Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Investigation of Two-Phase Flow in a Hydrophobic Fuel-Cell Micro-Channel

This paper presents a quantitative visualization study and a theoretical analysis of two-phase flow relevant to polymer electrolyte membrane fuel cells (PEMFCs) in which liquid water management is critical to performance. Experiments were conducted in an air-flow microchannel with a hydrophobic surface and a side pore through which water was injected to mimic the cathode of a PEMFC. Four distinct flow patterns were identified: liquid bridge (plug), slug/plug, film flow, and water droplet flow under small Weber number conditions. Liquid bridges first evolve with quasi-static properties while remaining pinned; after reaching a critical volume, bridges depart from axisymmetry, block the flow channel, and exhibit lateral oscillations. A model that accounts for capillarity at low Bond number is proposed and shown to successfully predict the morphology, critical liquid volume and evolution of the liquid bridge, including deformation and complete blockage under specific conditions. The generality of the model is also illustrated for flow conditions encountered in the manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The experiments provide a database for validation of theoretical and computational methods.

Evaporation and instability of an unbounded-axisymmetric liquid bridge between chemically similar and different substrates

HYPOTHESIS

In this manuscript we examine the stability of an evaporating-unbounded axisymmetric liquid bridge confined between parallel-planar similar or chemically different substrates using both theory and experiments. With a quasistatic assumption we use hydrostatics to estimate the minimum stable volume V_min via the Young-Laplace equation for Bond numbers 0⩽Bo⩽1, and top/bottom wall contact angles 5°<θ<175° although the primary focus is on wetting and partial wetting fluids. Solving the Young-Laplace equation requires knowledge of appropriate capillary pressure values, which appear as a constant, and may not provide unique solution. To examine uniqueness of numerical solutions and volume minima determined from the Young-Laplace equation for unbounded-axisymmetric liquid bridges we analyzed capillary pressure for large and small liquid volume-asymptotic limits at zero Bond number.

EXPERIMENTS

Experiments were performed to compare with the volume minima calculations for Bond numbers 0.04⩽Bo⩽0.65. Three substrates of varying surface energy were used, with purified water as the primary liquid. Volume estimates and contact angle data were extracted via image analysis and evaporation rates measured from this data are reported.

FINDINGS

Volume minima were in the range 0.1<V_min<20 μl depending on Bond number. There was good agreement when comparing predicted volume minima and those determined from experiments for the range of parameters studied.

Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions

The characterization of the extensional rheology of polymeric solutions is important in several applications and industrial processes. Filament stretching and capillary breakup rheometers have been developed to characterize the extensional properties of polymeric solutions, mostly for high-viscosity fluids. However, for low concentration polymer solutions, the measurements are difficult using available devices, in terms of the minimum viscosity and relaxation times that can be measured accurately. In addition, when the slow retraction method is used, solvent evaporation can affect the measurements for volatile solvents. In this work, a new setup was tested for filament breakup experiments using the slow retraction method, high-speed imaging techniques, and an immiscible oil bath to reduce solvent evaporation and facilitate particle tracking in the thinning filament. Extensional relaxation times above around 100 μs were measured with the device for dilute and semi-dilute polymer solutions. Particle tracking velocimetry was also used to measure the velocity in the filament and the corresponding elongation rate, and to compare with the values obtained from the measured exponential decay of the filament diameter.

Measurement of surface and interfacial tension using pendant drop tensiometry

Pendant drop tensiometry offers a simple and elegant solution to determining surface and interfacial tension - a central parameter in many colloidal systems including emulsions, foams and wetting phenomena. The technique involves the acquisition of a silhouette of an axisymmetric fluid droplet, and iterative fitting of the Young-Laplace equation that balances gravitational deformation of the drop with the restorative interfacial tension. Since the advent of high-quality digital cameras and desktop computers, this process has been automated with high speed and precision. However, despite its beguiling simplicity, there are complications and limitations that accompany pendant drop tensiometry connected with both Bond number (the balance between interfacial tension and gravitational forces) and drop volume. Here, we discuss the process involved with going from a captured experimental image to a fitted interfacial tension value, highlighting pertinent features and limitations along the way. We introduce a new parameter, the Worthington number, Wo, to characterise the measurement precision. A fully functional, open-source acquisition and fitting software is provided to enable the reader to test and develop the technique further.

Compound pendant drop tensiometry for interfacial tension measurement at zero bond number

A widely used method to determine the interfacial tension between fluids is to quantify the pendant drop shape that is determined by gravity and interfacial tension forces. Failure of this method for small drops or small fluid density differences is a critical limitation in microfluidic applications and when only small fluid samples are available. By adding a small spherical particle to the interface to apply an axisymmetric deformation, both the particle density and the interfacial tension can be simultaneously and precisely determined, providing an accurate and elegant solution to a long-standing problem.