Jets

Abstract

We create digital sub-millimeter bubble-jet emitting in gas-liquid co-flows at tapered chip zone for moderate $Re\sim [20,120]$. Self-similarity features are revealed at the tapered area and giving birth to a local model. Local self-scaling characteristic quantities, $W_{\text{local}}$ and $L_{\text{cone}}$, are introduced to scale energies and progresses at onsets of bubble-jets, which gives highly universal phase diagram and also scaling law of jet velocity. The phase diagram draws critical bubble-jetting line at $W{e}_d\sim C{a}_c^{-5.7}$ and jet-dropping line at $W{e}_d\sim C{a}_c^{-4.2}$, as well as orthogonally overlaping Taylor bubble area from annular flow pattern. And the jetting velocity expresses as $u_{\text{jet}}\sim [\ddot{I}{}_c^2\ddot{I}ƒ(Q_c+Q_d{)}^2]/(\hat{I}{¼}_c^3{W}_{\text{local}}^{1.6}{H}^{0.4})$, which clarifies the compound mechanisms for bubble-jet emitting by combined competing of interfacial tension, inertia, viscosity, and the local tapered geometries. These universalities confirm reciprocally similarities of the bubble-jet emitting processes on behaviors and flow structures at the local tapered zone.