Thin-sheet creation and threshold pressures in drop splashing
Abstract: A liquid drop impacting a smooth solid substrate splashes by emitting a thin liquid sheet from near the contact line of the spreading liquid. This sheet is lifted from the substrate and ultimately breaks apart. Surprisingly, the splash is caused by the ambient gas, whose properties dictate when and if the sheet is created. Here, I focus on two aspects of this process. Using high-speed imaging I find that the time of thin-sheet creation displays a different quantitative dependence on air pressure if the sheet is created during the early stages of spreading, rather than when the liquid has already spread to a large radius. This result sheds light on previously observed impact velocity regimes. Additionally, by measuring impacts of drops on surfaces comprised of both rough and smooth regions, I identify a new threshold velocity that limits the times at which the thin sheet can be created. This velocity determines the threshold pressure below which splashing is suppressed.
Summary (2 min read)
- Experiments have found that drops splash only above a certain gas pressure in a variety of systems [1, 2, 3, 4, 5], and have provided insight into the liquid and air dynamics during splashing [6, 7, 8, 9].
- When the liquid finally makes contact with the substrate , the air directly beneath the drop is trapped in a small bubble  and does not further influence the splashing process .
- Next, the liquid spreads radially outward in the form of a liquid sheet that remains in direct contact with the substrate, as shown in Fig. 1.1a [6, 16, 17].
- The majority of present theories of splashing do not take this mechanism into account.
- Together, the air-dependent time of thin-sheet creation and the air-independent threshold velocity, below which thin-sheet creation is suppressed, form a pair of necessary and sufficient conditions for thin-sheet creation.
- The experiments were conducted with a variety of liquids.
- Ethanol and silicone oils (PDMS, Clearco Products) were used to vary the drop viscosity from µ = 1.2 to 48mPa s, while keeping the surface tension approximately constant between σ = 18.7 and 21.6mN m−1.
- The time of etching was chosen to produce a root-mean-square roughness Rrms = 1.9µm, sufficient to prevent thin-sheet creation for the liquids used .
- This accuracy was provided by ultra-fast interference imaging, which measures the interference between the light reflected from the bottom surface of the spreading liquid and the top surface of the substrate .
- The thinnest air gap the authors can reliably detect, approximately 30nm, is set by the wavelength of the light source (ThorLabs LED, λ = 625nm), the sensitivity of the camera, and the exposure time.
TIME OF THIN-SHEET CREATION
- The thin-sheet creation time depends on a number of parameters, in particular on the ambient gas pressure .
- The phase diagram can be understood by considering distinct thresholds for small-r∗ and large-r∗ sheets.
- In the low velocity regime, the small-r∗ sheet persists to lower pressures and Psheet = Psmall-r∗ and the dependence of sheet threshold pressure on impact velocity follows from the properties of small-r∗ sheet creation.
- There, a thin sheet begins to be created, despite the fact that t > tsheet, while the part of the drop that remains in the rough region continues to spread smoothly on the surface.
- The ustop pressure independence has an important practical consequence, as it allows one to measure ustop by simply measuring usheet on a smooth surface.
DISCUSSION AND CONCLUSIONS
- The cause of the sharp transition between small-r∗ and large-r∗ sheets can potentially be understood by considering the geometry of the drop.
- Notably, ucritical and ustop differ with respect to surface tension.
- Further research in both forced wetting and splashing is necessary before the role of surface tension in both processes can be understood.
- Existing experiments  and a recent simulation  confirm that early during drop impact the contact line does in fact behave differently in the early and late stages of spreading.
- Here, I showed that the threshold pressure is set by two distinct conditions: the air-dependent time of thin-sheet creation, and the air-independent threshold velocity ustop that is related to contact line stability.
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