3.1. Control case

Figure 3 shows a series of characteristic images of the control case, i.e. the impact of a 4.1 mm drop at a velocity of $7.2~\text{m}~\text{s}^{-1}$ ( $\mathit{Fr}_{d}=1288$ ; $\mathit{We}_{d}=2964$ ) on artificial seawater without an oil slick. The time point of impact is defined as $t=0$ . The horizontal black line in the middle of each image is the water meniscus at the tank wall. Within 1 ms after impact (figure 3), a flat-bottomed disk-shaped cavity forms within the receiving fluid, and expands into a hemispherical shape. As noted by Engel (Reference Engel1966), the raindrop fluid is distributed along the bottom of this cavity and is stretched into a thin layer as the cavity grows. In addition to an initial spray of fine droplets (discussed in detail later), a layer of fluid is ejected upwards and outwards from the bulk and forms a thin-walled crown. This crown is surmounted by a thickened rim due to the effect of surface tension (Worthington & Cole Reference Worthington and Cole1896). Liquid ligaments emanate from fairly regularly spaced vertical extensions in the rim and eject droplets outwards and upwards. In Worthington & Cole (Reference Worthington and Cole1896) and Engel (Reference Engel1966) it is surmised that a very thin layer of the drop fluid is also distributed along the interior surface of the crown. The orientation of the ligaments transitions from almost horizontal to a steep angle in the first several milliseconds. Accordingly, the direction of droplet motion originating from these ligaments sweeps from outwards to upwards over the first 10 ms after impact. Thickening of the rim and its ligaments over this time period also results in an increase of the size of newly produced droplets. By 3 ms, while continuing to grow vertically, the radially outward progress of the upper rim of the sheet ceases, and it begins to move radially inwards under the influence of surface tension. At the same time, as the bulk fluid surface is forced outward by the widening and deepening cavity, more fluid travels up the widening and thickening sheet (Engel Reference Engel1966; Bisighini et al. Reference Bisighini, Cossali, Tropea and Roisman2010).

Table 3.

Characteristics of canopy bubble formation and rupture. Here, $n$ represents the number of replicates and NA indicates a case where measurement was not available.

By approximately 20 ms after impact (a sample at 17 ms is shown in figure 3), growth of the cavity depth stops, but it continues to expand radially. The upper rim of the sheet, bearing several residual ligaments, closes, creating a bubble canopy surmounted by a column of fluid. This closure produces a downward liquid jet evident at 31 ms, which pierces through the bottom of the cavity at 43 ms. Air entrained by this jet generates a few bubbles, seen at 85 ms, which remain under the cavity. Rebound of the cavity produces a broad upwards jet, evident at 85 ms, which merges with the previously generated central column of fluid, converting the bubble into a toroid. The column of fluid on top of the bubble canopy then flows down over this bubble exterior. Subsequently, the inner column thickens and coalesces with one of the bubble walls, creating a horseshoe-shaped bubble at 118 ms, which transforms into the hemispherical bubble seen at 420 ms. On average, this bubble eventually pops at 633 ms after impact (765 ms for the case in figure 3), and the hole in the film cap rapidly expands, with fluid collecting in the retracting rim (table 3). The rim becomes unstable and forms regularly spaced ligaments which shed airborne droplets (inset to figure 3 k). These ‘film drops’ are a well-studied source of marine aerosol (Resch, Darrozes & Afeti Reference Resch, Darrozes and Afeti1986; Blanchard Reference Blanchard1989; Afeti & Resch Reference Afeti and Resch1990; Resch & Afeti Reference Resch and Afeti1991; Lhuissier & Villermaux Reference Lhuissier and Villermaux2012). Table 3 shows that 35 film drops form on average for the control case; this number compares well with previous measurements of film drop production for similarly sized bubbles (Resch & Afeti Reference Resch and Afeti1991). Retraction of the bubble wall and the impact of these droplets also cause ejection of fine droplets into the air (marked by black arrows in the inset to figure 3 l, at 775 ms) and entrainment of air bubbles into the water at 785 ms. Before concluding, it should be noted that in a minority of cases (16 %), the crown fails to close into a bubble (table 3). Instead, the crown collapses and merges with the fluid jet rebounding from the crater. The stochastic nature of successful bubble canopy formation is also noted in Worthington (Reference Worthington1882).

3.2. The effect of oil layer thickness

Figure 4 shows the following three regimes of splash behaviour for crude oil layers of increasing thickness: immediate rupture and single crown, delayed rupture and double crown, and non-rupture and single crown. These three regimes will be illustrated with visualizations of droplet impact onto crude oil layers.

Figure 4.

Conceptual schematic of the cavity and splash crown behaviour for oil layers of various thicknesses at approximately 1–3 ms after drop impact. Dark grey areas, seawater; black lines, oil; light grey areas/lines, raindrop fluid. (a) The oil layer ruptures immediately on impact; a single crown is formed. (b) The oil layer remains initially stretched over the cavity but then undergoes delayed rupture; a double crown is formed. (c) The oil layer does not rupture; a single crown composed of the layer fluid forms.

Immediate rupture and single crown. The first regime (figure 4 a) occurs when the oil layer ruptures immediately upon impact (e.g. within the first millisecond). Rupture of the layer, illustrated in a series of images in figure 5(a–c) for $h=100~{\rm\mu}\text{m}$ , causes the oil to retract into thin threads and droplets and allows the freshwater raindrop to mingle with the surrounding seawater. Figure 5(d–i) shows the rupture of crude oil layers of $h=10$ , 30 and $100~{\rm\mu}\text{m}$ at two time points, with the presence of the layer becoming clearer with increasing thickness. For $h=30~{\rm\mu}\text{m}$ , after 1 ms, several threads of oil emanate from the central portion of a rapidly retracting veil of oil. By 8 ms, most of the oil is concentrated within a string, which splits into droplets, presumably via a capillary instability. This pattern is reminiscent of the ‘bubble chandeliers’ found by Thoroddsen et al. (Reference Thoroddsen, Thoraval, Takehara and Etoh2012) and Tran et al. (Reference Tran, de Maleprade, Sun and Lohse2013), where a thin layer of air is entrained during a low-We impact of a droplet on a water pool. They report that multiple ruptures occur simultaneously in an azimuthal ring due to stretching of the air layer, which creates air strings that extend from a thicker film at the base. In a similar manner, although at a higher We, the present crude oil layer is stretched and broken by the rapidly growing cavity. This pattern disappears for thicker layers, such as for $h=100~{\rm\mu}\text{m}$ , where the oil film ruptures on one side and retracts to the other, e.g. from right to left in the sample presented in figure 5(h,i), leaving oil droplets behind. After 8 ms, in all three cases, the oil is already collected into several droplets below the air cavity.

Shifting to the crown, figure 5(a–c) shows that the oil layer also induces changes to the dynamics of the surface-tension-dominated sheet ejected from the cavity. The darker canopy film (compared with the control case) in (b) is a result of the changing composition of the ejected sheet. As illustrated in figure 4(a), the outside of this sheet is coated with a thin layer of oil drawn up from the surrounding oil film. However, since the oil layer is ruptured, the interior of the crown contains water originating from both the raindrop and the bulk fluid. In addition, the canopy in (b) is closed while that of the control case is still open (quantification follows). The higher inward rim speed with the oily canopy surface causes shorter closure times. After crown closure, the extent of the upward liquid jets above the canopy and the depth of the entrained column of air under the cavity increase with oil layer thickness, as is evident from the images of the $100~{\rm\mu}\text{m}$ layers in (c). In the $100~{\rm\mu}\text{m}$ case, the entrained air is already partially broken into bubbles. The faster downward jet entrains a greater volume of air into the bulk fluid and forces the oil droplets under the air cavity to a larger depth. As will be shown later, the earlier closure of the crown for the $100~{\rm\mu}\text{m}$ oil layers also results in a smaller cavity and bubble canopy above the surface.

Figure 5.

(a–c) Sample images showing the impact of the water droplet (same as in figure 3) on an oil layer of thickness $h=100~{\rm\mu}\text{m}$ . The insets (all at the same magnification) show magnified sections of the images. The white inset scale bar at 1 ms in (a) is 2 mm: (a) 1 ms, (b) 8 ms and (c) 43 ms. (d–i) Magnified images showing the oil layer rupture and breakup for oil layer thicknesses of (d,e) $h=10~{\rm\mu}\text{m}$ , (f,g) $h=30~{\rm\mu}\text{m}$ and (h,i) $h=100~{\rm\mu}\text{m}$ . Here, $a$ is the air cavity, $r$ is the raindrop fluid layer and $s$ is the seawater. The arrows show the retracting oil film at 1 ms (d,f,h) and the collected oil droplets at 8 ms (e,g,i).

Figure 6.

(a–h) Sample images showing the impact of the water droplet (same as in figure 3) on an oil layer thickness of $h=200~{\rm\mu}\text{m}$ : (a) 1 ms, (b) 2 ms, (c) 4 ms, (d) 8 ms, (e) 19 ms, (f) 85 ms, (g) 380 ms, (h) 395 ms. The scale bars in the insets are 2 mm for that time point. The white arrows in (b–d) show the edge of the receding raindrop fluid. The white asterisks indicate examples of tracked lower crown rim positions. Magnified views showing the impact of the water droplet on an oil layer thickness of $h=200~{\rm\mu}\text{m}$ at (i) 1 ms, (j) 2 ms, (k) 15 ms and (l) 19 ms. Here, $a$ is the air cavity, $r$ is the raindrop fluid layer and $s$ is the seawater. The white arrows show the edge of the retracting raindrop fluid, the black arrows show the intact oil sheet in (i) and (j) and oil droplets in (k) and (l), and the dashed black arrows show the annular rim separating the upper and lower crowns in (i) and (k).

Delayed rupture and double crown. In the second regime, illustrated in figure 4(b), the floating oil layer no longer ruptures within the first millisecond of droplet impact. Instead, the oil layer becomes thinner but remains intact as the cavity grows. Accordingly, a continuous oil layer should presumably extend from the bottom of the cavity to the top of the crown, and to the undisturbed surrounding surface. This intact oil layer, shown in figure 6(a–c,i,j) for impact on a layer of $h=200~{\rm\mu}\text{m}$ , prevents the raindrop from mixing with the bulk fluid as would occur in the previously described immediate rupture cases. Instead, a thin layer of raindrop fluid travels up the crown wall and subsequently retracts down the wall, at speeds of up to $0.8~\text{m}~\text{s}^{-1}$ , to the cavity bottom. Retraction of the drop fluid into the cavity bottom is also reported by Fujimatsu et al. (Reference Fujimatsu, Fujita, Hirota and Okada2003) and by Lhuissier et al. (Reference Lhuissier, Sun, Prosperetti and Lohse2013) for water drops impacting silicone oil at lower We than that studied here that do not involve a crown. By this time ( ${\sim}8~\text{ms}$ ), due to the cavity growth, the oil layer lining its walls has been stretched to a thickness of approximately $4~{\rm\mu}\text{m}$ , estimated by assuming that the circular area underlying the droplet is stretched into a hemisphere. Passage of the retracting raindrop fluid over the thinned oil layer appears to cause its breakup into fine threads and droplets and allows the raindrop fluid to mix with the seawater, as the sample images in figure 6(d,e,k,l) demonstrate. For a thicker layer of $h=400~{\rm\mu}\text{m}$ , as shown in figure 7, passage of the retracting raindrop does not always rupture the layer. Instead, once the retracting droplet reaches the bottom of the cavity, it generates miniature upward and downward liquid jets. The downward jet may puncture the oil layer or may protrude through the oil layer and become encapsulated as a ‘vesicle’, a parcel of water coated with a light-coloured thin film of oil which may remain intact for at least several seconds (shown bursting in figure 7 j–m). Formation of similar structures is observed by Wacheul et al. (Reference Wacheul, Le Bars, Monteux and Aurnou2014) for liquid gallium falling through glycerine solutions.

Figure 7.

(a–h) Sample images showing the impact of a freshwater drop (same as in figure 3) on crude oil layer with thickness $h=400~{\rm\mu}\text{m}$ : (a) 2 ms, (b) 5 ms, (c) 8 ms, (d) 31 ms, (e) 52 ms, (f) 118 ms, (g) 219 ms, (h) 255 ms. The inset to (b) shows a magnified section. The scale bar in the inset is 2 mm. The white arrows show the edge of the retracting raindrop fluid, the black arrows show the vesicle, the dashed black arrows show the annular rim between the upper and lower crowns and the white asterisks indicate examples of lower crown rim positions. (i) Magnified view of double-crown formation at 2 ms. The dashed black arrows show the annular rim between the upper and lower crowns. (j–l) Sample images showing an oil vesicle rising to the surface and rupturing. The view is partially obscured by the oil layer at the tank wall: (j) 656 ms, (k) 761 ms, (l) 767 ms, (m) 773 ms.

Delayed rupture of the oil layer also affects the composition and behaviour of the crown. The floating oil layer is propelled upwards first and thus forms the upper part of a double crown. As the cavity grows, it also then propels the underlying seawater. Accordingly, the lower crown contains seawater, coated with oil, as illustrated in figure 4(b), and its thickened rim represents the upper extent of the seawater. For the $h=200~{\rm\mu}\text{m}$ oil layer, the film of the upper crown, which is composed of oil, collapses by 2 ms, leaving behind a skeleton of fragmenting ligaments protruding from the rim of the lower crown (figure 6 j). In comparison to the $200~{\rm\mu}\text{m}$ oil layer, raindrop impact on the $h=400~{\rm\mu}\text{m}$ oil layer produces a taller and more robust upper crown. For example, by comparing figures 6 and 7, the upper crown still exists at 5 ms for $h=400~{\rm\mu}\text{m}$ , while it has already disappeared at 2 ms for $h=200~{\rm\mu}\text{m}$ . The upper crown for $h=400~{\rm\mu}\text{m}$ also appears to be thicker, presumably since a greater oil volume is propelled upward. As the upper crown film collapses into ligaments by 8 ms, it also contracts inward, presumably under the effect of surface tension. Subsequently, the remaining ligaments stretch upward, while continuing their radially inward motion, and eventually, by 10–20 ms, break into droplets.

Figure 8.

Sample parts of a time series showing the impact of a freshwater drop (same as in figure 3) on a crude oil layer above artificial seawater with thickness of $h=2300~{\rm\mu}\text{m}$ : (a) 2 ms, (b) 8 ms, (c) 23 ms, (d) 113 ms. The white arrow shows the edge of the retracting raindrop fluid.

The lower crown for the $h=400~{\rm\mu}\text{m}$ layer appears slightly later than that for the $h=200~{\rm\mu}\text{m}$ layer, presumably since entrainment of the seawater begins later. With increased oil layer thickness, the lower crown is also less likely to close into a bubble canopy, with only 13 % of replicates successfully forming a bubble (table 3). While slow bubble canopy closure occurs for $h=200~{\rm\mu}\text{m}$ (slower than that of the control case or rupturing layers), it rarely occurs for $h=400~{\rm\mu}\text{m}$ , as the image in figure 7(e) shows. Instead, the crown falls on the periphery as the rebounding cavity forms a thick central jet evident at 118 ms. The collapse of this thick jet subsequently creates a high-speed jet (255 ms) with droplet ejection speeds of up to $9.9~\text{m}~\text{s}^{-1}$ . When oily canopy bubbles do form, they have shorter lifetimes, presumably due to lower surface tension, with a mean time from impact to bubble bursting of 215 ms for $h=200~{\rm\mu}\text{m}$ (table 3). Kientzler et al. (Reference Kientzler, Arons, Blanchard and Woodcock1954) also found shortened bubble lifetime with the addition of a surface-tension-lowering agent. In contrast to the control case, bursting of this large bubble does not produce ligaments and produces very few film drops (395 ms). Table 3 shows that no more than two film drops are produced on average for any of the cases with oil. The onset of the instability, which would corrugate the receding rim and produce ligaments and droplets, is probably delayed by the higher viscosity of the oil (Lhuissier & Villermaux Reference Lhuissier and Villermaux2012), which, based on colour, covers the entire canopy. Table 3 also shows that the receding rim for the oil layer cases moves more slowly than that of the control case. The rim for the control case travels at a mean speed of $1.8~\text{m}~\text{s}^{-1}$ while the oily rims travel at mean speeds of $0.9{-}1.2~\text{m}~\text{s}^{-1}$ due to the decreased surface tension of the oil.

Non-rupture and single crown. In the third regime, illustrated in figure 4(c), the floating oil layer is thick enough so that the influence of the underlying water on splash phenomena is greatly diminished. The oil layer thins as the cavity grows but is thick enough to remain intact as the raindrop retracts to the cavity bottom. As seen in figure 8 for an oil layer of $h=2300~{\rm\mu}\text{m}$ , because of the increased oil layer thickness, only oil is entrained into the crown, thus producing a single crown similar to the control or rupturing layer cases. Similarly to the rupturing cases, the crown closes more rapidly than the control (at 11 ms – not shown). The resulting oil-comprised bubble is small compared with those previously considered. The rapid closure also creates a jet of oil that moves downward through the splash cavity wall, as seen at 113 ms, and subsequently separates into several large oil droplets (2–6 mm in diameter) which float to the surface and rejoin the oil layer.

Figure 9.

Sample parts of a time series showing the impact of a freshwater drop (same as in figure 3) on artificial seawater with an $h=500~{\rm\mu}\text{m}$ thick layer of premixed 1:25 DOR oil–dispersant mixture: (a) $-2$  ms, (b) 1 ms, (c) 3 ms, (d) 18 ms, (e) 28 ms, (f) 43 ms, (g) 75 ms, (h) 111 ms, (i) 168 ms, (j) 241 ms, (k) 721 ms, (l) 2538 ms, inset to (j) 274 ms, inset to (k) 977 ms. The white scale bars in the insets are 2 mm. The dashed black arrows show the upper rim of the lower crown and the white arrow shows the hole in the oil–dispersant layer.

3.3. Oil premixed with dispersant

Figure 9 shows droplet impact on an $h=500~{\rm\mu}\text{m}$ layer of oil premixed with dispersant at a DOR of 1:25. As the subsurface cavity expands, the oil–dispersant layer becomes thinner and subsequently ruptures in multiple locations 2–4 ms after impact (inset to (c)). The ruptured oil–dispersant layer contracts into thin strands (e), allowing the freshwater to join with the bulk seawater. Both upper and lower crowns are evident early in the splash (inset to (b)), but, due to low interfacial tension (table 1), the boundary between these layers is not as distinct as those of the cases without dispersant. In contrast to oil layers of similar thicknesses, the front of the retracting raindrop fluid down the interior surface of the crown into the cavity is not as clear, also presumably due to the negligible interfacial tension. The space above the crown at 3–8 ms appears to contain many long ligaments, which stretch upwards as far as 1.5 cm above the crown rim. Their number and elevation are larger than those occurring without dispersant, presumably due to the lower capillary instability of the oil–dispersant mixture. When these ligaments eventually break up due to capillary instability, copious fine droplets appear. Also in contrast to the cases without dispersant, after the upper crown disintegrates, the lower crown collapses inward to form a canopy bubble in all of the replicates (table 3), followed by formation of an upward jet (18 ms) and a downward jet evident at 28 ms. This downward jet plunges through the bottom of the cavity at ${\sim}43~\text{ms}$ and, due to the reduced interfacial tension with the seawater, breaks up into a plume of fine oil droplets and threads as well as entrained air bubbles (43 ms and onward).

When the bubble canopy bursts (111 ms) at about the same time as the corresponding non-dispersant case (see the data in table 3), the receding rim travels slowly due to the low surface tension, and produces very few airborne film drops. However, the canopy collapse also causes entrainment of oil near the surface, starting from 168 ms. Many of the oil droplets entrained by both processes are smaller than the camera resolution ( $28.2~{\rm\mu}\text{m}~\text{pixel}^{-1}$ ), and appear from 168 ms onwards as clouds. As air bubbles generated by the jet impact rise to the surface, some pull threads of oil in their wakes (inset to (j)). The larger oil droplets also rise, although more slowly, and similarly pull oil threads in their wakes. The resulting oil microthreads and microdroplets appear to be similar to those found by Gopalan & Katz (Reference Gopalan and Katz2010, e.g. the inset to (k)). In the last recorded frame (l), the large droplets have already risen to the surface, but plumes of fine droplets, which have expanded and dispersed, remain. The mixing is caused by subsurface flows resulting from impingement of the downward jet (43 ms), collapse of the canopy walls, and rising bubbles and droplets. It should be noted that unlike the corresponding non-dispersant oil case (figure 7), which involves multiple upward and downward jets, interaction of the rebounding cavity with the bubble canopy (75 and 111 ms) prevents subsequent jet generation, similarly to the control case.

Figure 10.

The $\mathit{ReFr}_{h}{-}\mathit{We}_{h}$ plane showing classification of splash behaviour for droplet impact onto immiscible oil layers. Crown behaviour is classified by symbols into regimes separated by dashed lines. Oil layer behaviour is classified by colour into regimes separated by dotted lines. Alternate axes indicate directions of increasing oil layer viscosity ${\it\mu}_{h}$ , layer thickness $h$ , droplet impact speed $u$ and droplet diameter $d$ .

3.4. Scaling trends of oil layer breakup and crown behaviour

Visualizations from all of the experimental series, layer thicknesses and fluid properties, which are listed in table 2, have been examined and categorized based on crown and oil layer behaviours for the purpose of developing scaling trends. The contributing experiments cover broad ranges of droplet sizes (1.75–4.1 mm) and speeds ( $1.1{-}7.3~\text{m}~\text{s}^{-1}$ ), as well as oil layer thicknesses ( $5{-}21\,500~{\rm\mu}\text{m}$ ), viscosities (0.6–1286 cSt), surface tensions ( $16{-}72~\text{mN}~\text{m}^{-1}$ ) and interfacial tensions (0.28–58.3  $\text{mN}~\text{m}^{-1}$ ). For scaling purposes, we classify the crown behaviours as (i) a crown that closes into a canopy, (ii) a crown that does not close into a canopy and (iii) no crown formation, e.g. formation of a swell. For the cases with a crown, it is further classified as either a double crown or a single crown. The subsurface oil layer behaviours are categorized into (i) immediate rupture, (ii) delayed rupture and (iii) non-rupture. Immediate rupture refers to cases when the time for rupture is less than 7.5 % of the time required for the cavity to reach maximum depth. This constraint, in practice, limits this regime to ruptures within 1 ms after impact. Delayed rupture refers to cases for which the layer is ruptured at later times. Associated phenomena are discussed in the previous section. We have tested many combinations of dimensionless parameters in attempts to classify these behaviours, keeping in mind the parameters used in figure 1 and the observed influence of viscosity. A scaling that appears to work for all of the data is depicted in figure 10. While figure 1 involves only low-viscosity single-phase fluids, the present classification accounts for both the layer thickness and varying fluid properties. Here, the results are classified in terms of $\mathit{We}_{h}$ and a product of Re and $\mathit{Fr}_{h}$ , where $\mathit{We}_{h}={\it\rho}_{h}u^{2}h/{\it\sigma}_{h}$ , $\mathit{Re}={\it\rho}_{d}ud/{\it\mu}_{h}$ and $\mathit{Fr}_{h}=u^{2}/gh$ . Here, the subscripts $d$ and $h$ refer to droplet and oil layer properties respectively. These parameters account for the existence of two independent length scales, $d$ and  $h$ , and $\mathit{ReFr}_{h}={\it\rho}_{d}u^{3}d/{\it\mu}_{h}gh$ accounts for effects of inertia, viscosity and gravity. For convenience of interpretation, figure 10 also contains additional axes showing the directions of increasing $h$ , $u$ , $d$ and oil layer viscosity, ${\it\mu}_{h}$ . The oil layer behaviour is differentiated by colour while the crown behaviour is distinguished by symbols. Regimes of oil layer behaviour are bounded by dotted lines and crown behaviour by dashed lines. Immediate rupture occurs at high $\mathit{ReFr}_{h}$ and low $\mathit{We}_{h}$ , delayed rupture occurs at intermediate values of both, and non-rupture cases are confined to low $\mathit{ReFr}_{h}$ and high $\mathit{We}_{h}$ . The double-crown cases, which fall within the delayed rupture regime, are confined to relatively high $\mathit{ReFr}_{h}$ and $\mathit{We}_{h}$ , within this range. Regarding the crown behaviour, crowns are not formed at low $\mathit{ReFr}_{h}$ and $\mathit{We}_{h}$ either, due to the high oil layer viscosity or low impact speed. In this regime, the flow above the surface appears as an outward swell, in accordance with the swell and thin jet regime indicated in figure 1. For the most viscous oil layers and lowest impact speeds, even this outward swell becomes very small. Increasing $\mathit{ReFr}_{h}$ and $\mathit{We}_{h}$ brings us first to the intermediate range of crown, but no bubble canopy regime. Included are cases of crowns with smooth rims, rims with nubs (very short ligaments) and rims with fully formed ligaments. This regime is generally characterized by the same phenomena as the crown and thick jet domain discussed in the context of figure 1. A further increase in $\mathit{ReFr}_{h}$ and $\mathit{We}_{h}$ leads to the crown and bubble canopy regime, which represents phenomena that are similar to those of the bubble canopy regime in figure 1. However, within this range, when the rupture is delayed, many of the double-crown cases fail to close into a canopy, presumably since the upper crown is short lived.

Figure 11.

Cavity volume at maximum cavity depth ( $V_{c}^{max}/V_{d}$ ) as a function of Re for droplet impact on thick oil layers ( $h=5.7d$ ) and for droplet impact on water (both for $d=3.8~\text{mm}$ , $u=7.28~\text{m}~\text{s}^{-1}$ ). The symbols indicate crown behaviour and correspond to the same symbols as in figure 10.

Figure 12.

(a) Sample parts of a time series showing the impact of a freshwater drop ( $d=3.8~\text{mm}$ , $u=7.28~\text{m}~\text{s}^{-1}$ ) on a thick gasoline layer ( $h=5.7d$ ): (a) 1.3, 17.3 ms, (b) 2.7, 21.3 ms. (b) Sample parts of time series showing the impact of the same freshwater drop on a silicone oil layer ( $h=5.7d$ ) above artificial seawater. Here, $Y_{R}^{min}$ at $t=21.3~\text{ms}$ indicates the height of the bubble canopy after full expansion of the cavity. In (a,b), the layers float above artificial seawater not visible in the images. (c) Non-dimensionalized crown rim trajectories created for the same drop impact on various oil layers of $h=5.7d$ and on artificial seawater. The time delay between points in each trajectory is 0.65 ms and the starting point represents the edge of the falling raindrop on the fluid surface on impact ( $t=0~\text{ms}$ ).

Next, to demonstrate the effects of oil properties and to separate them from those of $h$ , we consider the transition from the no-crown to crown and canopy regimes for thick layers ( $h=5.7d$ ). For these cases (series 2), the oil composition is varied while the droplet speed and size are kept constant. The maximum depth and the radius of the cavity at the time of maximum depth are used to calculate the maximum cavity volume $V_{c}^{max}$ assuming an ellipsoidal shape. Values of $V_{c}^{max}$ normalized by the droplet volume $V_{d}$ are plotted as a function of Re in figure 11. With increasing Re, $V_{c}^{max}/V_{d}$ increases monotonically for the four most viscous fluids, for which there is no crown. Further increase in Re to 400 causes bifurcation in behaviour, where tests performed under the same conditions give different results. When a crown is formed, but fails to close, the cavity volume continues to grow substantially. When the crown closes, the cavity volume appears to plateau. Further increase in Re does not show clear trends in normalized cavity volume, including another case (seawater with no oil layer) where the volume involving canopy closure is smaller than that of a non-closure case. This lack of clear trends can be explained by considering the surface-tension-controlled timing and kinematics of crown formation and closure. As will be shown, they are associated with early closure of the canopy, which retards the cavity growth. Figure 12(a,b) shows sample images of the crown and cavity for thick gasoline (figure 12 a) and silicone oil (12 b) layers. Figure 12(c) shows the manually tracked horizontal and vertical positions of the upper rim of these crowns, $X_{R}$ and $Y_{R}$ respectively. Length scales and time are non-dimensionalized by $d$ and $d/u$ respectively. Consecutive points along each trajectory represent 0.65 ms time steps. The crown rim trajectories vary substantially in height, radial extent and time. The gasoline crown rises a shorter distance, does not extend as far outward radially and begins travelling radially inward earlier. This earlier retraction causes earlier closure of the bubble canopy. Figure 13(a,b) shows that the non-dimensionalized closure time, $t_{c}u/d$ (13 a), and the maximum crown rim height, $Y_{R}^{max}/d$ (13 b), both decrease with increasing $\mathit{We}_{t}$ , where $\mathit{We}_{t}={\it\rho}_{h}u^{2}d/{\it\sigma}_{h}$ is the target fluid Weber number. That is, a greater surface tension counterintuitively (presumably) leads to taller crowns and longer closure times. This trend can be explained by considering the growth phase of the crown. A crown with a high-surface-tension fluid, such as the control case shown in figure 3, contains more fluid within the crown walls and rim, allowing it to grow taller and wider while remaining intact. A crown with low-surface-tension fluid, such as the gasoline or silicone oil in figure 12(a,b), cannot ‘hold on’ to that fluid and breaks up into droplets earlier, resulting in thinner shorter crown walls and thinner crown rims. Consequently, the surface tension has to overcome much less inertia in order for the canopy to close. Conversely, crowns composed of high-surface-tension fluids have a higher mass, i.e. have greater upward and outward inertia, which requires a longer time to reverse direction and close.

Figure 13.

(a) Bubble canopy closure time $t_{c}u/d$ as a function of $\mathit{We}_{t}$ . (b) Maximum height of crown $Y_{R}^{max}/d$ as a function of $\mathit{We}_{t}$ . (c) Canopy ceiling fall distance $(Y_{R}^{max}-Y_{R}^{min})/Y_{R}^{max}$ as a function of canopy closure time $t_{c}u/d$ . The symbols correspond to the fluid types in figure 12.

Our observations suggest that closure of the bubble canopy affects the subsurface cavity dimensions. After canopy closure, if the cavity is still in its growth phase, it can only draw in air from within the canopy, by pulling the canopy ceiling downward. Consequently, one should expect that early closure at high $\mathit{We}_{t}$ would hinder the cavity growth. For example, in figure 12(a), the gasoline canopy is already pulled down by the cavity to the original fluid level, while for the higher-surface-tension silicone oil in figure 12(b), closure occurs later, and the canopy is not pulled down as much. To quantify this trend, $Y_{R}^{min}$ , which is illustrated in figure 12(b), is defined as the minimum height to which the canopy ceiling is pulled downwards before it starts rising again as the cavity starts shrinking. Figure 13(c) shows the value of $(Y_{R}^{max}-Y_{R}^{min})/Y_{R}^{max}$ , which represents the vertical displacement of the canopy ceiling while being pulled down (by the growing cavity), as a function of closure time. It shows results for the same cases as in figure 13(a,b). Clearly, with decreasing closure time, the canopy ceiling is pulled further down. Returning back to figure 11, for the viscosity-dominated regime, when there is no canopy closure, the cavity volume increases with Re. Transitioning to conditions where canopy closure does occur, where $\mathit{We}_{t}$ effects become important, the longer the canopy closure time, the less hindrance there is to cavity growth. Even for the same fluid in this regime, the cavity dimensions are dominated by whether the canopy closes. The cavity dimensions become a function of two competing effects, one dominated only by Re, and the other by $\mathit{We}_{t}$ as well. For the lowest Re, the energy dissipated in the fluid, based on kinematic measurements of cavity expansion (Deng et al. Reference Deng, Anilkumar and Wang2007), is approximately 40 % of the kinetic energy of the raindrop, whereas for the high-Re regime, a substantial portion of the raindrop energy goes into displacing cavity fluid and creating the surface area of the crown and canopy.

3.5. Crude oil layer splash kinematics

The galleries and scaling presented in the previous sections demonstrate that the introduction of an oil layer significantly modifies the characteristics of a splash produced by a falling raindrop. Oil layer thickness, viscosity and surface tension affect whether and at what stage the oil layer ruptures and also affect whether a crown is produced and the behaviour of that crown. Timing of crown closure into a canopy can also affect subsurface phenomena such as cavity size. In this section we provide quantitative information on the effect of crude oil slick thickness on the evolution of the cavity volume and crown rim, achieved by manually tracking the lip of the crown, as well as the cavity bottom and side (used to calculate the cavity volume as half an ellipsoid). These features have been measured in eight replicates for the control and $h=10$ , 30, 200 and $400~{\rm\mu}\text{m}$ cases, six replicates for $h=100~{\rm\mu}\text{m}$ and five replicates for the $h=500~{\rm\mu}\text{m}$ layer of oil premixed with dispersant. We provide limited cavity data for $h=1100$ and 2300, since the meniscus on the tank walls makes accurate measurements at the intersection of the cavity with the surface difficult. The following figures present averaged results with standard deviations indicated by error bars and with the origin located at the centre of the drop impact on the surface.

Figure 14.

Variation with time of the cavity volume $V_{c}/V_{d}$ for several crude oil layer thicknesses. The error bars indicate the standard deviation.

Figure 14 shows the cavity volume $V_{c}/V_{d}$ over the first 60 ms after impact. In all cases, the volume increases sharply until approximately $tu/d=15$ , at which point different trends begin to emerge. The trends can be divided into three groups. The smallest cavity volumes belong to the $h=30$ and $100~{\rm\mu}\text{m}$ ruptured layer cases and the $h=2300~{\rm\mu}\text{m}$ non-ruptured case. This group begins to diverge from the others at approximately $tu/d=20$ , which is just after their canopies have closed. In all three of these cases, a single crown is formed, and, as described previously, this crown rapidly closes into a canopy bubble, thereby preventing further expansion of the cavity. The largest cavity volumes correspond to the control, $h=10~{\rm\mu}\text{m}$ , $h=200~{\rm\mu}\text{m}$ and $h=400~{\rm\mu}\text{m}$ cases, which do not appear to greatly differ. As an immediate rupture case, the $h=10~{\rm\mu}\text{m}$ layer might be expected to exhibit rapid canopy closure, similarly to the $h=30$ and $100~{\rm\mu}\text{m}$ rupture layer cases. The $h=10~{\rm\mu}\text{m}$ crown, however, was erratic and closed to form a bubble canopy less than half of the time (table 3). This was attributed to incomplete oil coverage over the surface over the crown, which manifested itself as ‘extra’ bumps and ligaments which interfered with crown closure. The volume of the $h=10~{\rm\mu}\text{m}$ case was thus quite similar to the control case. The slightly higher cavity volume of the $h=400~{\rm\mu}\text{m}$ case could be attributed to the fact that the canopy almost never closes, thus allowing unrestrained growth of the cavity. The cavity volumes for $h=1100~{\rm\mu}\text{m}$ and the $h=500~{\rm\mu}\text{m}$ layer of oil mixed with dispersant are intermediate.

Figure 15.

Variation of the mean and standard deviation of the horizontal ( $X_{R}/d$ ) crown rim position with time for crude oil layer experiments for (a) the control and immediately rupturing cases, and (b) the control, delayed rupture and non-rupture cases (lower crown only).

The effects of surface tension on crown behaviour previously seen in the raindrop impacts on bulk fluids (i.e. thick fluid layers) are also seen in the crown behaviour for impacts on thin layers of crude oil. Figure 15(a) shows the mean horizontal $X_{R}/d$ position of the crown rim (the base of the thickened annular rim defining the upper boundary of a crown) for the control and immediately rupturing layer cases ( $h=10$ , 30 and $100~{\rm\mu}\text{m}$ ), while figure 15(b) shows the same parameter for the control, delayed rupture and non-rupturing cases ( $h=200$ , 400, 1100 and $2300~{\rm\mu}\text{m}$ ). The corresponding trajectories are shown in figure 16, where consecutive points along each trajectory represent 1 ms time steps. Over the first two milliseconds, figures 15(a) and 16(a) demonstrate that for the control and immediately rupturing layer cases, the rims rapidly move horizontally outwards and vertically upwards at ${\sim}50\,\%$ of the raindrop speed. However, as indicated by supporting information provided in table 4, after 2 ms, the rim speeds and vertical positions for cases with oil layers are significantly greater than those of the water only case. The substantially lower surface tension resisting the oil-coated crown growth, at least on the exterior of the crown (figure 4 a), is probably responsible for its more rapid growth. Similarly to the gasoline case examined before, lower surface tension also probably leads to thinner crown walls. This observation is supported by measurements of the rim thickness (table 4). The relatively thin crowns of the $h=30$ and $100~{\rm\mu}\text{m}$ cases begin to close at 2 ms after impact, reaching a maximum inward speed of approximately $0.76~\text{m}~\text{s}^{-1}$ , while still moving upwards. The thicker seawater (control) crown starts reversing ‘significantly’ later, 4 ms after impact, presumably because its higher surface tension allows it to retain a larger mass; the reversed motion is also much slower, approximately $0.27~\text{m}~\text{s}^{-1}$ . The crown rim height eventually plateaus and begins to decrease; this occurs slightly before the rims merge together to form the canopy. Again, closure of the crown for the $h=30$ and $100~{\rm\mu}\text{m}$ layers occurs noticeably sooner, at $tu/d=\sim 18$ , than that for the control canopy, at $tu/d=\sim 26$ . The rim trajectory for the $h=10~{\rm\mu}\text{m}$ layer differs from the others, as discussed before, and rarely closes as a result.

Figure 16.

Non-dimensionalized crown rim trajectories created by the control and (a) initially rupturing crude oil layers, (b) delayed and non-rupturing crude oil layers (lower crown only) and (c) crude oil layers with and without dispersant. The time delay between points in each trajectory is 1 ms, and the starting point represents the point where the crown first appears.

Table 4.

Kinematic characteristics of the crown and cavity for the control and immediately rupturing oil layers at 2 ms ( $tu/d=3.5$ ) after impact.

Moving on to the delayed rupture crude oil layers (figures 15 b and 16 b), for cases with upper and lower crowns, namely $h=200$ , 400 and $1100~{\rm\mu}\text{m}$ , which are illustrated in figure 4(b), we provide rim trajectory data for the lower crown. The upper crown rapidly disintegrates (within 2 ms for the $h=200~{\rm\mu}\text{m}$ layer but slightly later for the more robust upper crowns of the $h=400$ and $1100~{\rm\mu}\text{m}$ layers), and its rim kinematics are not presented. Disintegration of the upper crown means that the film is not available to form a canopy. Consequently, formation of oil-only upper crowns reduces the likelihood of successful canopy formation, as is evident from the present data (table 3). As expected, the water-containing lower crown rim appears at progressively later times after impact as $h$ increases from 200 to $1100~{\rm\mu}\text{m}$ . Specifically, it first appears 1, 2 and 4 ms post-impact for the 200, 400 and $1100~{\rm\mu}\text{m}$ layers respectively. Accordingly, the maximum vertical extent decreases and the horizontal extent increases with increasing layer thickness, as is evident from figure 16(b). This rim slowly travels upwards and outwards and then retracts inwards at a very slow pace. Consequently, the likelihood of lower crown closure to form a canopy is low, as table 3 shows. As described previously (figure 8), a single oil-comprised crown forms for the $h=2300~{\rm\mu}\text{m}$ non-rupturing layer. This crown rises quickly, even faster than the control case, presumably because of the lower surface tension of the oil, and it closes rapidly into a canopy bubble in over half of the replicates.

For the oil–dispersant mixture (figure 16 c), which has a slightly lower surface tension than that of the oil alone but much lower interfacial tension (table 1), the upper crown initial speed is similar to that of the other oil layer cases, suggesting that the initial upper crown motion is not affected strongly by interfacial tension. However, as noted before, the upper crown is short lived. Figure 16(c) compares the lower crown trajectory for $h=500~{\rm\mu}\text{m}$ for the oil–dispersant mixture with those of the control and $h=400~{\rm\mu}\text{m}$ . For the first ${\sim}4~\text{ms}$ , the rim for the oil–dispersant mixture follows a similar trajectory to that of the $h=400~{\rm\mu}\text{m}$ case, but at a significantly higher speed (2.2 versus $1.9~\text{m}~\text{s}^{-1}$ at 3 ms). Subsequently, they deviate, as the oil–dispersant crown continues to grow rapidly, reaching the maximum height observed for any of the present cases, and then closes to form a canopy bubble. The higher momentum and persistence of the lower crown are consistent with the smaller and shorter-lived upper crown. Presumably, near-elimination of the interfacial tension results in more of the oil–dispersant mixture rising together with the seawater shortly after impact.

Figure 17.

Example reconstructed holograms and vertical distribution of airborne droplets for (a) the control case, (b) crude oil with $h=30~{\rm\mu}\text{m}$ , (c) crude oil with $h=400~{\rm\mu}\text{m}$ and (d) an $h=500~{\rm\mu}\text{m}$ layer of dispersant–crude oil mixture with $\text{DOR}=1:25$ . The bottom of the field of view is located at $y=13~\text{mm}$ .