Nonreciprocal interactions give rise to fast cilium synchronization in finite systems.

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.

Asymmetric bistability of chiral particle orientation in viscous shear flows.

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a nonchiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here, we use a high-resolution microprinting technique to fabricate microparticles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these microparticles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments, we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations, and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport and bacterial rheotaxis and might allow the development of targeted delivery applications.

Walking is like slithering: A unifying, data-driven view of locomotion.

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

An effective and efficient model of the near-field hydrodynamic interactions for active suspensions of bacteria.

Near-field hydrodynamic interactions in active fluids are essential to determine many important emergent behaviors observed, but have not been successfully modeled so far. In this work, we propose an effective model capturing the essence of the near-field hydrodynamic interactions through a tensorial coefficient of resistance, validated numerically by a pedagogic model system consisting of an Escherichia coli bacterium and a passive sphere. In a critical test case that studies the scattering angle of the bacterium-sphere pair dynamics, we prove that the near-field hydrodynamics can make a qualitative difference even for this simple two-body system: Calculations based on the proposed model reveal a region in parameter space where the bacterium is trapped by the passive sphere, a phenomenon that is regularly observed in experiments but cannot be explained by any existing model. In the end, we demonstrate that our model also leads to efficient simulation of active fluids with tens of thousands of bacteria, sufficiently large for investigations of many emergent behaviors.

Low-Reynolds-number, biflagellated Quincke swimmers with multiple forms of motion.

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic-electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

Microswimmers learning chemotaxis with genetic algorithms.

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis (i.e., to move toward and to stay at high concentrations of nutrients), they adapt their swimming gaits in a nontrivial manner. Here, we propose a computational model, which features autonomous shape adaptation of microswimmers moving in one dimension toward high field concentrations. As an internal decision-making machinery, we use artificial neural networks, which control the motion of the microswimmer. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the genetic algorithm NeuroEvolution of Augmenting Topologies, surprisingly simple neural networks evolve. These networks control the shape deformations of the microswimmers and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network, the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple and interpretable internal decision-making machinery coupled to the environment allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells or for the simple nervous system of small multicellular organisms such as Caenorhabditis elegans.

A Novel Experimental Apparatus for Characterizing Flow Regime in Mechanically Stirred Tanks through Force Sensors.

Pressure fluctuations in a mixing tank can provide valuable information about the existing flow regime within the tank, which in turn influences the degree of mixing that can be achieved. In the present work, we propose a prototype for identifying the flow regime in mechanically stirred tanks equipped with four vertical baffles through the characterization of pressure fluctuations. Our innovative proposal is based on force sensors strategically placed in the baffles of the mixing tank. The signals coming from the sensors are transmitted to an electronic module based on an Arduino UNO development board. In the electronic module, the pressure signals are conditioned, amplified and sent via Bluetooth to a computer. In the computer, the signals can be plotted or stored in an Excel file. In addition, the proposed system includes a moving average filtering and a hierarchical bottom-up clustering analysis that can determine the real-time flow regime (i.e., the Reynolds number, Re) in which the tank was operated during the mixing process. Finally, to demonstrate the versatility of the proposed prototype, experiments were conducted to identify the Reynolds number for different flow regimes (static, laminar, transition and turbulent), i.e., 0≤Re≤ 42,955. Obtained results were in agreement with the prevailing consensus on the onset and developed from different flow regimes in mechanically stirred tanks.

Intrinsic dissolution rate modeling for the pharmacopoeia apparatus rotating disk compared to flow channel method.

For a solid understanding of drug characteristics, in vitro measurement of the intrinsic dissolution rate is important. Hydrodynamics are often emphasized as the decisive parameter influencing the dissolution. In this study, experiments and computational fluid dynamic (CFD) simulations showed that the mixing behavior in the rotating disc apparatus causes an inhomogeneous flow field and a systematic error in the calculation of the intrinsic dissolution rate. This error is affected by both the experimental time and the velocity. Due to the rotational movement around the tablet center, commonly utilized in pharmacopeia methods, a broad variance is present with regard to the impact of fluid velocity on individual particles of the specimen surface. As this is significantly reduced in the case of uniform overflow, the flow channel is recommended for investigating the dissolution behavior. It is shown that rotating disc measurements can be compared with flow channel measurements after adjusting the measured data for the rotating disc based on a proposed, representative Reynolds number and a suggested apparatus-dependent correction factor. Additionally, modeling the apparatus-independent intrinsic dissolution rate for different temperatures in the rotating disc apparatus is possible using the adapted Levich's equation.

Swimming microorganisms acquire optimal efficiency with multiple cilia.

Planktonic microorganisms are ubiquitous in water, and their population dynamics are essential for forecasting the behavior of global aquatic ecosystems. Their population dynamics are strongly affected by these organisms' motility, which is generated by their hair-like organelles, called cilia or flagella. However, because of the complexity of ciliary dynamics, the precise role of ciliary flow in microbial life remains unclear. Here, we have used ciliary hydrodynamics to show that ciliates acquire the optimal propulsion efficiency. We found that ciliary flow highly resists an organism's propulsion and that the swimming velocity rapidly decreases with body size, proportional to the power of minus two. Accordingly, the propulsion efficiency decreases as the cube of body length. By increasing the number of cilia, however, efficiency can be significantly improved, up to 100-fold. We found that there exists an optimal number density of cilia, which provides the maximum propulsion efficiency for all ciliates. The propulsion efficiency in this case decreases inversely proportionally to body length. Our estimated optimal density of cilia corresponds to those of actual microorganisms, including species of ciliates and microalgae, which suggests that now-existing motile ciliates and microalgae have survived by acquiring the optimal propulsion efficiency. These conclusions are helpful for better understanding the ecology of microorganisms, such as the energetic costs and benefits of multicellularity in Volvocaceae, as well as for the optimal design of artificial microswimmers.

Trophic guilds of suction-feeding fishes are distinguished by their characteristic hydrodynamics of swimming and feeding.

Suction-feeding in fishes is a ubiquitous form of prey capture whose outcome depends both on the movements of the predator and the prey, and on the dynamics of the surrounding fluid, which exerts forces on the two organisms. The inherent complexity of suction-feeding has challenged previous efforts to understand how the feeding strikes are modified when species evolve to feed on different prey types. Here, we use the concept of dynamic similarity, commonly applied to understanding the mechanisms of swimming, flying, walking and aquatic feeding. We characterize the hydrodynamic regimes pertaining to (i) the forward movement of the fish (ram), and (ii) the suction flows for feeding strikes of 71 species of acanthomorph fishes. A discriminant function analysis revealed that feeding strikes of zooplanktivores, generalists and piscivores could be distinguished based on their hydrodynamic regimes. Furthermore, a phylogenetic comparative analysis revealed that there are distinctive hydrodynamic adaptive peaks associated with zooplanktivores, generalists and piscivores. The scaling of dynamic similarity across species, body sizes and feeding guilds in fishes indicates that elementary hydrodynamic principles govern the trophic evolution of suction-feeding in fishes.

Transition to Turbulence Downstream of a Stenosis for Whole Blood and a Newtonian Analog Under Steady Flow Conditions.

Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in vitro flow system. The viscosity at a shear rate of 1000 s-1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ∼19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.

Ontogeny of swimming performance of hatchery-reared post-larvae and juvenile fish: a case of two threatened Mediterranean species.

Swimming performance is a well-established key physiological parameter of fish that is highly linked to their fitness in the wild. In the context of fish restocking purposes, it therefore appears crucial to study this specific behaviour. Here, the authors investigated intra and interspecies differences in the swimming performance of hatchery-reared post-larvae and juveniles belonging to two Mediterranean candidate threatened species, the common dentex, Dentex dentex (Sparidae), and the brown meagre, Sciaena umbra (Sciaenidae), with body sizes ranging from 8 to 37 mm total length (TL, from 24 to 58 days post-hatch). The swimming abilities were estimated through the calculation of their critical swimming speed (Ucrit ), their relative Ucrit and their Reynolds number (Re ). Two different patterns were observed between D. dentex and S. umbra, showing a different effect of ontogeny on the performance of both species. The relative Ucrit of S. umbra decreased linearly through ontogeny, whereas the relative Ucrit and Ucrit of D. dentex increased linearly through the range of sizes tested. The ontogenetic change in Ucrit of S. umbra occurred in two stages: a first stage of sharp improvement and a second stage of a slow decrease in performance. Both stages were separated by a breakpoint that coincided with the appearance of a refusal to swim behaviour that occurred shortly after the end of metamorphosis and can potentially be associated with the establishment of this species sedentary behaviour. The swimming performance of both species showed ontogenetic differences. Sciaena umbra had the highest relative performance when its body sizes were the smallest, whereas D. dentex showed the highest relative performance when its body sizes were the largest. These results will be linked to future research on both of these species concerning their escape, exploratory and predatory behaviours, and for restocking purposes to draw a more realistic overview of hatchery-reared juvenile performance. Knowledge of both species' behavioural and swimming performance through ontogeny is important to consider when using hatchery-reared fish juveniles for restocking, as size-at-release can have a large impact on fish survival and thus on restocking success.

Effect of flow regime on mass transfer diffusion and stability of aerobic granular sludge (AGS) in view of interfacial thermodynamic.

Aerobic granular sludge (AGS) technology has been widely studied as "The Next Generation Wastewater Treatment technology". The effect of hydraulic conditions on the structural stability of AGS has been widely studied. However, the function of flow regime on the AGS stability, especially dissolved oxygen (DO) mass transfer, is still unknown. In this study, we used the Reynolds number (Re) to quantify the flow regime and selected different stages of AGS as experimental subjects. Results showed that the relatively suitable Re (Re = 150) could create lower DO mass transfer limitation (Lc = 27.4 µm) and increase protein (PN) contents and the abundance of hydrophobic functional groups in AGS. At this condition (Re = 150), the interfacial Gibbs free energy of sludge-water (ΔGLSa) was at a lower state (-129.75 ± 2.15 mJ·m-2), which favored the stability of AGS. Principal component analysis (PCA) and correlation analysis indicated that the response of ΔGLSa was affected by Lc, PN, and hydrophobic groups. In addition, results obtained for unstable AGS further verified that suitable Re regulates the structural stability of AGS. This study deepens the understanding of Re as an important hydraulic parameter for structural stability of AGS, which is also of great significance for energy saving of sequential batch reactors (SBRs) with agitation in practical engineering.

The cilium as a force sensor-myth versus reality.

Cells need to sense their mechanical environment during the growth of developing tissues and maintenance of adult tissues. The concept of force-sensing mechanisms that act through cell-cell and cell-matrix adhesions is now well established and accepted. Additionally, it is widely believed that force sensing can be mediated through cilia. Yet, this hypothesis is still debated. By using primary cilia sensing as a paradigm, we describe the physical requirements for cilium-mediated mechanical sensing and discuss the different hypotheses of how this could work. We review the different mechanosensitive channels within the cilium, their potential mode of action and their biological implications. In addition, we describe the biological contexts in which cilia are acting - in particular, the left-right organizer - and discuss the challenges to discriminate between cilium-mediated chemosensitivity and mechanosensitivity. Throughout, we provide perspectives on how quantitative analysis and physics-based arguments might help to better understand the biological mechanisms by which cells use cilia to probe their mechanical environment.

Mathematical modeling of chemotaxis guided amoeboid cell swimming.

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-basedDictyostelium discoideum(Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. In this paper, we develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system consists of one deformable Dd amoeboid cell and a dilute suspension of bacteria, and the bacteria produce chemoattractant signals that attract the Dd cell. We use themathematical amoeba modelto generate Dd cell deformation and solve the resulting low Reynolds number flows, and use a moving mesh based finite volume method to solve the reaction-diffusion-convection equation. Using the computational model, we show that chemotaxis guides a swimming Dd cell to follow and catch bacteria, while on the other hand, bacterial rheotaxis may help the bacteria to escape from the predator Dd cell.

Aerodynamics and the role of the earth's electric field in the spiders' ballooning flight.

Some spiders aerially disperse relying on their fine fibres. This behaviour has been known as 'ballooning'. Observations on the ballooning behaviour of spiders have a long history and have more recently received special attention, yet its underlying physics is still poorly understood. It was traditionally believed that spiders rely on the airflows by atmospheric thermal convection to do ballooning. However, a recent experiment showed that exposure to an electric field alone can induce spiders' pre-ballooning behaviours (tiptoe and dropping/dangling) and even pulls them upwards in the air. The controversy between explanations of ballooning by aerodynamic flow or the earth's electric field has long existed. The major obstacle in studying the physics of ballooning is the fact that airflow and electric field are both invisible and our naked eyes can hardly recognise the ballooning silk fibres of spiders. This review explores the theory and evidence for the physical mechanisms of spiders' ballooning connects them to the behavioural physiology of spiders for ballooning. Knowledge gaps that need to be addressed in future studies are identified.

Anisotropic shear stress patterns predict the orientation of convergent tissue movements in the embryonic heart.

Myocardial contractility and blood flow provide essential mechanical cues for the morphogenesis of the heart. In general, endothelial cells change their migratory behavior in response to shear stress patterns, according to flow directionality. Here, we assessed the impact of shear stress patterns and flow directionality on the behavior of endocardial cells, the specialized endothelial cells of the heart. At the early stages of zebrafish heart valve formation, we show that endocardial cells are converging to the valve-forming area and that this behavior depends upon mechanical forces. Quantitative live imaging and mathematical modeling allow us to correlate this tissue convergence with the underlying flow forces. We predict that tissue convergence is associated with the direction of the mean wall shear stress and of the gradient of harmonic phase-averaged shear stresses, which surprisingly do not match the overall direction of the flow. This contrasts with the usual role of flow directionality in vascular development and suggests that the full spatial and temporal complexity of the wall shear stress should be taken into account when studying endothelial cell responses to flow in vivo.

Inertial flow focusing: a case study in optimizing cellular trajectory through a microfluidic MEMS device for timing-critical applications.

Although microfluidic micro-electromechanical systems (MEMS) are well suited to investigate the effects of mechanical force on large populations of cells, their high-throughput capabilities cannot be fully leveraged without optimizing the experimental conditions of the fluid and particles flowing through them. Parameters such as flow velocity and particle size are known to affect the trajectories of particles in microfluidic systems and have been studied extensively, but the effects of temperature and buffer viscosity are not as well understood. In this paper, we explored the effects of these parameters on the timing of our own cell-impact device, the µHammer, by first tracking the velocity of polystyrene beads through the device and then visualizing the impact of these beads. Through these assays, we find that the timing of our device is sensitive to changes in the ratio of inertial forces to viscous forces that particles experience while traveling through the device. This sensitivity provides a set of parameters that can serve as a robust framework for optimizing device performance under various experimental conditions, without requiring extensive geometric redesigns. Using these tools, we were able to achieve an effective throughput over 360 beads/s with our device, demonstrating the potential of this framework to improve the consistency of microfluidic systems that rely on precise particle trajectories and timing.

High aerodynamic lift from the tail reduces drag in gliding raptors.

Many functions have been postulated for the aerodynamic role of the avian tail during steady-state flight. By analogy with conventional aircraft, the tail might provide passive pitch stability if it produced very low or negative lift. Alternatively, aeronautical principles might suggest strategies that allow the tail to reduce inviscid, induced drag: if the wings and tail act in different horizontal planes, they might benefit from biplane-like aerodynamics; if they act in the same plane, lift from the tail might compensate for lift lost over the fuselage (body), reducing induced drag with a more even downwash profile. However, textbook aeronautical principles should be applied with caution because birds have highly capable sensing and active control, presumably reducing the demand for passive aerodynamic stability, and, because of their small size and low flight speeds, operate at Reynolds numbers two orders of magnitude below those of light aircraft. Here, by tracking up to 20,000, 0.3 mm neutrally buoyant soap bubbles behind a gliding barn owl, tawny owl and goshawk, we found that downwash velocity due to the body/tail consistently exceeds that due to the wings. The downwash measured behind the centreline is quantitatively consistent with an alternative hypothesis: that of constant lift production per planform area, a requirement for minimizing viscous, profile drag. Gliding raptors use lift distributions that compromise both inviscid induced drag minimization and static pitch stability, instead adopting a strategy that reduces the viscous drag, which is of proportionately greater importance to lower Reynolds number fliers.

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors.

Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.