Fluids are fascinating as their complex motion emerges out of seemingly simple processes. Indeed, some of the most stunning images in all of science are of liquids as they leave wakes upon flowing past barriers or break apart as they fall. Fluids are essential in many technologies and are crucial in scientific contexts ranging from the large scales of astronomical objects to the microscopic scales observed inside cells. However, fluids are notoriously difficult to model. The central theme of this proposal is to study the aesthetically stunning topological transitions in fluids. Such transitions occur, for example, when a liquid drop breaks into pieces. Experiments are proposed to study drop breakup and the spouts that occur as a fluid is sucked up into a straw. These studies are important for the basic understanding of these processes and, for biomedical application. The proposed studies provide an exceptional starting place for bringing young students into the laboratory. Because the phenomena are so aesthetically appealing, and the results of this research will be used in very effective outreach to the public in the form of museum exhibits.
Fluids are essential in many technologies and are crucial in scientific contexts ranging from the large scales of astronomical objects to the microscales observed inside cells. However, fluids are governed by non-linear equations that present difficult problems in applied mathematics. The central theme of this proposal is to study topological transitions that occur in fluids. Such transitions occur, for example, when a drop of fluid breaks into several pieces. Experiments are proposed to study drop breakup and selective withdrawal spouts. These studies are important for the basic understanding of how to handle singularities and can be generalized to similar behavior seen in many disparate areas of science. A specific biomedical application is proposed for coating biological material. Because much of the proposed research deals with macroscopic phenomena, it provides an exceptional starting place for bringing young, inexperienced students into the laboratory. Because the phenomena are so accessible and aesthetically appealing, this research affords excellent outreach to the public. Postdoctoral associates, graduate, and undergraduate students will be trained by working on the proposed projects.
Intellectual Merit: The research that was done under the auspices of this grant focused on the complex behavior of fluids and on glassy dynamics. Our work on dynamic singularities, in fluids, i.e., droplet breakup and coalescence, has led to a more comprehensive view of the complexities of these dynamical transitions - not all of them are universal as had been thought and the flows are often surprising. When a mass of liquid splits into two pieces, there is a change in topology that is associated with a dynamic singularity where the forcing at the point of disconnection diverges. Such singularities often control all the dynamics so that all information about the initial and boundary conditions is lost. This scenario had been thought to lead to universal behavior in which the dynamics depends only on material parameters and not on initial conditions. In contrast, by studying air bubbles disconnecting from an under-water nozzle, we have identified a different mechanism for a breakup singularity in which dynamics near a singularity is able to preserve detailed information about its early history. As an air bubble separates, small deviations from cylindrical symmetry in its initial shape are encoded by oscillations that we measured using two synchronized high-speed cameras. Close to the singularity, the amplitudes of these oscillations become fixed thus retaining information about the bubble’s initial conditions. When liquid drops merge, the topology changes as the fluid masses, originally separated, merge into a single entity. At first, the drops are separated by a narrow gap. Then a thin fluid bridge is formed between them that rapidly widens due to surface tension forces. We employed an electrical method to explore drop coalescence down to ten nanoseconds after the drops touch. In a low-viscosity liquid, we found that if the drops move together rapidly enough, there is a regime that is dominated by the overall deformability of the drops. By varying the liquid viscosity over two decades, we were able to conclude that, at a sufficiently low approach velocity, where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argued that the late crossover, not accounted for in the theory, could be explained by an appropriate choice of length scales present in the flow geometry. Our studies of liquid splashing have opened up new directions having to do with air entrainment. We investigated the interplay between substrate roughness and the surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associated two distinct forms of splashing with each of these control parameters: Prompt splashing is due to surface roughness and corona splashing is due to instabilities produced by the surrounding gas. The size distribution of ejected droplets reveals the length scales of the underlying droplet-creation process in both cases. After impact, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this thin-sheet formation. In addition, air bubbles are entrained underneath the spreading lamella only when the ejected sheet is present. The slow compaction of tapped granular matter is reminiscent of the low-temperature dynamics glasses. While the density displays glassy aging at low tapping amplitudes, the dynamic volumetric susceptibility gives no indication of a rapidly growing time scale. This suggests that granular compaction is controlled by statistically rare processes. Sorting the integers 1 through N into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally activated pair-wise exchanges of neighboring list elements, we found that sorting can display many features of a glass. This includes memory and rejuvenation effects during aging—two hallmarks of glassy dynamics that had previously been difficult to reproduce in standard glass simulations. Broader Impacts: During the course of this grant, postdoctoral associates and graduate students have been trained in the study of complex phenomena. Due to the fact that much of this research dealt with macroscopic phenomena, it provided an excellent starting place for bringing undergraduate and high-school students into a research laboratory. Because the phenomena are so accessible, this research also afforded an excellent mode of outreach to show the public some of what is occurring at the forefront of scientific research. This included museum exhibits at the Museum of Science and Industry in Chicago and the Exploratorium in San Francisco.
