Bian Qian

The motion, stability and breakup of a stretching liquid bridge with a receding contact line

The complex behaviour of drop deposition on a hydrophobic surface is considered by looking at a model problem in which the evolution of a constant-volume liquid bridge is studied as the bridge is stretched. The bridge is pinned with a fixed diameter at the upper contact point, but the contact line at the lower attachment point is free to move on a smooth substrate. Experiments indicate that initially, as the bridge is stretched, the lower contact line slowly retreats inward. However, at a critical radius, the bridge becomes unstable, and the contact line accelerates dramatically, moving inward very quickly. The bridge subsequently pinches off, and a small droplet is left on the substrate. A quasi-static analysis, using the Young–Laplace equation, is used to accurately predict the shape of the bridge during the initial bridge evolution, including the initial onset of the slow contact line retraction. A stability analysis is used to predict the onset of pinch-off, and a one-dimensional dynamical equation, coupled with a Tanner law for the dynamic contact angle, is used to model the rapid pinch-off behaviour. Excellent agreement between numerical predictions and experiments is found throughout the bridge evolution, and the importance of the dynamic contact line model is demonstrated.

Shape Transition and Propulsive Force of an Elastic Rod Rotating in a Viscous Fluid

The deformation of an elastic rod rotating in a viscous fluid is considered, with applications related to flagellar motility. The rod is tilted relative to the rotation axis, and experiments and theory are used to study the shape transition when driven either at constant torque or at constant speed. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly, and the rod forms a helical shape with increased propulsive force. We find good agreement between theory and experiment. A simple physical model is presented to capture and explain the essential behavior.

Micron-Scale Droplet Deposition on a Hydrophobic Surface Using a Retreating Syringe

Droplet deposition onto a hydrophobic surface is studied experimentally and numerically. A wide range of droplet sizes can result from the same syringe, depending strongly on the needle retraction speed. Three regimes are identified according to the motion of the contact line. In region I, at slow retraction speeds, the contact line expands and large droplets can be achieved. In region II, at moderate needle speeds, a quasicylindrical liquid bridge forms resulting in drops approximately the size of the needle. Finally, at high speeds (region III), the contact line retracts and droplets much smaller than the syringe diameter are observed. Scaling arguments are presented identifying the dominant mechanisms in each regime. Results from nonlinear numerical simulations agree well with the experiments, although the accuracy of the predictions is limited by inadequate models for the behavior of the dynamic contact angle.

Large apparent slip at a moving contact line

Two different particle tracking velocimetry techniques are used to measure the fluid velocities close to the substrate in the vicinity of both receding and advancing contact lines. The slip velocity is found to be as much as 60% of the substrate speed near the contact line and persists as far as 10 μm from the liquid-gas interface. The estimated slip length near the contact line singularity requires a measurement of the shear rate close the substrate which depends strongly on the spatial resolution of the measurement technique. The slip length is found to be approximately 5 μm when flood illumination is used and approximately 500 nm when total internal reflection fluorescence illumination is used.