Partial coalescence of soap bubbles

A bubble coalesces with an initially planar soap film.

We present the results of an experimental investigation of the merger of a soap bubble with a planar soap film. When gently deposited onto a horizontal film, a bubble may interact with the underlying film in such a way as to decrease in size, leaving behind a smaller daughter bubble with approximately half the radius of its progenitor. The process repeats up to three times, with each partial coalescence event occurring over a time scale comparable to the inertial-capillary time. Our results are compared to the recent numerical simulations of Martin and Blanchette (2015) and to the coalescence cascade of droplets on a fluid bath.

See paper here:  Pucci, Harris & Bush (2015)

See related Gallery of Fluid Motion winner here:  Pucci, Harris & Bush (2016) , where you can link to the Video directly.

The hydraulic bemp: no, not bump


When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact, provided a critical flow rate is exceeded.We here examine a phenomenon that arises below this jump threshold, a circular deflection of relatively small amplitude on the free surface that we call the hydraulic bump. The form of the circular bump can be simply understood in terms of the underlying vortex structure and its height simply deduced with Bernoulli arguments. As the incoming flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps. The relation between this polygonal instability and that arising in the hydraulic jump is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking nested structures with polygonal jumps bound within polygonal bumps. The absence of a pronounced surface signature on the hydraulic bump indicates the dominant influence of the subsurface vorticity on its instability.

See paper:  Labousse & Bush (2013)

Drops bouncing on a wet inclined plane

High-speed imaging of a drop splitting into three after striking an incline.

We present the results of an experimental investigation of fluid drops impacting an inclined rigid surface covered with a thin layer of high viscosity fluid. We deduce the conditions under which droplet bouncing, splitting and merger arise. Particular attention is given to rationalizing the observed contact time and coefficients of restitution, the latter of which require a detailed consideration of the drop energetics. The study provides further insight into the dynamics of drops bouncing and walking on a vibrating fluid bath.

See paper: Gilet & Bush (2012)

Water entry and cavity dynamics

We present the results of a combined experimental and theoretical investigation of the vertical impact of low-density spheres on a water surface. Particular attention is given to characterizing the sphere dynamics and the influence of its deceleration on the shape of the resulting air cavity. A theoretical model is developed which yields simple expressions for the pinch-off time and depth, as well as the volume of air entrained by the sphere. Theoretical predictions compare favorably with our experimental observations, and allow us to rationalize the form of water-entry cavities resulting from the impact of buoyant and nearly buoyant spheres.

See Aristoff, Truscott, Techet & Bush (2010)


Water impact of small hydrophobic bodies

The development of the air cavity behind a hydrophobic sphere striking the water surface from above..

We considered the impact of small hydrophobic spheres on a water surface. Particular attention was given to characterizing the shape of the resulting air cavity when the cavity collapse is driven principally by surface tension rather than gravity. A parameter study revealed the dependence of the cavity structure on the governing dimensionless groups. A theoretical description based on the solution to the Rayleigh–Besant problem was developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time and the sphere’s depth at cavity pinch-off.

See paper Aristoff & Bush, JFM (2009) .

The dynamics of viscous sheets

We present the results of a combined theoretical and numerical investigation of the rim-driven retraction of flat fluid sheets in both planar and circular geometries. Particular attention is given to the influence of the fluid viscosity on the evolution of the sheet and its bounding rim. In both geometries, after a transient that depends on the sheet viscosity and geometry, the film edge eventually attains the Taylor– Culick speed predicted on the basis of inviscid theory. The emergence of this result in the viscous limit is rationalized by consideration of both momentum and energy arguments. We first consider the planar geometry and deduce new analytical expressions forthe speed of the film edge at the onset of rupture and the evolution of the maximum film thickness for viscous films. In order to consider the expansion of a circular hole, we develop an appropriate lubrication model that predicts the form of the early stage dynamics of film rupture. Simulations of a broad range of flow parameters confirm the importance of geometry on the dynamics, verifying the exponential hole growth reported in early experimental studies.

See paper:   Savva & Bush, JFM (2009).

The expansion of a hole in a soap film following puncture by a needle. The hole expands at high speed in response to surface tension.

Drop propulsion in tapered tubes

We present the results of a combined experimental and theoretical investigation of the motion of wetting droplets in tapered capillary tubes. We demonstrate that drops may move spontaneously towards the tapered end owing to the Laplace pressure gradient established along their length. The influence of gravity on this spontaneous motion is examined by studying drop motion along a tilted tube with its tapered end pointing upwards. Provided the tube taper varies, an equilibrium height may be achieved in which the capillary force is balanced by the drop’s weight. We deduce the family of tube shapes that support a stable equilibrium.

See paper:  Renvoise, Bush, Prakash & Quere (2009).

Spontaneous oscillations of a floating fluid lens


When an oil drop is placed on a water surface, it assumes the form of a sessile lens. We consider the curious behaviour that may arise when the oil contains a water-insoluble surfactant: the lens radius oscillates in a quasi-periodic fashion. While this oscillatory behaviour has been reported elsewhere, a consistent physical explanation has yet to be given. We present the results of an experimental investigation that enable us to elucidate the subtle mechanism responsible. Videomicroscopy reveals that the beating behaviour is generated by a subtle process of partial emulsification at the lens edge and sustained by evaporation of surfactant from the water surface.

See paper here:  Stocker & Bush (2007)

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Surface tension and the hydraulic jump

The circular hydraulic jump may arise when a fluid jet falling vertically at high Reynolds number strikes a horizontal plate. Fluid is expelled radially, and the layer generally thins until reaching a critical radius at which the layer depth increases abruptly. Predictions for the jump radius based on inviscid theory were presented by Rayleigh (1914). The dominant influence of fluid viscosity on the jump radius was elucidated by Watson (1964), who developed an appropriate description of the boundary layer that develops from the lower boundary. We have elucidated the influence of surface tension on the circular hydraulic jump, both its size ( Bush & Aristoff, JFM 2003 ) and stability ( Bush, Aristoff & Hosoi, JFM 2006 ), through  combined theoretical and experimental investigations.

Circular Jumps and Crowns

Figures 1 and 2 illustrate the laminar circular hydraulic jump, and Figure 3 shows a turbulent circular jump with a pronounced outer crown.

The polygonal regime

Elegaard et al. (1998, 1999) first demonstrated that the axisymmetry of the viscous hydraulic jump may be broken, resulting in steady polygonal jumps. We have further examined these striking flow structures.

The clover regime

In addition to the polygonal forms, we have discovered a new class of steady asymmetric jumps that include structures resembling cat’s eyes, three and four-leaf clovers, bowties and butterflies (Figures 7-12). We have conducted a parameter study that reveals the dependence of the jump structure on the governing parameters. We acknowledge Jeff Leblanc for his assistance with our study.



Bush, J.W.M. & Aristoff, J.M., 2003. The influence of surface tension on the circular hydraulic jump. J. Fluid Mech. 489, 229-238. (Linked above.)

Bush, J.W.M., Aristoff, J.M., Hosoi, A.E., 2006. An experimental investigation of the stability of the circular hydraulic jump. J. Fluid Mech. 558, 33-52. (Linked above)

Ellegaard, C, Hansen, A.E., Haaning, A., Marcussen, A., Bohr, T., Hansen, J.L. and Watanabe, S., 1998. Creating corners in kitchen sink flows. Nature, 392, 767-768.

Ellegaard, C, Hansen, A.E., Haaning, A., Hansen, K., Marcussen, A., Bohr, T., Hansen, J.L. and Watanabe, S., 1999. Polygonal hydraulic jumps. Nonlinearity, 12, 1-7.

Rayleigh, L., 1914. On the theory of long waves and bores. Proc. Roy. Soc. Lond. A. 90, 324.

Watson, E.J., 1964. The spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481-499.

Fluid chains and fishbones

 We examine the form of the free surface flows resulting from the collision of equal jets at an oblique angle. Glycerol-water solutions with viscosities of 15-50 cS were pumped at flow rates of 10-40 cc/s through circular outlets with diameter 2 mm. Characteristic flow speeds are 1-3 m/s. Figures 3-9 were obtained through strobe illumination at frequencies in the range 2.5-10 kHz. Figure 1: At low flow rates, the resulting stream takes the form of a steady fluid chain, a succession of mutually orthogonal fluid links, each comprised of a thin oval sheet bound by relatively thick fluid rims. The influence of viscosity serves to decrease the size of successive links, and the chain ultimately coalesces into a cylindrical stream. As the flow rate is increased, waves are excited on the sheet, and the fluid rims become unstable. The rim appears blurred to the naked eye (Figure 2); however, strobe illumination reveals a remarkably regular and striking flow instability ( Figures 3-6). Droplets form from the sheet rims but remain attached to the fluid sheet by tendrils of fluid that thin and eventually break. The resulting flow takes the form of fluid fishbones, with the fluid sheet being the fish head and the tendrils its bones. Increasing the flow rate serves to broaden the fishbones. Figures 7-9: In the wake of the fluid fish, a regular array of drops obtains, the number and spacing of which is determined by the pinch-off of the fishbones.

Some of these photos have appeared in Hasha & Bush, Gallery of Fluid Motion (2002). A combined theoretical and investigation of fluid chains and fishbones is presented in Bush & Hasha, JFM (2004) .

Figures 1-3


Figures 4-6.

Figures 7-9.

“Music is only mathematics, falling through water.”   
 — Gavin Bantock





The coalescence cascade meets Marangoni


The flows generated when a water drop merges with an alcohol bath.

When a water drop coalesces into a puddle or pond, the dynamics is much more rich than casual observation would suggest. High-speed video imaging reveals that instead of simply disappearing into the underlying bath, it undergoes a series of partial coalescence events in which the droplet radius decreases by roughly 50 percent (Blanchette and Bigioni 2006). In Blanchette, Messio and Bush (2006) , we examine the role of surface tension gradients on the coalescence cascade.

“All know that the drop merges into the ocean,

but few know that the ocean merges into the drop.”

– Kabir


For a clip of our appearance on Discovery Channel’s Time Warp, see the video below.

PRESS:  New York Times


Fluid pipes: jets impinging on a fluid bath












When a pure water jet impinges on a reservoir, capillary waves are excited and propagate up the jet at the same speed that the jet falls, thus giving rise to the standing field of capillary waves evident in Figures 1 and 2. When the reservoir is contaminated by the presence of surfactant, a surface tension gradient between the reservoir and jet arises, and draws surfactant onto the base of the jet. The surfactant serves to impart to the jet surface an effective elasticity, thus suppressing both the capillary wave field and the extensional surface motions expected on the falling jet. The surface tension gradient balances viscous stresses at the jet surface, so that the surface at the base of the jet is entirely quiescent. The jet enters the contaminated reservoir as if through a rigid pipe (Figures 3 and 4).

The results of our combined experimental and theoretical investigation of the fluid pipe phenomenon is presented Hancock & Bush, JFM (2002).

The dynamics of fluid sheets and bells

Photo 1

Photo 2

Photo 3

Photo 4


Photo 6

When a vertical water jet strikes a circular horizontal impactor, the water is deflected into a horizontal sheet. At sufficiently high speeds, the flow results in a circular water sheet, whose radius is set by a balance between inertial and curvature forces. At lower speeds, the sheet sags significantly under the influence of gravity, and

Photo 5

may close, giving rise to a water bell (Figure 1). We have conducted a series of experiments in order to investigate the influence of increasing fluid viscosity on fluid sheets and bells. The circular fluid sheets are marked by an axisymmetry-breaking instability that results in polygonal structures (Figure 2). Fluid streams from the sheet, into then along the rim, and finally streams from the corners of the polygon. In certain parameter regimes, the streams emerging from the corners take the form of a linked chain (Figure 3). The minimum number of sides observed on the polygons was four. By deflecting the sheet from the horizontal, one may produce sagging structures ressembling fluid umbrellas (Figure 4) or fluid parasols (Figure 5). Axisymmetry is also broken in the fluid bells, which assume the form of polyhedra (Figure 6).

This series of photos appears in Buckingham & Bush, Gallery of Fluid Motion (2001) .


“In my courtyard a fountain leaps and sinks back into itself,
Nun-hearted and blind to the world.”

– Sylvia Plath

The dynamics of wine tears

“Who hath sorrow, who hath woe? They that tarry long at the wine. Look not though upon the strong red wine that moveth itself aright. At the end, it biteth like a serpent and stingeth like an adder.”   — Proverbs 23:29-32

In a wine glass, evaporation of alcohol creates Marangoni stresses that cause the wine to climb to the top of the thin film, where it accumulates in a band that grows until becoming gravitationally unstable and releasing the `tears of wine’. The tears of wine are evident in the picture, a plan view of a wine glass. Also evident is a fine radial spoke pattern in the meniscus, which accompanies the tears of wine in strong alcoholic beverages.

We have demonstrated that this spoke pattern results from ridge-like elevations of the free surface supported by evaporatively-driven Marangoni convection within the thin film. Vortices associated with small-scale convective motions are aligned in the streamwise direction by the surface tension gradient responsible for the sustenance of the tears. The convective motions are revealed by adding Kalliroscope to the fluid. Finally, when the angle of inclination of the glass is very small, the meniscus region is marked by a dendritic free-surface structure.



The results of our combined experimental, theoretical and numerical models of evaporatively-driven convective instabilities in climbing films is presented in Hosoi & Bush, JFM (2001)

Evaporative instabilities in soap films


A vertical soap film supported on a rectangular wire frame of height 3.5 cm and width 15 cm drains under the influence of gravity in an unsaturated environment. Evaporation at the top of the film disrupts the film shape, giving rise to a horizontal bump which grows in amplitude until becoming gravitationally unstable and generating a series of sinking plumes of relatively thick film. The plumes penetrate a finite distance into the film, giving rise to a turbulent mixed layer which slowly erodes the underlying region of stably stratified film. Note the black film adjoining the wire frame at the top of the film, and the relatively weak convective motions, associated with marginal regeneration, evident near the base of the film.


See article: Skotheim & Bush (2000)

Bubble motion in a thin gap

The anomalous wake accompanying a penny-shaped air bubble of diameter 8 cm rising through a thin gap of water bound between glass plates inclined at 3 degrees relative to the horizontal. The image on the left is a schematic of the flow, and that on the right is a digitized image indicating the motion of particles suspended in the flow in the bubble frame of reference. Note the vigorous reversed surface flow and the bounding streamline, both of which are reminiscent of thermocapillary bubble motion in microgravity. A physical explanation and theoretical model of this peculiar flow structure is given by Bush, JFM (1997) .

Drop motion in rapidly rotating flows


Motivated by an interest in vigorous convection in the Earth’s molten outer core, I devoted my doctoral research to the motion of buoyant fluid drops rising through a rapidly rotating fluid.

The figures illustrate silicone drops rising slowly along the rotation axis of a rapidly rotating tank of water rotating at 60 rpm. Note the blocked regions, or `Taylor columns’ accompanying the drop motion. A theoretical and experimental study of axial drop motion in rapidly rotating fluids is presented in a pair of papers: Bush, Stone and Bloxham (1992) and Bush, Bloxham and Stone (1993).

A review of this and related subsequent work is presented in Bush, Stone & Tanzosh (1994) .