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Active fluids have potential applications in micromixing, but little is known about the mixing kinematics of such systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP was used to activate controlled regions of microtubule-kinesin active fluid inducing a propagating active-passive interface. The mixing process of the system from non-uniform to uniform activity as the interface advanced was observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progressed toward the inactive area in a diffusion-like manner and at high Péclet numbers (convective transport), the active-inactive interface progressed in a superdiffusion-like manner. The results show mixing in non-uniform active fluid systems evolve from a complex interplay between the spatial distribution of ATP and its active transport. This active transport may be diffusion-like or superdiffusion-like depending on Péclet number and couples the spatiotemporal distribution of ATP and the subsequent localized active stresses of active fluid. Our work will inform the design of future microfluidic mixing applications and provide insight into intracellular mixing processes. *T.E.B., E.H.T., J.H.D., and K.-T.W. acknowledge support from the National Science Foundation (NSF-CBET-2045621). C.-C. C. was supported through the National Science and Technology Council (NSTC), Taiwan (111-2221-E-006-102-MY3). M.M.N. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0022280). 

Active fluids with spatiotemporally varying activity have potential applications to micromixing; however previously existing active fluids models are not prepared to account for spatiotemporally-varying active stresses. Our experimental work used UV-activated caged ATP to activate controlled regions of microtubule-kinesin active fluid inducing a propagating active-passive interface. Here, we recapitulate our experimental results with two models. The first model redistributes an initial ATP distribution by Fick's law and translates the ATP distribution into a velocity profile by Michaelis-Menton kinetics. This model reproduces our experimental measurements for the low-Péclet number limit within 10% error without fitting parameters. However, as the model is diffusion based, it fails to capture the convective based superdiffusive-like behaviour at high Péclet numbers. Our second model introduces a spatiotemporally varying ATP field to an existing nematohydrodynamic active fluid model and then couples the active stresses to local ATP concentrations. This model is successful in qualitatively capturing the superdiffusive-like progression of the active-inactive interface for high Peclet number (convective transport) experimental cases. Our results show that new model frameworks are necessary for capturing the behaviour of active fluid with spatiotemporally varying activity. *T.E.B., E.H.T., J.H.D., and K.-T.W. acknowledge support from the National Science Foundation (NSF-CBET-2045621). C.-C. C. was supported through the National Science and Technology Council (NSTC), Taiwan (111-2221-E-006-102-MY3). M.M.N. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0022280). 

Abstract Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices. 

Abstract Active fluid droplets surrounded by oil can spontaneously develop circulatory flows. However, the dynamics of the surrounding oil and their influence on the active fluid remain poorly understood. To investigate interactions between the active fluid and the passive oil across their interface, kinesin-driven microtubule-based active fluid droplets were immersed in oil and compressed into a cylinder-like shape. The droplet geometry supported intradroplet circulatory flows, but the circulation was suppressed when the thickness of the oil layer surrounding the droplet decreased. Experiments with tracers and network structure analyses and continuum models based on the dynamics of self-elongating rods demonstrated that the flow transition resulted from flow coupling across the interface between active fluid and oil, with a millimeter–scale coupling length. In addition, two novel millifluidic devices were developed that could trigger and suppress intradroplet circulatory flows in real time: one by changing the thickness of the surrounding oil layer and the other by locally deforming the droplet. This work highlights the role of interfacial dynamics in the active fluid droplet system and shows that circulatory flows within droplets can be affected by millimeter–scale flow coupling across the interface between the active fluid and the oil. 

Active matter consumes local fuels to self-propel. When confined in a closed circular boundary, they can self-organize into a circulatory flow. Such coherence originates from the interactions between the active matter and boundaries, and boundary conditions play an important role on self-organization of active fluid. Herein, we probed how fluid boundaries influenced the self-organization of active fluid. The fluid boundaries were created by confining the active fluid in a compressed water-in-oil droplet. Due to surface tension, the droplet shaped into a cylinder-like geometry. Since water and oil were both fluids, their interface was fluid. We systematically probed how droplet shapes and the amount of oil surrounding the droplet influenced the development of circulation. We found that the formation of circulatory flows depended on the thickness of the oil layer surrounding the droplet, implying that the fluid dynamics between the active fluid within the droplet and the oil outside the droplet were coupled. We used a 3D COMSOL-based simulation successfully reproduced such oil-layer dependence. Finally, we developed two milli-fluidic devices to deform the droplet and alter the oil layer thickness manually to trigger and suppress the intra-droplet circulatory flow in real time. 

Fluid dynamics of conventional passive fluid are known to be affected by boundary condition. For example, flow rates in a pipe depend on slipperiness of pipe surface. Similarly, active fluid, which consumes fuels locally to flow spontaneously, was reported to self-flow along a meter-long tubing with the flow rate depending on tubing geometry. However, how boundary condition influences fluid dynamics in an active fluid system remains poorly understood. Here, we investigated how a fluid boundary influenced self-organization of confined active fluid by establishing a 3D COMSOL-based nemato-hydrodynamic simulation platform where active fluid was confined in a compressed cylindrical water-in-oil droplet. Since the droplet interface was fluid, the fluid dynamics within and outside the droplet were coupled. Our simulation demonstrated that flow behaviors of intra-droplet active fluid were influenced by the amount of oil that surrounded the droplet: Without altering the droplet geometry, expanding the volume of oil could induce a circulatory flow within the droplet, which resembled our experimental observation. Our work suggested the feasibility of controlling the fluid dynamics of a confined active fluid system across a fluid interface.