Digital Sub-millimeter Bubble-Jets

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 $We_d\sim Ca_c^{-5.7}$ and jet-dropping line at $We_d\sim Ca_c^{-4.2}$, as well as orthogonally overlaping Taylor bubble area from annular flow pattern. And the jetting velocity expresses as $u_{\text{jet}}\sim [\rho_c^2\sigma (Q_c + Q_d)^2]/(\mu_c^3 W_{\text{local}}^{1.6}H^{0.4})$, 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.