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Surface Driven Flows : Liquid Bridges, Drops and Marangoni Propulsion

Molecules sitting at a free liquid surface against vacuum or gas have weaker binding than molecules in the bulk. The missing (negative) binding energy can therefore be viewed as a positive energy added to the surface itself. Since a larger area of the surface contains larger surface energy, external forces must perform positive work against internal surface forces to increase the total area of the surface. Mathematically, the internal surface forces are represented by surface tension, defined as the normal force per unit of length. One common manifestation of surface tension is the difference in pressure it causes across a curved surface. This is the main principle behind capillary breakup extensional rheometry (CaBER). The other manifestation is the Marangoni flow which drives the interface towards the direction of the increasing surface tension gradient. The surface tension gradient can be caused by concentration gradient or by a temperature gradient (surface tension is a function of temperature). Both of these phenomenon will be investigated through various experimental techniques. Predicting and controlling the rheology of polymeric fluids as a function of molecular chemistry has been of great interest in both academia and industry. While extensional rheology measurements of polymer melts have been performed in the past, those experiments were performed under nitrogen and at temperatures chosen to avoid polymer degradation and reaction. In this work we will explore the effect that oxygen at high temperatures can have on both the shear and extensional rheology of a series of polymer melts. We will demonstrate the high temperature evolution of extensional viscosity of three selected commercially available polycarbonates – one linear, one branched and one hyper-branched. The measurements were performed using a custom built high temperature capillary extensional break up rheometer (CABER). The experiments were performed in the temperature range of T= 250C and 370C both in air and nitrogen. We will present a stark difference in the extensional behavior of the three grades of polycarbonate and demonstrate an obvious differentiation between random chain scission which is the first phase of polymer degradation and repolymerization or crosslinking which takes place at higher temperatures. In a number of recent studies, the large extensional viscosity of dilute polymer solutions has been shown to dramatically delay the breakup of jets into drops. For the low shear viscosity solutions, the jet breakup is initially governed by a balance of inertial and capillary stresses before transitioning to a balance of viscoelastic and capillary stresses at later times. This transition occurs at a critical time when the radius decay dynamics shift from a 2/3 power law to an exponential decay as the increasing deformation rate imposed on the fluid filament results in large molecular deformations and rapid crossover into the elastocapillary regime. By experimental fits of the elasto-capillary thinning diameter data, relaxation time as low as 40 microseconds have been successfully measured. In this work, we will show that with better understand of the transition from the inertia-capillary to the elasto-capillary breakup regimes that relaxation times close to a single microsecond can be measured with the relaxation time resolution limited only by the frame rate and spatial resolution of the high speed camera. In this work, the dynamics of drop formation and pinch-off will be presented using Dripping onto Substrate Extensional Rheometry (DoS) for a series of dilute solutions Polyethylene Oxide in water and in a water and glycerin mixture. Four different molecular weights between 100k and 1M g/mol will be shown with varying solvent viscosities between 1mPa-s and 22mPa-s and at concentrations between 0.004 and 0.5c*. We will show the dependence of the relaxation time and extensional viscosity on these varying parameters while searching for the lower limit in solution elasticity that can be detected. We will also show that this approach is a powerful technique for characterizing a notoriously difficult material, namely low-viscosity printing inks. In this last project we have investigated the flow dynamics around a cylindrical disk propelled by Marangoni propulsion. Self-propulsion was achieved by coating one quarter of the disk with either soap or isopropyl alcohol in order to generate and then maintain a surface tension gradient across the surfer. As the propulsion strength and the resulting disk velocity were increased, a transition from a straight-line translational motion to a rotational motion was observed. Although spinning has been observed before for asymmetric objects, these are the first observations of spinning of a symmetric Marangoni surfer. Particle tracking and Particle Image Velocimetry (PIV) measurements were used to interrogate the resulting flow field and understand the origin of the rotational motion of the disk. These measurements showed that as the Reynolds number was increased, interfacial vortices attached to sides of the disk were formed and intensified. Beyond a critical Reynolds number of Re > 120, a single vortex was observed to shed resulting in an unbalanced torque on the disk that caused it to rotate. The interaction between the disk and the confining wall of the Petri dish was also studied. Upon approaching the bounding wall, a transition from straight-line motion to rotational motion was observed at significantly lower Reynolds numbers than on an unconfined interface. Interfacial curvature was found to either enhance or eliminate rotation motion depending on whether the curvature was repulsive (concave) or attractive (convex). Along with investigations done for the case of a disk shaped Marangoni surfer, we have also look at the effect of shape and orientation of motion on the on the stability of these surfers. We have looked at spherical shaped Marangoni surfers and also at elliptical disks. The stability of the elliptical disks were found to be strongly linked to their aspect ratio and their orientation. While looking at shape effects on Marangoni propulsion we have also investigated the effect of reverse flow underneath the surfer and its effect on the motion. We were experimentally able to observe the phenomenon of reverse Marangoni propulsion of surfers which was found to be a function of water depth underneath the surfer. We performed a parametric study on the effect of depth of water on the mode of motion of a cylindrical disk shaped and a spherical shaped surfer. Along with critical depth, it was found that the Reynolds number also played a critical role in flow reversal. At higher Reynolds number, no reverse phenomenon was observed as inertia dominated the motion of the disk whereas at low Reynolds numbers and at the critical Depth, flow reversal was observed.
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