We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy $k_{B}T$ to the swimmer’s activity $k_{s}T_{s}={\it\zeta}U_{0}^{2}{\it\tau}_{R}/6$, where ${\it\zeta}$ is the Stokes drag coefficient, $U_{0}$ is the swim speed and ${\it\tau}_{R}$ is the reorientation time of the active particles. The theory, which is valid on all length and time scales, has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behaviour when the boundary size is large compared to the swimmer’s run length $\ell =U_{0}{\it\tau}_{R}$. The theory is used to predict the motion of bodies of all sizes immersed in active matter.

When a drop impacts onto a solid surface, the lubrication pressure in the air deforms its bottom into a dimple. This makes the initial contact with the substrate occur not at a point but along a ring, thereby entrapping a central disc of air. We use ultra-high-speed imaging, with 200 ns time resolution, to observe the structure of this first contact between the liquid and a smooth solid surface. For a water drop impacting onto regular glass we observe a ring of microbubbles, due to multiple initial contacts just before the formation of the fully wetted outer section. These contacts are spaced by a few microns and quickly grow in size until they meet, thereby leaving behind a ring of microbubbles marking the original air-disc diameter. On the other hand, no microbubbles are left behind when the drop impacts onto molecularly smooth mica sheets. We thereby conclude that the localized contacts are due to nanometric roughness of the glass surface, and the presence of the microbubbles can therefore distinguish between glass with 10 nm roughness and perfectly smooth glass. We contrast this entrapment topology with the initial contact of a drop impacting onto a film of extremely viscous immiscible liquid, where the initial contact appears to be continuous along the ring. Here, an azimuthal instability occurs during the rapid contraction at the triple line, also leaving behind microbubbles. For low impact velocities the nature of the initial contact changes to one initiated by ruptures of a thin lubricating air film.

The wake behind a circular cylinder in Mach 4 flow is examined experimentally in the Reynolds number range $2\times 10^{4}$ to $5\times 10^{5}$. Periodic oscillations of the sliplines in the wake are observed. The Strouhal number of the oscillations based on the diameter of the cylinder is found to increase monotonically from 0.30 to 0.50 with increasing Reynolds number. If the Strouhal number is formed using the length of the sliplines, however, it has a constant value of approximately 0.48 for all Reynolds numbers studied. This scaling indicates that the oscillations in supersonic flow are likely driven by acoustic signals propagating back and forth through the subsonic region between the separation points on the cylinder and the neck where the sliplines converge, unlike in subsonic flow where oscillations are caused by vortices shed from the cylinder surface.