John Hinch

Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface

We numerically investigated liquid droplet impact behavior onto a dry and flat surface. The numerical method consists of a coupled level set and volume-of-fluid framework, volume/surface integrated average based multimoment method, and a continuum surface force model. The numerical simulation reproduces the experimentally observed droplet behavior quantitatively, in both the spreading and receding phases, only when we use a dynamic contact angle model based on experimental observations. If we use a sensible simplified dynamic contact angle model, the predicted time dependence of droplet behavior is poorly reproduced. The result shows that precise dynamic contact angle modeling plays an important role in the modeling of droplet impact behavior.

Spreading fronts and fluctuations in sedimentation

A diffuse interface or “front” at the top of the suspension is investigated experimentally and numerically. The width of the front is found to grow linearly in time, mainly due to a polydispersity of particle size in the very dilute experiments, and due only to fluctuations in particle density in the simulations. Away from the front, the fluctuations in the particle velocities are found not to decay.

Plethora of transitions during breakup of liquid filaments

Significance Fluid flows, governed by nonlinear equations, permit formation of singularities. Often, singularities are artifacts of neglecting physical effects. However, free-surface flows exhibit observable singularities including filament pinch-off. As filaments thin, slightly (highly) viscous filaments are expected from theory to transition from an inertial (viscous) regime where viscosity (density) is negligible to an inertial–viscous regime where viscous and inertial effects are important. Previous works show this transition either does not occur or occurs for filament radii well below theoretical predictions. We demonstrate that thinning filaments unexpectedly pass through a number of intermediate transient regimes, thereby delaying onset of the final regime. The findings raise the question if similar dynamical transitions arise in problems that are not necessarily hydrodynamic in nature. Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial–viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. Here, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial–viscous regime. The new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.

Hydrodynamic interactions in deep bed filtration

Deep bed filtration has been studied experimentally and numerically for small non‐Brownian particles flowing into a random packing of monosize glass spheres at low Reynolds number. It was discovered that packets of particles penetrated further than the same number of particles released one at a time. These collective effects are attributed to hydrodynamic phenomena, one plausible explanation being the existence of relaunchable ‘‘hydrodynamic captures’’ in addition to ‘‘geometric captures.’’

A perspective of Batchelor's research in micro-hydrodynamics

Batchelor made his name with research in turbulence in the 1940s and 1950s. He became disillusioned with turbulence at the Marseille meeting in 1961. At the end of the 1960s, he started his second wave of research on low-Reynolds-number suspensions of particles. Ten years after he died, I will describe his key results, what was before and what followed. Eight of his 10 most cited papers are in micro-hydrodynamics.