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This work has uncovered a number of dynamical regimes in active fluids at scales ranging from polymers (<1µm), particles (1-10µm), and phase-separated mixtures (>100 µm). These uncon- ventional dynamics have broad implications for particle transport in active fluids and suggest means to control the material properties of active soft environments. In the following, I highlight these implications and provide my recommendations for extending this work.

Diffusion to Sedimentation: Role of hydrodynamic interactions

By investigating the diffusion of passive particles in active fluids, I found that particle diffusivity - unexpectedly - is non-monotonic in particle size [1]. This unexpected dependence highlights the interplay between passive and active components in a living fluid and their mediation through hydro- dynamic interactions. In passive fluids, the role of hydrodynamic interactions on particle transport, which may be negligible at dilute concentrations, becomes increasing more important as particles interact at higher concentrations. Understanding the role of hydrodynamic interactions on parti- cle transport has been a long-standing challenge in passive fluids. In passive fluids, hydrodynamic interactions suppress particle diffusivity [4, 5]. Hydrodynamic interactions also play a role in the sedimentation of a dilute colloidal suspension: a single particle sediments at a velocity that is pro- portional to its size; while at higher particle concentrations, hydrodynamic interactions cause the mean particle sedimentation velocity to decrease [2] and can drive large density fluctuations. This phenomena has been the focus of intense research and debate [3, 6, 7] but is understood to be due to long-range hydrodynamic interactions [2] combined with a Debye-like screening of particle’s velocity disturbances [8]. Given the importance of particle diffusion and sedimentation in our understanding of passive fluids, an exciting new focus of research would be particle sedimentation in active fluids. Because particle diffusivity is non-monotonic in size in active fluids, it opens up the possibility that particle sedimentation velocities may also have a non-monotonic dependence: can smaller particle sediment faster than larger particles? As in passive fluids, it would be interesting to investigate the hydrodynamic interactions between passive particles sedimenting in active fluids: do bacteria enhance or hinder particle interactions? These questions may have important implications for the sedimentation and transport of sediment and toxins in microbe-filled lakes and oceans [9].

Rheology of active polymeric fluids

My investigation [10] of E. coli swimming dynamics in polymer solutions highlights a fasci- nating coupling between microbe motility and fluid rheology. I found that bacteria can stretch individual polymer molecules, increasing their average end-to-end distance. This finding suggests that increased polymer stretching may lead to an additional elastic stress in active polymeric flu- ids. An important next step is to understand how this bacteria-mediated stretching influences the time-dependent rheology of the fluid: do bacteria enhance or hinder the relaxation of individual polymers and how does this bacteria-polymer interaction influence the relaxation time of the bulk fluid? Microfluidic-based rheology methods are an appealing experimental design to investigate the rheology of active polymeric fluids. Microfluidic techniques allow for the simultaneous visualiza- tion of the microstructure and measurement of steady [11] and time-dependent [3] bulk material properties. By measuring polymer configurations through fluorescently-stained polymers [13, 14] or tethered polymer experiments [15], the end-to-end statistics of polymers can be measured under the influence of swimming bacteria and under applied flow. Furthermore, the polymers influence the dynamic of the swimmingE. coli (speed, diffusivity) [10], which could simultaneously be measured in a microfluidic device. How this two-way coupling influences the bulk rheology is new ground for exploration. An important application may be in understanding the formation of biofilms [16], in which bacterial colonies excrete and assemble polymer molecules into protective shelters that are both soft and active.

Swarms: Particle transport and fluid rheology

The interesting particle and polymer dynamics observed in dilute bacterial suspensions [1] nat- urally lends weight to the the case of dense suspensions. In dense suspensions, bacteria exhibit collective motions with emergent vortical flows. This introduces a new length scale - or spectrum of length scales - that particles in dense suspensions would sample. It would be interesting to in- vestigate how the non-monotonic particle size dependence in dilute suspensions is influenced by collective flows at higher bacterial concentrations. This has biological implications including how bacteria communicate: bacteria package of chemical-signal into micron-sized vesicles [17], which are observed throughout biofilms [18]. It would be interesting to explore the connection between vesicle size, collective motion, and the biochemical adaptability of bacteria.

Lastly, the role of extracellular polymers in the collective dynamics of bacteria is an ample area of research. I have found that polymer molecules enhance the speed and diffusivity of non- interacting swimming bacteria [10]. It would be interesting to explore the role of polymer molecules in the collective motions of bacteria and how elastic stresses may enhance or hinder their collective transport. Recent observations have shown that extracellular polymers are important in aligning and directing flows of bacteria on surfaces [19]. Thus, an exciting avenue of research would be to investigate the bio-mechanical coupling between bacteria polymer excretion and swimming dynamics which may allow bacteria to collectively invade and gain new territories on surfaces and in fluid.