Session ML: Bio-Fluids: Wakes and Mixing II

Strategy Dependent Swimming Dynamics Change among a Predatory Algae Species with Different Strains

Digital holographic microscopic cinematography is used for measuring the 3D, time resolved, swimming behavior of toxic and non-toxic strains the marine dinoflagellate \textit{Karlodinium veneficum}. We focus on the response of predators of the same species, but with different predation strategy, to the presence of prey, \textit{Storeatula major}. Experiments are performed in a 3$\times $3 mm cuvette, at densities extending to 100,000 cells/ml. Holograms are recorded at 60fps and at 20X magnification. In each case, we simultaneously track 200-500 cells in the 3mm deep sample, at a spatial resolution of 0.4$\times $0.4$\times $2 $\mu $m. We show that responses are largely dependent on the predation strategy. \textit{K. veneficum} 2064, a toxic mixotroph, slows down and decreases the helix radius and clusters around the prey. Conversely, MD5, a non-toxic, autotrophic-like strain is completely oblivious to prey. Strain 1974, which is toxic and twice as motile, shows heterotrophic-like responses with characteristics of an active hunter. Also, on going spectral analysis of the 3-D motion provides quantitative insight on the swimming dynamics of microorganisms.   

Flows generated by bacteria settled upon a solid surface

Free-swimming Bacillus subtilis are propelled by rotating helical flagella distributed over the the cell body surface. Rearward-oriented coherent bundles of these organelles propel the organisms forward. This directional polarity is a dynamically self-organized aspect of swimming. A swimming cell generates only local disturbance of the fluid. But, when such a cell settles on a surface, the cell body becoming immobile, the flagella adopt bi-polar ordering, inferred from the production of a circulating ($\sim$10 $\mu$m $\sim$10 cell diameters) flow. Such flows can be significant for cell-cell communication and the transport of small molecules involved in metabolism or larger ones involved in the local synthesis of biofilms. Experimental results and associated mathematical models provide cross-validation for this remarkable discovery.   

Dynamics and stability of low Reynolds number swimming near a plane wall

Low Reynolds number swimming of microorganisms or tiny robotic swimmers in confined environments poses open questions on the existence of steady swimming parallel to the boundary, as well as the stability of such solutions under perturbations. In this work we formulate the dynamics of a simple swimmer near a plane wall. The swimmer is modeled as an assemblage of spheres attached to a rigid frame and being actively rotated about their attachment points. Using the model developed by Swan and Brady (Physics of Fluids 19, 113306, 2007) to account for the far-field hydrodynamic interactions between the spheres and the wall, we formulate the dynamic equations of swimming. We prove that steady solution of parallel swimming exists for a swimmer with two rotating spheres. We then discuss the interplay between symmetry and stability, and show that one must break the symmetry in order to obtain passive stabilization. Next, we show that parallel swimming with three spheres can be passively stable in a wide range of orientations, and present numeric simulation results. Finally, we discuss the existence and stability of periodic orbits, and the relation to effects of attraction and alignment of swimming bacteria near a plane boundary.   

Interaction of rotating helical bacterial flagella with nearby solid

The axes of the rotating flagella of bacteria whose body is immobilized at a surface may initially be oriented in arbitrary directions. Through simulations using the method of Regularized Stokeslets, it is seen that the hydrodynamic interaction of the flagella with the neighboring solid surface produces attraction of the flagella toward that surface. Furthermore, the rotation generates a drag such that the flagella ``roll'' toward the cell body from which they emerge. This phenomenon requires that the flagella are initially or eventually oriented at an angle (between axis and plane) such that the hydrodynamic attraction overcomes thermal fluctuations. This interaction converts a three-dimensional initial situation into the two dimensional transport-generating phenomenon discussed in the previous abstract.   

Numerical simulation of a self-propelled copepod during escape

Obtaining the 3D flow field, forces, and power is essential for understanding the high accelerations of a copepod during the escap. We carry out numerical simulations to study a free swimming copepod using the sharp-interface immersed boundary, fluid-structure interaction (FSI) approach of Borazjani et al. (J Compu Phys, 2008, 227, p 7587-7620). We use our previous tethered copepod model with a realistic copepod-like body, including all the appendages with the appendages motion prescribed from high-resolution, cinematic dual digital holography. The simulations are performed in a frame of reference attached to the copepod whose velocity is calculated by considering the forces acting on the copepod. The self-propelled simulations are challenging due to the destabilizing effects of the large added mass resulting from the low copepod mass and fast acceleration during the escape. Strongly-coupled FSI with under-relaxation and the Aitken acceleration technique is used to obtain stable and robust FSI iterations. The computed results for the self-propelled model are analyzed and compared with our earlier results for the tethered model.   

Breakdown of the scallop theorem with swimmer inertia

According to the scallop theorem, a swimmer executing a time-reversible (or ``reciprocal'') motion cannot propel itself in the limit of zero Reynolds number. How much inertia is necessary for a reciprocal motion to become propulsive? Here, we study the breakdown of the scallop theorem for dense swimmers, for which only particle inertia is significant. We apply Lorentz's reciprocal theorem to derive general differential equations that govern the locomotion kinematics of a dense swimmer. We then apply these results to several spatially-asymmetric swimmers and show that they are able to propel themselves at any arbitrarily small value of the particle Reynolds number, even in the absence of fluid inertia.   

Swimming in Complex Fluids

Many flagella-propelled microorganisms swim through gels and non-Newtonian fluids. We address how swimming velocities are affected in nonlinearly viscoelastic fluids. Working to leading order in the deflection of the swimmer, we find that swimming velocities are diminished by nonlinear viscoelastic effects. The implications of our results for Purcell's ``scallop theorem" are examined.   

Nature's Microfluidic Transporter: Rotational Cytoplasmic Streaming at High P{\'e}clet Numbers

Cytoplasmic streaming circulates the fluid contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by ``rotational streaming'' found in Characean algae we solve the Stokesian advection-diffusion dynamics of flow in a cylinder with bi-directional helical forcing at the wall. Transverse to the cylinder's long axis is generated circulatory flow akin to Dean vortices at finite Reynolds numbers. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse P{\'e}clet number is sufficiently large, with scaling laws arising from the effects of boundary layers.   

Velocity and stress correlations in suspensions of swimming microorganisms: theory and simulation

Large collections of swimming microorganisms are able to produce collective motions on a scale much larger than the scale of a single organism. In particular, the collective behavior leads to velocities larger than that of an isolated organism, fluid structures larger than the size of an organism, enhanced transport in the fluid, and enhanced stress fluctuations which produce altered rheological properties. We show theoretically how these phenomena are linked to the interactions between the organisms and compare the predictions with the results from computer simulations. In this way we can understand how the behavior scales with concentration, the importance of the method of swimming used, the influence of run-and-tumble like motions of the organisms, and how the interactions can lead to large-scale fluid structures. In periodic geometries, the large-scale fluid structures lead to simulation results that depend on the simulation box size.   

Numerical analysis of a stable waltzing pair of Volvox

When we placed suspensions of Volvox in glass-topped chambers, we observed the frequent formation of stable bound state of two colonies orbiting each other, referred to as a waltzing motion. In this study, we computationally investigate the mechanism of the waltzing motion. In modelling a Volvox computationally, we assumed that a Volvox was a rigid sphere generating force distribution slightly above the surface. The flow field around a Volvox was assumed to be Stokesian, and sedimentation and bottom-heaviness were taken into account. Equation for the flow field was solved by a boundary element method by coupling with the force-torque conditions of the cell bodies. If we initially place two Volvox blow the wall, they first swim towards the wall and show steady hovering motion adjacent to the wall. Then, they tend to attract each other gradually until they come to close contact. Finally, they show stable waltzing motion with steady rotational velocities, in a similar manner with the experimental observations. We conclude that the wall boundary, the bottom-heaviness and the swirl velocity are necessary in reproducing the waltzing motion.