Cell movements play a central role in a host of biological processes, such as fertilization, bacterial infection, and transport of mucus and fluid in the body. The complex fluids that motile cells encounter are laden with polymers. When deformed by a swimming cell, the polymers stretch, leading to an elastic resistance in addition to the viscous resistance of the fluid. The microstructure of biological materials is often anisotropic as well. The goal of this research is to use theory and experimental models to establish the fundamental principles of swimming in viscoelastic media such as mucus and biofilms. To study swimming mechanics in a controlled environment, the PIs will develop a series of table-top macroscopic scale experiments. These experiments will determine how swimming speed depends on viscoelastic properties for a swimmer with a prescribed stroke, how viscoelastic forces can alter the shape of a beating filament, and the role of viscoelasticity in the hydrodynamic synchronization of beating cilia. The PIs will develop new theories for these phenomena, and also study how non-Newtonian effects change the hydrodynamic interactions between nearby swimmers and boundaries, and the nature of the collective motion of dense populations of swimmers. The basic hydrodynamic theory for microorganisms swimming in a Newtonian liquid such as water has been largely established. Nevertheless, the field continues to be very active since many issues such as hydrodynamic interactions between cells, synchronized ciliary beating, and the actuation of flagella are only partially understood. The natural environments of microorganisms are predominantly non-Newtonian, and every basic element of the theory must be considered anew. Our work will also establish the design principles required to build artificial microswimmers capable of negotiating viscoelastic as well as viscous fluids. The PIs will work with the K-12 Teacher Training program within the Brown MRSEC outreach program to develop new demonstrations of cell motility. The PIs will continue to build on their successful history of recruiting under-represented groups. Finally, the fundamental principles of this work have the potential to impact applications such human fertility, the treatment of bacterial infections and diseases such as cystic fibrosis, and the artificial insemination of livestock.
A new experimental apparatus was designed and built to measure the speed of a mechanical swimmer moving through a fluid. A primary motivation of this collaborative study conducted by physicists and engineers at Clark University in Worcester Massachusetts and Brown University in Providence Rhode Island was to understand the effect of visco-elasticity of the medium on the measured speeds of micro-swimmers such as sperm and bacteria. Unlike viscous fluids such as corn syrup, visco-elastic fluids such as mucus have an elastic response. This makes swimming through them fundamentally different from viscous fluids, just as swimming through low viscosity fluids such as water is for fishes and humans where inertial effects are important. Many examples of microorganisms swimming through visco-elastic fluids can be found in Nature, including sperm swimming through cervical mucus and Helicobacter pylori in gastric mucus. Because of the complexity of these fluids, and the shape and stroke of the swimmer, the problem is difficult to solve analytically. Therefore, model systems are necessary to capture the essential features of the system and to understand the variables important to determining the swimming speed. Accordingly, a mechanical apparatus was designed so that the effect of the swimming stroke could be separated from other complex interactions with the fluid. (A schematic diagram is shown in the uploaded image.) The working part of the swimmer consists of a flexible cylindrical belt which is driven by motors and gears in the form of a travelling wave. This wave-form pushes on the fluid propelling the swimmer. The net force on the swimmer is always zero because the propulsive force is balanced by the viscous drag force exerted back by the fluid and the swimmer moves with constant speed. Employing a mechanical swimmer also allows use of model liquids whose visco-elastic properties can be simplified and varied without the constraint of having to make the medium habitable for a living organism. Fluids with viscosity which were at least a thousand times that of water were used to be in the so called low-Reynolds regime. Over the course of the grant period, the swimming speeds measured in the apparatus were found to be consistent with analytical calculations and numerical simulations developed during the course of the grant period starting with the Stokes equation for viscous Newtonian fluids. However, in case of visco-elastic fluids not only were swimming speeds greater than compared with Newtonian fluids, but also could be smaller depending on the rheological properties of the fluid. This was a great surprise because all analytical calculations so far have argued for a systematic decrease in the swimming speed. The results, which show both increasing and decreasing trends in the same apparatus with the various visco-elastic fluids, point to a pressing need for a broad series of experiments, theory and numerical simulations in systems with varieties of geometries before one can fully understand how microorganisms swim in visco-elastic fluids. The newly designed swimming apparatus has the potential to be developed as system to measure expected swimming speeds for a various non-Newtonian fluids just as a rheometer is used to measure viscosity and elasticity properties of a fluid. Further, the grant funds were used to train undergraduate and graduate students towards STEM careers, and reports were prepared to disseminate the results of our study to experts in the field through workshops and conferences, and more widely through society journals.
