Figure 1

Absolute or convective instability transition loci in the $\{\mathrm{Re},\mathrm{We}\}$ plane for different values of $\{\alpha ,\beta \}$. Regions below (above) the curves correspond to absolutely (convectively) unstable configurations. The region of absolute (convective) instability corresponds to bubbling (jetting).Reuse & Permissions

Figure 2

Bubbling to jetting. Liquid: ethanol-water $50/50\%\mathrm{vv}$, $\mu =0.002\mathrm{Pa}·\mathrm{s}$, $\sigma =0.023\mathrm{N}·{\mathrm{m}}^{-1}$), $T=28°\mathrm{C}$. Orifice diameter $D=200\mu \mathrm{m}$. (a) $Q_l\sim 13\mathrm{mL}/\min$, $Q_g\sim 0.65\mathrm{mL}/\min$; (b) $Q_l\sim 23\mathrm{mL}/\min$, $Q_g\sim 0.25\mathrm{mL}/\min$; (c) $Q_l\sim 23\mathrm{mL}/\min$, $Q_g\sim 0.5\mathrm{mL}/\min$. The arrow indicates the flow direction; i.e., the nozzle is at the left of the photographs.Reuse & Permissions

Figure 3

Experimental values of $\{\mathrm{Re},\mathrm{We}\}$ for four selected liquids (circles: $\{\alpha =760,\beta =68\}$; diamonds: $\{\alpha =800,\beta =324\}$; triangles: $\{\alpha =850,\beta =544\}$; squares: $\{\alpha =746,\beta =139\}$) from data in Ref. 26, and their corresponding $C/A$ instability transition curve under the assumption that $R_j\ll D$. The three square points (a), (b), and (c) correspond to the experiments given in Figs. 2a, 2b, 2c, respectively.Reuse & Permissions

Figure 4

(1) and (2) illustrative experimental configuration to produce a gas jet in an extensional viscous flow. A liquid (glucose syrup $\mu \simeq 7\mathrm{Pa}·\mathrm{s}$) is forced to flow out of a capillary tube with 1 mm O.D. Inside it, a concentric tube with 0.4 mm O.D. feeds a continuous stream of gas. In this case, the liquid domain is not infinite since the extensional flow is produced by an external focusing gas forced through a $800\mu \mathrm{m}$ orifice aligned with the concentric tubes at an offset adjustable distance from 0.5 mm to 1 mm, as sketched [see Ref. 27 ]. The orifice is bored in a $150\mu \mathrm{m}$ thick plate. The gas pressure drop through the orifice is about 10 kPa. (3) A liquid jet with a gas core issuing from the orifice, as seen downstream. In (3)-(I) the jet is convectively unstable, while in (3)-(II) the jet “bubbles” right at the nozzle exit, indicating absolute instability.Reuse & Permissions