Bouncing jet: A Newtonian liquid rebounding off a free surface

We find that a liquid jet can bounce off a bath of the same liquid if the bath is moving horizontally with respect to the jet. Previous observations of jets rebounding off a bath (e.g., the Kaye effect) have been reported only for non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian fluids, including mineral oil poured by hand. A thin layer of air separates the bouncing jet from the bath, and the relative motion replenishes the film of air. Jets with one or two bounces are stable for a range of viscosity, jet flow rate and velocity, and bath velocity. The bouncing phenomenon exhibits hysteresis and multiple steady states.

Figure 1

A liquid jet bounces twice before merging with the bath, which is moving to the right. The jet and bath are silicone oil of the same viscosity. The upper and lower pictures were taken from above and from below the bath surface; the images were not obtained at the same time or the same angle, so small differences exist. The jet’s image can be seen reflected on the surface. Parameters: liquid viscosity $\mu =102\text{mPa}\text{s}$ (about 100 times more viscous than water), jet flow rate $Q=0.35{\text{cm}}^3∕\text{s}$, falling height $H=5.0\text{cm}$, and horizontal velocity of the bath $V_{bath}=15.7\text{cm}∕\text{s}$.

Figure 2

Experimental setup: a bath of silicone oil is rotated under a falling stream of the same oil. A camera in the laboratory frame records the motion through the tank’s clear acrylic side.

Figure 3

Photographs (top) and schematic drawings (bottom) of the jet for different horizontal velocities of the bath, $V_{bath}$: (a) 0.656 cm/s, a jet bouncing nearly vertically; (b) 3.28 cm/s, a jet bouncing more obliquely; (c) 42.3 cm/s, a trailing (nonbouncing) jet. Increasing $V_{bath}$ imparts more horizontal momentum to the rebounding jet. The schematics exaggerate the thickness of the layer of air between the jet and bath. For (a) and (b), the dark horizontal line is the surface’s meniscus on the outer tank wall; in (c), the top and bottom images were taken above and below the surface, so that the surface extends back in perspective. Parameters in (a) and (b) were $\mu =349\text{mPa}\text{s}$, $Q=0.16{\text{cm}}^3∕\text{s}$, $H=4.2\text{cm}$; in (c), $\mu =102\text{mPa}\text{s}$, $Q=0.35{\text{cm}}^3∕\text{s}$, $H=5.0\text{cm}$.

Figure 4

Photographs of the bouncing jet for flow rates $Q$: (a) $0.23$ and (b) $0.44{\text{cm}}^3∕\text{s}$; the top and bottom pictures in each case are, respectively, above and below the surface. The jet with the greater flow rate pushes the surface deeper and the jet rebounds to a lower height. Each jet rebounds moving more slowly than its initial speed (so that, by continuity, the jet becomes thicker). The inset in (b) is a top view of the area with the dashed outline; this region in the picture is just below the bath level and is in shadow. The closed black curves within the inset show a horizontal cross section of the interfaces just below the bath level. Parameters for both (a) and (b): $\mu =102\text{mPa}\text{s}$, $H=5.0\text{cm}$, $V_{bath}=15.7\text{cm}∕\text{s}$.

Figure 5

Conditions for which the jet bounces. (a) Bounces could be initiated between the lines with closed and open points but could not be initiated below the lines with closed points or above the open points; a trailing jet was often observed above the open points [viscosity values $\mu =53$ (◼, ◻), 102 (▴, ▵), 211 (●, ○), and 349 mPa s (▾, ▿)]. The bath velocity at which the transitions occur was reproducible typically within 4%; the uncertainty was greater where the transition curves have a steeper slope. (b) Dependence of the region of stable bounce on $V_{jet}$ and $V_{bath}$; the range of $V_{jet}$ $\left(38-170\text{cm∕s}\right)$ corresponds to $H$ values 1.7–14.1 cm. Error bars show the uncertainty of each transition point. Around $V_{jet}\approx 100\text{cm}∕\text{s}$, there is a greater uncertainty corresponding to a transition from a nonentraining jet to an air-entraining jet as $V_{jet}$ is increased.

Figure 6

Multiplicity: the three states (a)–(c) are stable for the same conditions. The bath surface is at the top of each photograph, and below each photograph is a corresponding schematic diagram. (a) Plunging jet with air entrainment and no bounce; bubbles break off from the top edge of the entrained air sheath. (b) Half-entraining jet, which entrains air only on its lower edge; bubbles (blurred to a faint line by the long exposure) break off from the entrained air skirt. (c) Bouncing jet, whose curved surface refracts light and produces a distorted image of the background. Parameters: $\mu =106\text{mPa}\text{s}$, $Q=0.35{\text{cm}}^3∕\text{s}$, $H=6.4\text{cm}$, $V_{bath}=15.2\text{cm}∕\text{s}$.

Figure 7

Plunging is argued to be energetically favored below the curves while bouncing is energetically favored above the curves (see text). The data for four viscosity values (ranging by a factor of 7) collapse onto the same approximate curve. The energy $E_{plunging}$, given in (5) using the length $L$ of (7), is from the viscous drag of the plunging jet. The energy $E_{bouncing}$, given in (1), is from the surface area of the bouncing jet. The solid symbols and data points are the same as in Fig. 5a. Inset: the penetration length $S$ [see Fig. 6c] varies linearly with $Q$ $\left(\mu =211\text{mPa}\text{s}\right)$ for different bath velocities $V_{bath}=7.0\text{cm}∕\text{s}$ $(◁)$, 14.0 cm/s $(+)$, 17.5 cm/s $(◇)$, 21.0 cm/s $(\times )$.