Dynamics of bouncing-versus-merging response in jet collision

A new regime of oblique jet collision, characterized by low impact inertia and jet merging through bridge formation, is observed and thereby completes the entire suite of possible jet collision outcomes of (soft) merging, bouncing, and (hard) merging with increasing inertia. These distinct regimes, together with the observed dependence of the collision outcome on the impact angle and liquid properties, are characterized through scaling analysis by considering the competing effects of impact inertia, surface tension, and viscous thinning of the interfacial air gap leading to merging.

Figure 1

Time-resolved imaging (time stamps in ms are in brackets) of head-on collisions of hydrocarbon droplets in 1 atm air: (I) regime I, soft merging, $\mathrm{We}=0.2$; (II) regime II, bouncing, $\mathrm{We}=0.5$; (III) regime III, hard merging, $\mathrm{We}=32.8$; and (IV) regime IV, separation after merging, $\mathrm{We}=61.4$. (Abstracted from Qian and Law [10]. Here the Weber number (We) is defined as $\mathrm{We}=\left(2{\rho }_l{U}_{}^{2}R\right)/\sigma$, where $U$ is the relative velocity between the impacting droplets, $R$ is the droplet radius, ${\rho }_l$ is the liquid density, and $\sigma$ is the surface tension.)

Figure 2

(I)–(IV) Images showing the complete suite of the collision response with increasing collision velocity (or impact inertia): (I) merging, (II) bouncing (inset: zoomed view of the interface), (III) merging (with subsequent chain structure), and (IV) merging followed by sheet formation and further breakup. Liquid: $n$-hexadecane; pressure: 1 bar. (a) Viscous loss through internal motion results in a smaller angle between bounced jets. Blue arrows show the direction of motion; $a$ is the impact angle, and $\beta$ is the rebound angle. (b) Shape oscillation of the bounced jets. (c) Sketch of the jet cross-section deformation and dimple formation. The deformation is not drawn to scale: the height of the dimple is much less than the dimple width.

Figure 3

Quantitative regime boundaries of (a) $n$-hexadecane, (b) $n$-tetradecane, (c) $n$-dodecane, and (d) n-decane, showing the similar trend.

Figure 4

Soft transition (open symbols) and hard transition (solid symbols) boundaries on a St-Γ map. St is the Stokes number, $\mathrm{St}=\left({\rho }_{l}RU\right)/{\eta }_g$; $\mathrm{\Gamma }$ is the velocity ratio, $\mathrm{\Gamma }=V/V_c=V{({\rho }_{l}R/\sigma )}^{1/2}$, where $U$ is the effective impact velocity, $U=Vsin\alpha , V$ is the jet velocity, $\alpha$ is the half angle between the jets, $R$ is the jet radius, ${\rho }_l$ is liquid density, ${\eta }_g$ is gas viscosity, and $\sigma$ is the surface tension.