Marangoni flow induced by a raindrop

Why rain matters

Rain changes how fast gases such as CO₂ and oxygen move between the atmosphere and a waterbody. A drop that lands on the surface sets up vortices that carry gas-rich surface water down into the bulk, over an area many times larger than the impact itself.

The top millimeter or so of the sea, the sea surface microlayer, is where that exchange happens, and its salt and surfactant content differ from the water a few centimeters below. A raindrop is fresh water. When it merges with the surface, it lowers the local concentration of both, and that is what this study is about.

The physics

Dissolved salt raises the surface tension of water, and surfactants lower it. Seawater at 35 g/kg has a surface tension of about 73.3 mN/m against 72.4 mN/m for fresh water, while enough soap pulls it down to about 42 mN/m. A freshwater drop dilutes both, so it pushes the local surface tension in opposite directions depending on which solute dominates. Flow along a surface runs from low surface tension toward high surface tension. This is the Marangoni effect.

Saltwater

Dilution lowers the surface tension at the impact point.

Solutocapillary flow runs outward, away from the impact

Surfactant-laden water

Dilution raises the surface tension at the impact point.

Reverse Marangoni flow runs inward, toward the impact

Three dimensionless groups set the outcome. The Weber number We compares the drop's inertia with surface tension. The salt and surfactant Marangoni numbers, Ma₁ and Ma₂, measure how strongly each solute drives flow along the surface. For 35 g/kg salt, Ma₁ = 5.2 × 10⁶. Across our surfactant concentrations, Ma₂ spans 1.5 × 10³ to 9.4 × 10⁹.

Fig. 1 · Interactive sketch

Fig. 1. Click or tap to drop a raindrop, and switch the waterbody to compare. A simplified illustration of the two flow regimes, not a simulation.

Plot of surface tension against the natural log of soap concentration, for water with and without 35 g/kg salt. Surface tension stays near 72 to 74 dyn/cm at low concentration, then drops steeply to about 42 dyn/cm. — **Fig. 2.** Measured surface tension of water against surfactant concentration, with no salt and with 35 g/kg salt. Salt adds roughly the same small increase at every surfactant level. Verma et al. (2023), Fig. 3

Experiments

A syringe pump running at 50 µl/min fed an 18-gauge needle with a 0.838 mm bore, which released freshwater drops 3.4 mm in diameter onto a 30 × 30 × 10 cm glass tank of distilled, salt or surfactant water. Raising the needle from 5 to 60 cm above the surface set the impact speed, 0.9 to 2.9 m/s, and the Weber number, 40 to 385.

The water was seeded with silver-coated hollow glass particles, 8 to 12 µm across. A 40 mW, 532 nm laser sheet lit a vertical plane through the impact point, and a Phantom Miro-Lab320 high-speed camera recorded it at right angles, at 300 frames per second. PIVlab turned the particle motion into velocity fields. A light source behind the tank gave silhouette images for the height of the water column.

Schematic of the setup on an optical table: a laser system projects a green sheet into a square water tank, a syringe pump feeds a needle above the tank, and a high-speed camera views the tank. — **Fig. 3.** The experimental setup. Verma et al. (2023), Fig. 4

Release height and the resulting impact conditions
Drop height	Impact velocity	Weber number	Reynolds number
5 cm	0.9 m/s	40.2	213
10 cm	1.3 m/s	78.5	298
20 cm	1.8 m/s	148.3	410
40 cm	2.4 m/s	272.8	556
60 cm	2.9 m/s	384.8	660

Four high-speed frames of a drop impact: the drop on the surface, a crater with a splashing crown, a thin water column rising with a droplet at its tip, and a single droplet falling back toward a flat surface. — **Fig. 4.** A drop released from 20 cm. (a) Top view at impact, (b) the crater at 0.02 s, (c) the water column at 0.15 s, and (d) a droplet that broke off the column falling back at 0.19 s. Verma et al. (2023), Fig. 5

Fresh water

Saltwater, 35 g/kg

Surfactant water

Video 1. What the camera records, slowed down. Each speck is a tracer particle in the laser sheet, and the bright horizontal line is the air–water interface seen edge-on. On saltwater, the outward surface flow opens a wider particle-free gap along the interface. With surfactant the gap stays small, and the flow below the impact runs downward.

Fresh water: a vortex, little surface flow

On a freshwater body, the impact drives a vortex ring down into the water. For a drop from 5 cm, it descended at about 13.1 cm/s. The surface itself barely moves. Particles at the impact point were carried under, but those just outside it stayed put, and the flow at the surface died out within about half a second.

Two PIV vector fields below the air-water interface. At 0.003 s the vectors point down from the impact center; at 0.12 s a pair of vortices sits well below the surface. — **Fig. 5.** Velocity field in a vertical plane through the impact on fresh water, We = 40.2. (a) 0.003 s after impact, the flow is mostly downward. (b) At 0.12 s, the drop's water has penetrated the surface as a descending vortex, while the surface flow stays weak. Verma et al. (2023), Fig. 1

Saltwater: a stronger, longer outward flow

On 35 g/kg saltwater, the drop's dilution sets up a solutocapillary doublet. Fluid runs outward along the surface and back toward the impact point just beneath it. The vortex is slower, about 8.6 cm/s, but the surface flow lasted roughly 2.6 s, about seven times longer than on fresh water, and it swept a larger region clear of particles.

Buoyancy helps. The drop's fresh water is lighter than the seawater, so after its momentum carries it down, it rises back to the surface, mixing as it goes, and keeps feeding the outward flow.

Four PIV vector fields comparing fresh water (top row) and saltwater (bottom row) for drops from 5 cm and 20 cm. The saltwater fields show strong outward vectors along the surface. — **Fig. 6.** Velocity fields after impact on (a) fresh water and (b) saltwater, for drops from (i) 5 cm and (ii) 20 cm, at 0.12 to 0.37 s. The outward flow along the saltwater surface is clear in both cases. Verma et al. (2023), Fig. 8

Surfactant: the flow turns around

With surfactant in the water, the outward flow from the impact reverses quickly, and the region cleared of particles closes up within fractions of a second. Above about 1 mg/kg (Ma₂ ≥ 1.5 × 10⁷), the vortex gives way to a continuous jet below the impact point. For drops released from 20 cm, the jet reached about 2.4 cm into the water, and its speed increased with concentration.

At high surfactant concentrations, adding 35 g/kg salt made little difference, because the reverse Marangoni flow suppressed the solutocapillary flow.

Four PIV vector fields at 0.37 s for surfactant concentrations of 0.01, 0.1, 10 and 100 mg/kg. The downward jet below the impact grows longer and stronger as concentration increases. — **Fig. 7.** Velocity fields 0.37 s after a drop from 20 cm lands on water with (i) 0.01, (ii) 0.1, (iii) 10 and (iv) 100 mg/kg surfactant. The downward jet grows with concentration. Verma et al. (2023), Fig. 10b

Trends with impact speed

The particle-free region is a direct gauge of the outward surface flow. Its diameter grew with the Weber number and with salt, and shrank as surfactant concentration rose: surfactant halved it, from 30.7 mm to 15.2 mm. Above 1 mg/kg the reverse flow closed it before it could be measured.

Three plots of particle-free region diameter against Weber number for saltwater, surfactant solutions, and salt plus surfactant, each compared with fresh water. — **Fig. 8.** Diameter of the particle-free region against Weber number for (a) saltwater, (b) surfactant solutions and (c) saltwater with surfactant, each against fresh water. Verma et al. (2023), Fig. 9

Fresh water

Saltwater, 35 g/kg

Surfactant, 1 mg/kg

Salt and surfactant

Video 2. The water column after a drop falls 20 cm (We = 148), filmed from the side and slowed down. On fresh water, a droplet pinches off at the top of the column. On saltwater the column is shorter. With surfactant, alone or with salt, it reaches about the same height as on fresh water.

The column of water that rises after impact grows taller with the Weber number. Salt lowers it slightly. Surfactant above 1 mg/kg makes it taller for drops released from higher than 10 cm. Each point is an average of over 20 drops, with a standard deviation under 1.6 mm.

Three plots of water column height against Weber number for saltwater, surfactant solutions, and salt plus surfactant, each compared with fresh water. — **Fig. 9.** Water column height against Weber number for (a) fresh and saltwater, (b) surfactant solutions and (c) saltwater with surfactant. Verma et al. (2023), Fig. 7

Why it matters

The ocean surface is rarely clean. Natural surfactants collect in the surface microlayer, and salinity shifts with rain, river inflow and melting ice. The same raindrop can stir that surface outward for seconds or send a jet straight down, depending on its chemistry. Both carry gas-rich surface water into the bulk, which is why this flow matters when estimating how rain affects the exchange of gases between air and water.

The same questions carry into my dissertation, which measures how fast CO₂ crosses the air–water interface as salt and surfactant concentrations change.

Verma, S., Benouaguef, I., Musunuri, N., Fischer, I. S., Singh, P. (2023). Marangoni flow induced in a waterbody by the impact of a raindrop. Mechanics Research Communications 133, 104187. doi:10.1016/j.mechrescom.2023.104187. Figures 2 to 9 are reproduced from this article, © 2023 Elsevier Ltd.