Robert D. Guy

The classical problem of steady streaming induced by an oscillating object has been studied extensively, but prior work has focused almost exclusively on single-frequency oscillations, which result in symmetric, quadrupole-like flows. Here we demonstrate that dual-frequency oscillations induce asymmetric steady streaming with a non-zero net flux in a direction determined by the polarity of the oscillation – the oscillator serves as a pump. We use numerical simulations and asymptotic analysis at small amplitude to examine two-dimensional steady streaming around a cylinder, first focusing on frequency ratio 2. The computational experiments show asymmetrical streaming and pumping, i.e. net flux downstream. It is well known from asymptotic analysis that steady streaming is second order in amplitude, and we show that pumping occurs at third order. We then extend the analysis to general frequency ratios, where we give necessary conditions for pumping, and predict the order in amplitude at which pumping occurs. Finally, we corroborate the theoretical results with computational simulations for different frequency ratios, and we discuss the implications for using dual-mode vibrations to pump fluids in lab-on-a-chip and other applications.

Many different microswimmers propel themselves using flagella that beat periodically. The shape of the flagellar beat and swimming speed have been observed to change with fluid rheology. We quantify changes in the flagellar waveforms of Chlamydomonas reinhardtii in response to changes in fluid viscosity using (i) shape mode analysis and (ii) a full swimmer simulation to analyse how shape changes affect the swimming speed and to explore the dimensionality of the shape space. By decomposing the gait into the time-independent mean shape and the time-varying stroke, we find that the flagellar mean shape substantially changes in response to viscosity, while the changes in the time-varying stroke are more subtle. Using the swimmer simulation, we quantify how the swimming speed is affected by the dimensionality of the flagellar shape reconstruction, and we show that the observed change in swimming speed with viscosity is explained by the variations in mean flagellar shape and beat frequency, while the changes in swimming speed from the different time-varying strokes are on the scale of variation between cells. This article is part of the theme issue ‘Biological fluid dynamics: emerging directions’.

Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacings, different limb coordinations are selected. Across all resulting strokes, the fastest stroke is dependent on the number of paddles; however, the most efficient stroke is a back-to-front wave-like stroke regardless of the number of paddles. Graphical

Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacings, different limb coordinations are selected. Across all resulting strokes, the fastest stroke is dependent on the number of paddles, however, the most efficient stroke is a back-to-front wave-like stroke regardless of the number of paddles.

Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii . The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.

Ruminant animals rely on microbes for the conversion of complex plant material into host accessible metabolites. During this anaerobic conversion of plant biomass, termed enteric fermentation, methanogenic archaea convert hydrogen into the potent greenhouse gas methane (CH ₄ ). The search for methane mitigation strategies to combat climate change has identified the red seaweed Asparagopsis taxiformis as a promising feed additive that, when added to a regular cattle diet, reduced enteric CH ₄ by over 80%. A more complete understanding of microbial interactions during enteric fermentation is needed for ongoing improvement to mitigation methods. Mathematical models that permit in silico simulation of enteric fermentation allow for the identification of key parameters that drive rumen methane production. Here we built upon an existing rumen fermentation model and calibrated it using a preliminary classification of functional microbial groups and gas emission data from a previously published in vitro rumen fermentation experiment, but many microbes remained functionally unclassified. The model was then used to conduct an in silico experiment to explore how the partition of functionally unclassified microbes into functional groups affects methane output. These in silico experiments identified that model methane production is more sensitive to microbial variation in the presence of A. taxiformis versus without. The use of local and global sensitivity analysis approaches revealed other rumen parameters to also be drivers of enteric methane production. In the presence of A. taxiformis , parameters modulating methane production include bromoform concentration, methanogen abundance, total microbial concentration, a parameter effecting the inhibition of methanogen growth rate by the action of bromoform, and the maximum specific utilization rate of hydrogen. Without A. taxiformis , feed composition parameters, the hydrolysis rate constant of cell wall carbohydrates, and a parameter affecting the yield factors during sugar utilization were found to be most significant. For possible methane reduction without A. taxiformis , we propose an adjustment in feed composition parameters that reduces predicted methane by 25.6%.

Polydiacetylene (PDA) Langmuir films are well known for their blue‐to‐red chromatic transitions in response to a variety of stimuli, including UV light, heat, bio‐molecule bindings, and mechanical stress. In this work, the ability to tune PDA Langmuir films to exhibit discrete chromatic transitions in response to applied mechanical stress is detailed. Normal and shear‐induced transitions are quantified using the Surface Forces Apparatus and established to be binary and tunable as a function of film formation conditions. Both monomer alkyl tail length and metal cations are used to manipulate the chromatic transition force threshold to enable discrete force sensing from ≈50 to ≈500 nN µm⁻² for normal loading and ≈2 to ≈40 nN µm⁻² for shear‐induced transitions, which are appropriate for biological cells. The utility of PDA thin‐film sensors is demonstrated with the slime mold Physarum polycephalum. The fluorescence readout of the films enabled: the area explored by Physarum to be visualized, the forces involved in locomotion to be quantified, and revealed novel puncta formation potentially associated with Physarum sampling its environment.

Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how inter-paddle phase-difference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearest-neighbor paddles maintain an approximate 20%–25% phase-difference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of paddles depend on RE; we see a qualitative transition in the dynamics of flow generated by metachronal propulsion as RE rises above 80. Roughly speaking, in terms of average flux generation, a tight paddle spacing is preferred when RE is less than 10, but a wider spacing becomes clearly favored when RE is close to or above 100. In terms of efficiency of flux generation, at RE 0.1 the maximum efficiency occurs at two paddles, and the efficiency decreases as the number of paddles increases. At RE 100 the efficiency increases as the number of paddles increases, and it appears to saturate by eight paddles, whereas using four paddles is a good tradeoff for both low and intermediate RE.

Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) case, and similar stress behavior is observed. The flow around tips of a time-reversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories, and the stress response exhibits similar transitions. However in the high amplitude, high De regime the stress feedback on the flow leads to non time-reversible particle trajectories that experience asymmetric stretching and compression, and the stress grows more significantly in this regime. These results help explain past observations of large stress concentration for large amplitude swimmers and non-monotonic dependence on De of swimming speeds.