Transport of Particles and Organisms in Stratified and Viscoelastic Fluids

Rajat Dandekar, Purdue University

Abstract

The motion of small-scale organisms migrating in natural environments such as oceans, lakes or pools typically occurs in a low Reynolds number regime. In this regime, the viscous forces dominate the inertial forces and the organisms have to generate propulsion forces which counter the viscous drag. Evolution has forced these aquatic organisms to adapt in such a way that they generate a non-reciprocal motion, i.e., the forward stroke is not identical in shape to the backward stroke. As an example, the motion of the bacteria Escherichia coli demonstrates the use of transverse waves as a mechanism to counter the perils of reciprocity, which causes the swimmer surface to bend one way during the first half and the other way during the second half, similar to an oar. At low Reynolds numbers, the fluid response to the motion of the organisms is instantaneous, as the velocity perturbations decay rapidly. Hence the organisms experience a net force and torque which is identical to zero. In addition to microorganisms, settling of rigid particles in natural environments at low Reynolds numbers is a common phenomenon. Several examples of settling particles can be found in oceans (settling of microparticles), galaxies in space (transport of bubbles across clusters) and geological environments (mixing of magmas). In this work, we will predominantly focus on transport of particles and organisms at low-Reynolds numbers.Spatial variations of ambient conditions such as temperature, light intensity, humidity or salinity is inherently present in natural environments including aquatic environments, atmosphere and galaxies. This causes macroscopic fluid properties like density and viscosity to vary spatially as well. Organisms and particles moving in such environments have to navigate these stratified fluids and the variation in the macroscopic fluid properties can have a significant influence on their motion. As an example of a localized stratified environment, consider the example of the Deepwater Horizon oil spill incident in the Gulf of Mexico which created spatial variations of density and viscosity owing to the mixing of different fluids including soluble and insoluble petroleum. Additionally, such fluids can exhibit complex rheological behavior such as shear rate dependent solvent viscosity, viscoelasticity or a combination of both. Even a marginal deviation of the solvent from a Newtonian behavior has been shown to affect the dynamics of the suspended particles in non-trivial ways [1] and has been exploited for several particle manipulation and control applications [2]–[5]. Towards successfully predicting the behavior of a suspension of interacting organisms and swimmers immersed in a complex fluid, understanding the binary interactions of particles forms a fundamental building block which demands attention. Our work sheds light on the hydrodynamic behavior of particles and organisms in such stratified or viscoelastic environments.To understand the transport of particles and organisms in natural environments, theoretical models are useful. In particular, such models shed light on the key physical mechanisms underpinning the transport. Typical theoretical models include a mathematical approximation of the particle/organism and the surrounding fluid. The first theoretical model of microorganism can be traced back to 1951, where Taylor developed a swimming sheet model [6], which approximated the swimming motion by small amplitude transverse waves deforming the swimmer surface. Subsequently, the Taylor swimming sheet has been used extensively to understand the motion of organisms in several scenarios including fluid inertia, wall confinements, gels, porosity and viscoelasticity.

Degree

Ph.D.

Advisors

Ardekani, Purdue University.

Subject Area

Fluid mechanics|Geology|Materials science|Mechanics|Microbiology|Recreation|Sedimentary Geology

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