Thermo-responsive hydrogels are smart materials that rapidly switch between hydrophilic (swollen) and hydrophobic (shrunken) states when heated past a threshold temperature, resulting in order-of-magnitude changes in gel volume. Modelling the dynamics of this switch is notoriously difficult, and typically involves fitting a large number of microscopic material parameters to experimental data. In this paper, we present and validate an intuitive, macroscopic description of responsive gel dynamics and use it to explore the shrinking, swelling and pumping of responsive hydrogel displacement pumps for microfluidic devices. We finish with a discussion on how such tubular structures may be used to speed up the response times of larger hydrogel smart actuators and unlock new possibilities for dynamic shape change.

We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for nonintersecting three-dimensional center lines, with arbitrary chemical patterning and varying (circular) cross-sectional radius, allowing a broad class of slender active loops and knots to be studied. The theory is amenable to closed-form solutions in simpler cases, allowing us to analytically derive the swimming speed of chemically patterned tori, and the pumping strength (stresslet) of a uniformly active slender torus. Using simple numerical solutions of our asymptotic equations, we then elucidate the behavior of many exotic active particle geometries, such as a bumpy uniformly active torus that spins and a Janus trefoil knot, which rotates as it swims forwards. Published by the American Physical Society 2024

In engineering, the design of a product relies heavily on a design specification; a co-creation of customer and engineer which captures the requirements. Subjectivity is intrinsic to this process. Whilst engineers typically have a high appreciation of the technical aspects of design, the detailed knowledge of environmental and socioeconomic (ESE) implications are often held elsewhere. As such, efficient and effective design is critically dependent on the processes underpinning knowledge transfer. However, the information interfaces between engineering and the requirements of our swiftly changing civilization remain indirect and suboptimal, and the unintended consequences of design choices are becoming increasingly serious. Transdisciplinary engineering bridges knowledge boundaries interfacing with engineering (e.g. social science). This paper explores whether topology (a branch of pure mathematics) presents an opportunity to analyse the complex interdependency of transdisciplinary engineering information. Topology and geometry describe the structure of objects such as connectedness or the number of holes and have recently provided a suite of powerful and robust tools for analysing high-dimensional data sets. However, the real-world implementation of the term topology is still evolving. Interviews with engineering organisations, revealed that topology is predominately interpreted as ‘Topology Optimisation’ in the context of advanced design and manufacturing. To date, mathematical processes for critically and systematically examining the topology of systems have not been transferred through to the engineering industry. This paper contrasts how topology is interpreted by the engineering industry compared to academic literature and reflects on the opportunities of applying the mathematical theory of topological analysis to transdisciplinary engineering data.

Hydrogels are hydrophilic polymer scaffolds surrounded by adsorbed water. From a dry state, they are capable of swelling in volume by up to two orders of magnitude – becoming up to 99% water - whilst still remaining solid (if a little squishy). Responsive hydrogels lose this affinity for water – sometimes quite profoundly – when an environmental stimulus, such as temperature or pH, transitions beyond a critical value. Conformational changes in the scaffold squeeze the water out, and the gel shrivels dramatically. This volume change is reversible (albeit non-reciprocal), allowing for cycles of activation and deactivation. As such, responsive hydrogels have important and exciting applications in microscale actuators. This talk will describe some of the big open areas of hydrogel modelling, before detailing two (very) recent unpublished theoretical pieces of work on 1) thermoresponsive displacement pumps for microfluidic devices, and 2) coupling pH-responsive gels to oscillating reactions to enable communication and synchronisation.

This article provides a review of the recent development of biomimicking behaviors in active colloids. While the behavior of biological microswimmers is undoubtedly influenced by physics, it is frequently guided and manipulated by active sensing processes. Understanding the respective influences of the surrounding environment can help to engineering the desired response also in artificial swimmers. More often than not, the achievement of biomimicking behavior requires the understanding of both biological and artificial microswimmers swimming mechanisms and the parameters inducing mechanosensory responses. The comparison of both classes of microswimmers provides with analogies in their dependence on fuels, interaction with boundaries and stimuli induced motion, or taxis.

We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for non-intersecting 3D centrelines, with arbitrary chemical patterning and varying (circular) cross-sectional radius, allowing a broad class of slender active loops and knots to be studied. The theory is amenable to closed-form solutions in simpler cases, allowing us to analytically derive the swimming speed of chemically patterned tori, and the pumping strength (stresslet) of a uniformly active slender torus. Using simple numerical solutions of our asymptotic equations, we then elucidate the behaviour of many exotic active colloids, such as a bumpy uniformly active torus that spins and a Janus trefoil knot, which rotates as it swims forwards.

Thermo-responsive hydrogels are a promising material for creating controllable actuators for use in micro-scale devices, since they expand and contract significantly (absorbing or expelling fluid) in response to relatively small temperature changes. Understanding such systems can be difficult because of the spatially- and temporally-varying properties of the gel, and the complex relationships between the fluid dynamics, elastic deformation of the gel and chemical interaction between the polymer and fluid. We address this using a poro-elastic model, considering the dynamics of a thermo-responsive spherical hydrogel after a sudden change in the temperature that should result in substantial swelling or shrinking. We focus on two model examples, with equilibrium parameters extracted from data in the literature. We find a range of qualitatively different behaviours when swelling and shrinking, including cases where swelling and shrinking happen smoothly from the edge, and other situations which result in the formation of an inwards-travelling spherical front that separates a core and shell with markedly different degrees of swelling. We then characterise when each of these scenarios is expected to occur. An approximate analytical form for the front dynamics is developed, with two levels of constant porosity, that well-approximates the numerical solutions. This system can be evolved forward in time, and is simpler to solve than the full numerics, allowing for more efficient predictions to be made, such as when deciding dosing strategies for drug-laden hydrogels.

Autophoretic microswimmers self-propel via surface interactions with a surrounding solute fuel. Chemically-active filaments are an exciting new microswimmer design that augments traditional autophoretic microswimmers, such as spherical Janus particles, with extra functionality inherent to their slender filament geometry. Slender Phoretic Theory (SPT) was developed by Katsamba et al. to analyse the dynamics of chemically-active filaments with arbitrary three-dimensional shape and chemical patterning. SPT provides a line integral solution for the solute concentration field and slip velocity on the filament surface. In this work, we exploit the generality of SPT to calculate a number of new, non-trivial analytical solutions for slender autophoretic microswimmers, including a general series solution for phoretic filaments with arbitrary geometry and surface chemistry, a universal solution for filaments with a straight centreline, and explicit solutions for some canonical shapes useful for practical applications and benchmarking numerical code. Many common autophoretic particle designs include discrete jumps in surface chemistry; here we extend our SPT to handle such discontinuities, showing that they are regularised by a boundary layer around the jump. Since our underlying framework is linear, combinations of our results provide a library of analytic solutions that will allow researchers to probe the interplay of activity patterning and shape.

The viscous drag on a slender rod by a wall is important to many biological and industrial systems. This drag critically depends on the separation between the rod and the wall and can be approximated asymptotically in specific regimes, namely far from, or very close to, the wall, but is typically determined numerically for general separations. In this note we determine an asymptotic representation of the local drag for a slender rod parallel to a wall which is valid for all separations. This is possible through matching the behaviour of a rod close to the wall and a rod far from the wall. We show that the leading order drag in both these regimes has been known since 1981 and that they can used to produce a composite representation of the drag which is valid for all separations. This is in contrast to a sphere above a wall, where no simple uniformly valid representation exists. We estimate the error on this composite representation as the separation increases, discuss how the results could be used as resistive-force theory and demonstrate their use on a two-hinged swimmer above a wall.

Hydrogels have received increased attention due to their biocompatible material properties, adjustable porosity, ease of functionalization, tuneable shape, and Young's moduli. Initial work has recognized the potential that conferring out‐of‐equilibrium properties to these on the microscale holds and envisions a broad range of biomedical applications. Herein, a simple strategy to integrate multiple swimming modes into catalase‐propelled hydrogel bodies, produced via stop‐flow lithography (SFL), is presented and the different dynamics that result from bubble expulsion are studied. It is found that for “Saturn” filaments, with active poles and an inert midpiece, the fundamental swimming modes correspond to the first three fundamental shape modes that can be obtained by buckling elastic filaments, namely, I, U, and S‐shapes.

The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface deformation. We describe a meshless approach enabling the inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial-slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretisation on a notebook computer with the inclusion of the double layer ranging from no-slip to free-slip limits; the neglect of the double-layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a small percent error when the double-layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and nonslender swimmers, whether or not the double layer is included, which may be due to the deformation’s ‘locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. The inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.

Artificial microswimmers, or 'microbots', have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their environment. Traditionally, self-phoretic particles are point like, but slender phoretic rods have become an increasingly prevalent design. While there has been substantial interest in creating efficient asymptotic theories for slender phoretic rods, hitherto such theories have been restricted to straight rods with axisymmetric patterning. However, modern manufacturing methods will soon allow fabrication of slender phoretic filaments with complex three-dimensional shapes. In this paper, we develop a slender body theory for the solute of self-diffusiophoretic filaments of arbitrary three-dimensional shape and patterning. We demonstrate analytically that, unlike other slender body theories, first-order azimuthal variations arising from curvature and confinement can make a leading-order contribution to the swimming kinematics.

The systematic breaking of left–right body symmetry is a familiar feature of human physiology. In humans and many animals, this process originates with asymmetric fluid flow driven by rotating cilia, occurring in a short-lived embryonic organizing structure termed the node. The very low–Reynolds number fluid mechanics of this system is reviewed; important features include how cilia rotation combines with tilt to produce asymmetric flow, boundary effects, time dependence, and the interpretation of particle tracking experiments. The effect of perturbing cilia length and number is discussed and compared in mouse and zebrafish. Whereas understanding of this process has advanced significantly over the past two decades, there is still no consensus on how flow is converted to asymmetric gene expression, with most research focusing on resolving mechanical versus morphogen sensing. The underlying process may be more subtle, probably involving a combination of these effects, with fluid mechanics playing a central role.

Microscale propulsion is integral to numerous biomedical systems, for example biofilm formation and human reproduction, where the surrounding fluids comprise suspensions of polymers. These polymers endow the fluid with non-Newtonian rheological properties, such as shear-thinning and viscoelasticity. Thus, the complex dynamics of non-Newtonian fluids presents numerous modelling challenges, strongly motivating experimental study. Here, we demonstrate that failing to account for out-of-plane effects when analysing experimental data of undulatory swimming through a shear-thinning fluid results in a significant overestimate of fluid viscosity around the model swimmer C. elegans. This miscalculation of viscosity corresponds with an overestimate of the power the swimmer expends, a key biophysical quantity important for understanding the internal mechanics of the swimmer. As experimental flow tracking techniques improve, accurate experimental estimates of power consumption using this technique will arise in similar undulatory systems, such as the planar beating of human sperm through cervical mucus, will be required to probe the interaction between internal power generation, fluid rheology, and the resulting waveform.

Self-diffusiophoretic particles exploit local concentration gradients of a solute species in order to self-propel at the micron scale. While an isolated chemically- and geometrically-isotropic particle cannot swim, we show that it can achieve self-propulsion through interactions with other individually-non-motile particles by forming geometrically-anisotropic clusters via phoretic and hydrodynamic interactions. This result identifies a new route to symmetry-breaking for the concentration field and to self-propulsion, that is not based on an anisotropic design, but on the collective dynamics of identical and homogeneous active particles. Using full numerical simulations as well as theoretical modelling of the clustering process, the statistics of the propulsion properties are obtained for arbitrary initial arrangement of the particles. The robustness of these results to thermal noise, and more generally the effect of Brownian motion of the particles, is also discussed.

Microscale propulsion is integral to numerous biomedical systems, including biofilm formation and human reproduction, where the surrounding fluids comprise suspensions of polymers. These polymers endow the fluid with non-Newtonian rheological properties, such as shear-thinning and viscoelasticity. Thus, the complex dynamics of non-Newtonian fluids present numerous modelling challenges. Here, we demonstrate that neglecting ‘out-of-plane’ effects during swimming through a shear-thinning fluid results in a significant overestimate of fluid viscosity around the undulatory swimmer Caenorhabditis elegans . This miscalculation of viscosity corresponds with an overestimate of the power the swimmer expends, a key biophysical quantity important for understanding the internal mechanics of the swimmer. As experimental flow-tracking techniques improve, accurate experimental estimates of power consumption in similar undulatory systems, such as the planar beating of human sperm through cervical mucus, will be required to probe the interaction between internal power generation, fluid rheology, and the resulting waveform.

Artificial microswimmers are a new technology with promising microfluidics and biomedical applications, such as directed cargo transport, microscale assembly, and targeted drug delivery. A fundamental barrier to realising this potential is the ability to control the trajectories of multiple individuals within a large group. A promising navigation mechanism for "fuel-based" microswimmers, for example autophoretic Janus particles, entails modulating the local environment to guide the swimmer, for instance by etching grooves in microchannels. However, such techniques are currently limited to bulk guidance. This paper will argue that by manufacturing microswimmers from phoretic filaments of flexible shape-memory polymer, elastic transformations can modulate swimming behaviour, allowing precision navigation of selected individuals within a group through complex environments.