Collective Dynamics in Flowing Suspensions of Swimming Micro-organisms

Download or read book Collective Dynamics in Flowing Suspensions of Swimming Micro-organisms written by Amir Alizadeh Pahlavan and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Micro-organisms first appeared on earth about 3.8 billion years ago and can be found almost everywhere now. In terms of number and biomass, they in fact constitute the majority of terrestrial life and despite their tiny size play a vital role in a wide variety of phenomena. Although there has been a long history of studying characteristics of individual bacteria, their large-scale collective motions have just recently received attention from scientists. It has been reported that, as concentration of such systems increases beyond a threshold, complex correlated dynamics on length scales much larger than the size of individual bacteria can be observed. It has recently been suggested that these correlated motions can be explained in terms of hydrodynamic interactions between particles. Although different types of swimmers use a wide variety of different mechanisms, universal features exist in their associated hydrodynamics. In particular, as they swim they exert a force dipole on the fluid; this force induces a disturbance flow in the fluid, the characteristics of which are universal in the far field. This universality allows the development of mean-field theories to describe such suspensions over length scales much larger than the particle dimensions. In this work, we make use of a recently developed kinetic model to investigate pattern formation in a dilute suspension of swimming micro-organisms in the presence of an external shear flow. Doing so allows us to simulate more realistic situations where ambient flow is present, as in oceans where motility could influence bacterial ecology and the role of bacteria in oceanic biogeochemistry. Moreover, we can investigate their rheological properties, which have recently been reported to show unexpected behaviors. In the first part of this work, we investigate the effect of shear flow on the flow structures using a linear stability analysis and three-dimensional numerical simulations. The external shear flow is found to dampen the instabilities that occur in these suspensions by controlling the orientation of the particles. We demonstrate that the rate of damping is direction-dependent: it is fastest in the flow direction, but slowest the direction perpendicular to the shear plane. Consequently, transitions from three- to two- to one-dimensional instabilities are observed to occur, as shear rate increases, and above a certain shear rate the instabilities disappear altogether. The density patterns and flow structures that arise at long times in the suspensions are also analyzed from the numerical simulations using standard techniques from the literature on turbulent flows. The imposed shear flow is found to have an effect on both density patterns and flow structures, which typically align with the extensional axis of the external flow. The disturbance flows in the simulations are shown to exhibit similarities with turbulent flows, and in particular two of the seemingly universal characteristics of turbulent flows also occur, namely: (i) the alignment of the vorticity vector with the intermediate strain-rate eigenvector, and (ii) the bias of Q0́3R plots toward second and fourth quadrants, corresponding to stable focus/stretching and unstable node/saddle/saddle topologies, respectively. However, the flows described herein also differ significantly from turbulent flows owing to the strong predominance of large scales, as exemplified by the very rapid decay of the kinetic energy spectrum, an effect further enhanced after the transitions to two- and one-dimensional instabilities. Then, we move on to investigate the effect of hydrodynamic interactions and flow instabilities on the rheology of dilute flowing suspensions of swimming micro-organisms. The effect of external shear on the orientation distribution and the relative alignment of flow rheological properties is investigated. It is found that regions of negative particle viscosity are aligned with more concentrated areas of the flow; this alignment suggests that, as particles form clusters, it becomes easier for them to swim. This phenomenon could be the origin of correlated motions observed in experiments and simulations. The particle viscosity is also found to be slightly aligned with the director field and vorticity axis; this alignment becomes more pronounced as the flow becomes 2D. Moreover, we investigate time evolution of the rheological properties and the effect of shear on them and compare them with the results obtained from single-active-particle rheology. The spatiallyaveraged properties oscillate in time and these oscillations become damped with the shear. It appears that the effect of shear on the rheological properties is not expected a priori; the properties almost do not vary with shear as long as the flow is 3D, but as the flow becomes 2D, they start to approach the predictions of single self-propelled particle rheology and they match very well in the limit of high shear rates, where all the instabilities are damped by the external shear and the flow becomes spatially uniform.