Thin-sheet creation and threshold pressures in drop splashing.

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.

Comparison of splashing in high- and low-viscosity liquids.

We explore the evolution of a splash when a liquid drop impacts a smooth dry surface. There are two splashing regimes that occur when the liquid viscosity is varied as is evidenced by its dependence on ambient gas pressure. A high-viscosity drop splashes by emitting a thin sheet of liquid from a spreading liquid lamella long after the drop has first contacted the solid. Likewise, we find that there is also a delay in the ejection of a thin sheet when a low-viscosity drop splashes. We show how the ejection time of the thin sheet depends on liquid viscosity and ambient gas pressure.

Creation of prompt and thin-sheet splashing by varying surface roughness or increasing air pressure.

A liquid drop impacting a solid surface may splash either by emitting a thin liquid sheet that subsequently breaks apart or by promptly ejecting droplets from the advancing liquid-solid contact line. Using high-speed imaging, we show that surface roughness and air pressure influence both mechanisms. Roughness inhibits thin-sheet formation even though it also increases prompt splashing at the advancing contact line. If the air pressure is lowered, droplet ejection is suppressed not only during thin-sheet formation but also for prompt splashing.

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale.

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.