Pinch-off of a stretching viscous filament and drop transport

Abstract

This study is focused on the stretching and breakup of a Newtonian liquid bridge between two parallel plates, one of which moves with a constant acceleration. The experimental device is designed to achieve high acceleration (up to 200 m s −2 ) with high precision. The shape evolution of the liquid bridge and its pinch-off are captured using a high-speed video system. At high enough acceleration the evolution of the midpoint diameter of the bridge is universal; it depends neither on the acceleration nor on the liquid viscosity. Moreover, at high acceleration rates even the breakup time does not depend on the acceleration, but is determined solely by the liquid viscosity. A model is proposed which predicts the instant of the liquid bridge pinch-off. Finally, the volumes of the residual liquid on both fixed and moving plates (which do not include the total volume of the residual secondary drops) is measured. It is shown that the volume on the fixed plate remains almost constant, the volume on the accelerating plate reduces as the acceleration increases.

Plant-inspired pipettes

“…At low velocities, m increased with increasing v, until reaching its maximum value m max , after which it remained almost constant (or slightly decreasing) in the high-velocity regime studied here. During high-velocity withdrawal, a liquid ligament developed and axially stretched as shown in figure 3b [33][34][35]. When it finally broke, its upper part was captured by the ribs (electronic supplementary material, movie S1, filmed with a high-speed camera (Ditect, Japan)).…”

The break-up of free films pulled out of a pure liquid bath

“…where we approximate the initial condition (29c) onū using the value resulting from equation (22a) in stationary regime. At first sight, the system of equations (22)(23) should require five boundary conditions: two on the thickness h, two on the vertical velocityū and one on the mean curvature K. However, the order of differentiation onū can by reduced by one by defining λ = ∂ x h as an intermediate variable. Using the mass conservation h∂ xū = −∂ t h −ūλ in equation (22b), only first-order spatial derivative for the variables h, λ, K andū are left in the system.…”

“…These parameters will henceforth be set to x 0 = 0.1 and L 0 = √ 2, as justified in appendix A. The system of partial differential equations (22)(23), supplemented by the initial solutions (29) and boundary conditions (30)(31), is solved using the direct solver MUMPS in COMSOL 5.0. Since the problem involves a moving boundary -the fiber which is lifted at a constant velocity to create the film -the domain geometry is changing with time.…”

“…The critical thickness varies more slowly than ε −1 below ε ∼ 10 −1 , but faster than ε −1 for ε 10 −1 , hence the non-monotonic behaviour of the dimensional critical thickness H × h * as a function of the fiber half-width H, as shown in figure 6e. This change in behaviour for ε 10 −1 is likely due to the ε 2 term in the denominator of the mean curvature (23), which becomes non-negligible. Such a power law behaviour for the critical thickness as a function of the Hamaker constant had already been predicted by [29] for small horizontal liquid films.…”

“…For a liquid bridge between two parallel horizontal disks, [21] have explored the influence of surface wettability on the transition from a quasi-static (capillary dominated) to a dynamic stretching (dominated by viscous and inertial forces). On the same system, experiments and simulations have been performed to understand the influence of the stretching velocity [22] or acceleration [23] on the time of liquid bridge break-up.…”