Lagrangian stretching reveals stress topology in viscoelastic flows.

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Bacterial scattering in microfluidic crystal flows reveals giant active Taylor-Aris dispersion.

The natural habitats of planktonic and swimming microorganisms, from algae in the oceans to bacteria living in soil or intestines, are characterized by highly heterogeneous fluid flows. The complex interplay of flow-field topology, self-propulsion, and porous microstructure is essential to a wide range of biophysical and ecological processes, including marine oxygen production, remineralization of organic matter, and biofilm formation. Although much progress has been made in the understanding of microbial hydrodynamics and surface interactions over the last decade, the dispersion of active suspensions in complex flow environments still poses unsolved fundamental questions that preclude predictive models for microbial transport and spreading under realistic conditions. Here, we combine experiments and simulations to identify the key physical mechanisms and scaling laws governing the dispersal of swimming bacteria in idealized porous media flows. By tracing the scattering dynamics of swimming bacteria in microfluidic crystal lattices, we show that hydrodynamic gradients hinder transverse bacterial dispersion, thereby enhancing stream-wise dispersion [Formula: see text]-fold beyond canonical Taylor-Aris dispersion of passive Brownian particles. Our analysis further reveals that hydrodynamic cell reorientation and Lagrangian flow structure induce filamentous density patterns that depend upon the incident angle of the flow and disorder of the medium, in striking analogy to classical light-scattering experiments.

Disorder Suppresses Chaos in Viscoelastic Flows.

Viscoelastic flows through microstructured geometries transition from steady to time dependent and chaotic dynamics under critical flow conditions. However, the implications of geometric disorder for flow stability are unknown. We measure the onset of spatiotemporal velocity fluctuations for a viscoelastic flow through microfluidic pillar arrays, having controlled variations of geometric disorder. Introducing a small perturbation into the pillar array (∼10% of the lattice constant) delays the onset of the instability to higher flow speed, and yet larger disorders (≥25%) suppress the transition to chaos. We show that disorder introduces preferential flow paths that promote shear over extensional deformation and enhance flow stability by locally reducing polymer stretching.

Vortical ciliary flows actively enhance mass transport in reef corals.

The exchange of nutrients and dissolved gasses between corals and their environment is a critical determinant of the growth of coral colonies and the productivity of coral reefs. To date, this exchange has been assumed to be limited by molecular diffusion through an unstirred boundary layer extending 1-2 mm from the coral surface, with corals relying solely on external flow to overcome this limitation. Here, we present direct microscopic evidence that, instead, corals can actively enhance mass transport through strong vortical flows driven by motile epidermal cilia covering their entire surface. Ciliary beating produces quasi-steady arrays of counterrotating vortices that vigorously stir a layer of water extending up to 2 mm from the coral surface. We show that, under low ambient flow velocities, these vortices, rather than molecular diffusion, control the exchange of nutrients and oxygen between the coral and its environment, enhancing mass transfer rates by up to 400%. This ability of corals to stir their boundary layer changes the way that we perceive the microenvironment of coral surfaces, revealing an active mechanism complementing the passive enhancement of transport by ambient flow. These findings extend our understanding of mass transport processes in reef corals and may shed new light on the evolutionary success of corals and coral reefs.

Sperm chemotaxis promotes individual fertilization success in sea urchins.

Reproductive success fundamentally shapes an organism's ecology and evolution, and gamete traits mediate fertilization, which is a critical juncture in reproduction. Individual male fertilization success is dependent on the ability of sperm from one male to outcompete the sperm of other males when searching for a conspecific egg. Sperm chemotaxis, the ability of sperm to navigate towards eggs using chemical signals, has been studied for over a century, but such studies have long assumed that this phenomenon improves individual male fitness without explicit evidence to support this claim. Here, we assessed fertilization changes in the presence of a chemoattractant-digesting peptidase and used a microfluidic device coupled with a fertilization assay to determine the effect of sperm chemotaxis on individual male fertilization success in the sea urchin Lytechinus pictus We show that removing chemoattractant from the gametic environment decreases fertilization success. We further found that individual male differences in chemotaxis to a well-defined gradient of attractant correlate with individual male differences in fertilization success. These results demonstrate that sperm chemotaxis is an important contributor to individual reproductive success.

Enhancement of biomixing by swimming algal cells in two-dimensional films.

Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and presents a fascinating stochastic process. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-two-dimensional liquid films by simultaneously tracking the motion of the cells and that of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the concentration of swimmers, which is explored over a wide range. The mean square displacements are well described by a stochastic Langevin model, which is used to parameterize the mixing. The effective diffusion coefficient D grows rapidly with the swimmer concentration Φ as D âˆ¼ Φ(3/2), as a result of the increasing frequency of tracer-swimmer interactions and the long-range hydrodynamic disturbances created by the swimmers. Conditional sampling of the tracer data based on the instantaneous swimmer position shows that the rapid growth of the diffusivity enhancement with concentration must be due to particle interactions with multiple swimmers simultaneously. Finally, the anomalous probability distributions of tracer displacements become Gaussian at high concentration, but manifest strong power-law tails at low concentration, while the tracer displacements always grow diffusively in time.

Multiplexed Microfluidic Platform for Parallel Bacterial Chemotaxis Assays.

The sensing of and response to ambient chemical gradients by microorganisms via chemotaxis regulates many microbial processes fundamental to ecosystem function, human health, and disease. Microfluidics has emerged as an indispensable tool for the study of microbial chemotaxis, enabling precise, robust, and reproducible control of spatiotemporal chemical conditions. Previous techniques include combining laminar flow patterning and stop-flow diffusion to produce quasi-steady chemical gradients to directly probe single-cell responses or loading micro-wells to entice and ensnare chemotactic bacteria in quasi-steady chemical conditions. Such microfluidic approaches exemplify a trade-off between high spatiotemporal resolution of cell behavior and high-throughput screening of concentration-specific chemotactic responses. However, both aspects are necessary to disentangle how a diverse range of chemical compounds and concentrations mediate microbial processes such as nutrient uptake, reproduction, and chemorepulsion from toxins. Here, we present a protocol for the multiplexed chemotaxis device (MCD), a parallelized microfluidic platform for efficient, high-throughput, and high-resolution chemotaxis screening of swimming microbes across a range of chemical concentrations. The first layer of the two-layer polydimethylsiloxane (PDMS) device comprises a serial dilution network designed to produce five logarithmically diluted chemostimulus concentrations plus a control from a single chemical solution input. Laminar flow in the second device layer brings a cell suspension and buffer solution into contact with the chemostimuli solutions in each of six separate chemotaxis assays, in which microbial responses are imaged simultaneously over time. The MCD is produced via standard photography and soft lithography techniques and provides robust, repeatable chemostimulus concentrations across each assay in the device. This microfluidic platform provides a chemotaxis assay that blends high-throughput screening approaches with single-cell resolution to achieve a more comprehensive understanding of chemotaxis-mediated microbial processes. Key features • Microchannel master molds are fabricated using photolithography techniques in a clean room with a mask aligner to fabricate multilevel feature heights. • The microfluidic device is fabricated from PDMS using standard soft lithography replica molding from the master molds. • The resulting microchannel requires a one-time calibration of the driving inlet pressures, after which devices from the same master molds have robust performance. • The microfluidic platform is optimized and tested for measuring chemotaxis of swimming prokaryotes.

Multiplexed microfluidic screening of bacterial chemotaxis.

Microorganism sensing of and responding to ambient chemical gradients regulates a myriad of microbial processes that are fundamental to ecosystem function and human health and disease. The development of efficient, high-throughput screening tools for microbial chemotaxis is essential to disentangling the roles of diverse chemical compounds and concentrations that control cell nutrient uptake, chemorepulsion from toxins, and microbial pathogenesis. Here, we present a novel microfluidic multiplexed chemotaxis device (MCD) which uses serial dilution to simultaneously perform six parallel bacterial chemotaxis assays that span five orders of magnitude in chemostimulant concentration on a single chip. We first validated the dilution and gradient generation performance of the MCD, and then compared the measured chemotactic response of an established bacterial chemotaxis system (Vibrio alginolyticus) to a standard microfluidic assay. Next, the MCD's versatility was assessed by quantifying the chemotactic responses of different bacteria (Psuedoalteromonas haloplanktis, Escherichia coli) to different chemoattractants and chemorepellents. The MCD vastly accelerates the chemotactic screening process, which is critical to deciphering the complex sea of chemical stimuli underlying microbial responses.

Many microorganisms such as bacteria swim to explore their fluid habitats, which range from the human digestive system to the oceans. They can detect minute traces of food, toxins and other chemicals in their environment, and ­ through a process called chemotaxis ­ respond by swimming towards or away from them. Chemical concentrations naturally decrease with distance away from their source, forming gradients. By sensing these chemical gradients, and adjusting their swimming direction accordingly, cells can locate nutrients and other resources in harsh environments as well as avoid toxins and potential predators. Over the past 20 years, laboratory devices that manipulate minute volumes of fluid ­ known as microfluidics devices ­ have been indispensable for studying chemotaxis. They enable researchers to generate gradients of chemicals in carefully designed networks of microscopic channels, controlling the conditions that swimming cells are exposed to and mimicking their natural habitats. However, large-scale studies of chemotaxis have been limited by the sheer range of chemicals that are present at different levels in natural environments. Conventional microfluidic devices often compromise between distinguishing how individual cells behave, precise control over the chemical gradient, or the ability to execute multiple assays at the same time. Here, Stehnach et al. designed a microfluidic device called the Multiplexed Chemotaxis Device. The device generates five streams of precise dilutions of a chemical and then uses these streams ­ alongside a control stream lacking the chemical ­ to measure chemotaxis in six different conditions at the same time. The device was tested using a well-studied bacterium, Vibrio alginolyticus, which is commonly found in marine environments. The device reliably examined the chemotaxis response of the population to various chemicals, was able to carry out multiple assays more rapidly than conventional devices, and can be easily applied to study the response of individual bacteria under the same conditions. The Multiplexed Chemotaxis Device is relatively easy to manufacture using standard methods and therefore has the potential to be used for large-scale chemotaxis studies. In the future, it may be useful for screening new drugs to treat bacterial infections and to help identify food sources for communities of microbes living in marine environments.

Fluidic bacterial diodes rectify magnetotactic cell motility in porous environments.

Directed motility enables swimming microbes to navigate their environment for resources via chemo-, photo-, and magneto-taxis. However, directed motility competes with fluid flow in porous microbial habitats, affecting biofilm formation and disease transmission. Despite this broad importance, a microscopic understanding of how directed motility impacts the transport of microswimmers in flows through constricted pores remains unknown. Through microfluidic experiments, we show that individual magnetotactic bacteria directed upstream through pores display three distinct regimes, whereby cells swim upstream, become trapped within a pore, or are advected downstream. These transport regimes are reminiscent of the electrical conductivity of a diode and are accurately predicted by a comprehensive Langevin model. The diode-like behavior persists at the pore scale in geometries of higher dimension, where disorder impacts conductivity at the sample scale by extending the trapping regime over a broader range of flow speeds. This work has implications for our understanding of the survival strategies of magnetotactic bacteria in sediments and for developing their use in drug delivery applications in vascular networks.

Silk reservoir implants for sustained drug delivery.

Biomaterial implants for the sustained delivery of therapeutics can be utilized to deliver drugs at near-constant rates over extended time frames to provide an alternative to daily oral medications. The biomaterials used to construct these systems, however, are often not bioresorbable and thus require a secondary surgery for removal from the body, and fabrication of these systems may require the use of harsh chemical solvents. To address these shortcomings, a fabrication process was developed to generate biodegradable drug reservoir systems from regenerated silk fibroin protein solution (23% w/v). The tubular systems, with an inner diameter of 2.0 mm and wall thickness < 250µm, were developed using an all-aqueous solution-gel-solid phase transition curing process. Two different clinically-relevant therapeutics were released at near-constant rates for 30 days (> 100µg/day). The protein secondary structure of the devices consisted of 40% crystalline beta sheet. Mechanically, radial compression (1mm/min) of unloaded systems demonstrated Young's moduli similar to cancellous (spongy) bone (100 to 250 MPa) and the systems showed good recovery under cyclic compression (to 17.5% strain). The devices could be generated in complex shapes (e.g., hollow cylinders) via an additive molding process, offering the potential for drug delivery but also for broader applications in tissue engineering and diagnostics.

Oscillatory flows induced by microorganisms swimming in two dimensions.

We present the first time-resolved measurements of the oscillatory velocity field induced by swimming unicellular microorganisms. Confinement of the green alga C. reinhardtii in stabilized thin liquid films allows simultaneous tracking of cells and tracer particles. The measured velocity field reveals complex time-dependent flow structures, and scales inversely with distance. The instantaneous mechanical power generated by the cells is measured from the velocity fields and peaks at 15 fW. The dissipation per cycle is more than 4 times what steady swimming would require.

Flagellar kinematics reveals the role of environment in shaping sperm motility.

Swimming spermatozoa from diverse organisms often have very similar morphologies, yet different motilities as a result of differences in the flagellar waveforms used for propulsion. The origin of these differences has remained largely unknown. Using high-speed video microscopy and mathematical analysis of flagellar shape dynamics, we quantitatively compare sperm flagellar waveforms from marine invertebrates to humans by means of a novel phylokinematic tree. This new approach revealed that genetically dissimilar sperm can exhibit strikingly similar flagellar waveforms and identifies two dominant flagellar waveforms among the deuterostomes studied here, corresponding to internal and external fertilizers. The phylokinematic tree shows marked discordance from the phylogenetic tree, indicating that physical properties of the fluid environment, more than genetic relatedness, act as an important selective pressure in shaping the evolution of sperm motility. More broadly, this work provides a physical axis to complement morphological and genetic studies to understand evolutionary relationships.

Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms.

In contexts such as suspension feeding in marine ecologies there is an interplay between brownian motion of nonmotile particles and their advection by flows from swimming microorganisms. As a laboratory realization, we study passive tracers in suspensions of eukaryotic swimmers, the alga Chlamydomonas reinhardtii. While the cells behave ballistically over short intervals, the tracers behave diffusively, with a time-dependent but self-similar probability distribution function of displacements consisting of a gaussian core and robust exponential tails. We emphasize the role of flagellar beating in creating oscillatory flows that exceed brownian motion far from each swimmer.

Microfluidic quantification and separation of yeast based on surface adhesion.

Fungal adhesion is fundamental to processes ranging from infections to food production to bioengineering. Yet, robust, population-scale quantification methods for yeast surface adhesion are lacking. We developed a microfluidic assay to discriminate and separate genetically-related yeast strains based on adhesion strength, and to quantify effects of ionic strength and substrate hydrophobicity on adhesion. This approach will enable the rapid screening and fractionation of yeast based on adhesive properties for genetic protein engineering, anti-fouling surfaces, and a host of other applications.

Flow-induced buckling dynamics of sperm flagella.

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows are known to enhance sperm-egg fertilization rates through hydrodynamic guidance. However, strong flows have the potential to mechanically inhibit flagellar motility through elastohydrodynamic interactions-a phenomenon that remains poorly understood. Here we explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For nonmotile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit a local flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. The flagellar beating frequency also influences the maximum curvature of motile sperm by facilitating sperm reorientation relative to the compressional axis of the flow near stagnation points. These combined simulations and experiments directly illustrate the microscopic elastohydrodynamic mechanisms responsible for inhibiting flagellar motility in flow and have possible implications for our understanding of external fertilization in dynamic marine systems.

Bacterial chemotaxis in a microfluidic T-maze reveals strong phenotypic heterogeneity in chemotactic sensitivity.

Many microorganisms have evolved chemotactic strategies to exploit the microscale heterogeneity that frequently characterizes microbial habitats. Chemotaxis has been primarily studied as an average characteristic of a population, with little regard for variability among individuals. Here, we adopt a classic tool from animal ecology - the T-maze - and implement it at the microscale by using microfluidics to expose bacteria to a sequence of decisions, each consisting of migration up or down a chemical gradient. Single-cell observations of clonal Escherichia coli in the maze, coupled with a mathematical model, reveal that strong heterogeneity in the chemotactic sensitivity coefficient exists even within clonal populations of bacteria. A comparison of different potential sources of heterogeneity reveals that heterogeneity in the T-maze originates primarily from the chemotactic sensitivity coefficient, arising from a distribution of pathway gains. This heterogeneity may have a functional role, for example in the context of migratory bet-hedging strategies.

Fungal networks shape dynamics of bacterial dispersal and community assembly in cheese rind microbiomes.

Most studies of bacterial motility have examined small-scale (micrometer-centimeter) cell dispersal in monocultures. However, bacteria live in multispecies communities, where interactions with other microbes may inhibit or facilitate dispersal. Here, we demonstrate that motile bacteria in cheese rind microbiomes use physical networks created by filamentous fungi for dispersal, and that these interactions can shape microbial community structure. Serratia proteamaculans and other motile cheese rind bacteria disperse on fungal networks by swimming in the liquid layers formed on fungal hyphae. RNA-sequencing, transposon mutagenesis, and comparative genomics identify potential genetic mechanisms, including flagella-mediated motility, that control bacterial dispersal on hyphae. By manipulating fungal networks in experimental communities, we demonstrate that fungal-mediated bacterial dispersal can shift cheese rind microbiome composition by promoting the growth of motile over non-motile community members. Our single-cell to whole-community systems approach highlights the interactive dynamics of bacterial motility in multispecies microbiomes.

Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton.

Fluid flow, ubiquitous in natural and man-made environments, has the potential to profoundly impact the transport of microorganisms, including phytoplankton in aquatic habitats and bioreactors. Yet, the effect of ambient flow on the swimming behaviour of phytoplankton has remained poorly understood, largely owing to the difficulty of observing cell-flow interactions at the microscale. Here, we present microfluidic experiments where we tracked individual cells for four species of motile phytoplankton exposed to a spatially non-uniform fluid shear rate, characteristic of many flows in natural and artificial environments. We observed that medium-to-high mean shear rates (1-25 s(-1)) produce heterogeneous cell concentrations in the form of regions of accumulation and regions of depletion. The location of these regions relative to the flow depends on the cells' propulsion mechanism, body shape and flagellar arrangement, as captured by an effective aspect ratio. Species having a large effective aspect ratio accumulated in the high-shear regions, owing to shear-induced alignment of the swimming orientation with the fluid streamlines. Species having an effective aspect ratio close to unity exhibited little preferential accumulation at low-to-moderate flow rates, but strongly accumulated in the low-shear regions under high flow conditions, potentially owing to an active, behavioural response of cells to shear. These observations demonstrate that ambient fluid flow can strongly affect the motility and spatial distribution of phytoplankton and highlight the rich dynamics emerging from the interaction between motility, morphology and flow.

Hydrodynamic irreversibility in particle suspensions with nonuniform strain.

A dynamical phase transition from reversible to irreversible behavior occurs when particle suspensions are subjected to uniform oscillatory shear, even in the Stokes flow limit. We consider a more general situation with nonuniform strain (e.g., oscillatory channel flow), which is observed to exhibit markedly different dynamics. The onset of irreversibility is delayed, and occurs simultaneously across the entire channel. This behavior is only partially explained by self-organization and shear-induced migration. The onset is accompanied by long-range correlated particle motion even at the channel center, where the strain is negligible; this motion prevents the system from evolving into a reversible state.