Magnetic-field-induced propulsion of jellyfish-inspired soft robotic swimmers.

The multifaceted appearance of soft robots in the form of swimmers, catheters, surgical devices, and drug-carrier vehicles in biomedical and microfluidic applications is ubiquitous today. Jellyfish-inspired soft robotic swimmers (jellyfishbots) have been fabricated and experimentally characterized by several researchers that reported their swimming kinematics and multimodal locomotion. However, the underlying physical mechanisms that govern magnetic-field-induced propulsion are not yet fully understood. Here, we use a robust and efficient computational framework to study the jellyfishbot swimming kinematics and the induced flow field dynamics through numerical simulation. We consider a two-dimensional model jellyfishbot that has flexible lappets, which are symmetric about the jellyfishbot center. These lappets exhibit flexural deformation when subjected to external magnetic fields to displace the surrounding fluid, thereby generating the thrust required for propulsion. We perform a parametric sweep to explore the jellyfishbot kinematic performance for different system parameters-structural, fluidic, and magnetic. In jellyfishbots, the soft magnetic composite elastomeric lappets exhibit temporal and spatial asymmetries when subjected to unsteady external magnetic fields. The average speed is observed to be dependent on both these asymmetries, quantified by the glide magnitude and the net area swept by the lappet tips per swimming cycle, respectively. We observe that a judicious choice of the applied magnetic field and remnant magnetization profile in the jellyfishbot lappets enhances both these asymmetries. Furthermore, the dependence of the jellyfishbot swimming speed upon the net area swept (spatial asymmetry) is twice as high as the dependence of speed on the glide ratio (temporal asymmetry). Finally, functional relationships between the swimming speed and different kinematic parameters and nondimensional numbers are developed. Our results provide guidelines for the design of improved jellyfish-inspired magnetic soft robotic swimmers.

Magnetically actuated artificial cilia: the effect of fluid inertia.

Natural cilia are hairlike microtubule-based structures that are able to move fluid on the micrometer scale using asymmetric motion. In this article, we follow a biomimetic approach to design artificial cilia lining the inner surfaces of microfluidic channels with the goal of propelling fluid. The artificial cilia consist of polymer films filled with superparamagnetic nanoparticles, which can mimic the motion of natural cilia when subjected to a rotating magnetic field. To obtain the magnetic field and associated magnetization local to the cilia, we solve the Maxwell equations, from which the magnetic body moments and forces can be deduced. To obtain the ciliary motion, we solve the dynamic equations of motion, which are then fully coupled to the Navier-Stokes equations that describe the fluid flow around the cilia, thus taking full account of fluid inertial forces. The dimensionless parameters that govern the deformation behavior of the cilia and the associated fluid flow are arrived at using the principle of virtual work. The physical response of the cilia and the fluid flow for different combinations of elastic, fluid viscous, and inertia forces are identified.

Actuating and sensing properties of nanoporous gold.

We show that variations in the relative humidity give rise to reversible macroscopic dimensional changes in nanoporous gold exposed to ambient air. The macroscopic strain is the consequence of changes in the nanoporous gold surface stress. We have measured reversible strain amplitudes up to 0.02% in response to a 15% change in relative humidity. The direct conversion into mechanical work of the energy involved in the liquid to vapor phase transition of water is attractive for environmentally friendly short-stroke actuator and sensor applications.

Nature-inspired microfluidic propulsion using magnetic actuation.

In this work we mimic the efficient propulsion mechanism of natural cilia by magnetically actuating thin films in a cyclic but non-reciprocating manner. By simultaneously solving the elastodynamic, magnetostatic, and fluid mechanics equations, we show that the amount of fluid propelled is proportional to the area swept by the cilia. By using the intricate interplay between film magnetization and applied field we are able to generate a pronounced asymmetry and associated flow. We delineate the functional response of the system in terms of three dimensionless parameters that capture the relative contribution of elastic, inertial, viscous, and magnetic forces.

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins.

Flagella are hair-like projections from the surface of eukaryotic cells, and they play an important role in many cellular functions, such as cell-motility. The beating of flagella is enabled by their internal architecture, the axoneme, and is powered by a dense distribution of motor proteins, dyneins. The dyneins deliver the required mechanical work through the hydrolysis of ATP. Although the dynein-ATP cycle, the axoneme microstructure, and the flagellar-beating kinematics are well studied, their integration into a coherent picture of ATP-powered flagellar beating is still lacking. Here we show that a time-delayed negative-work-based switching mechanism is able to convert the individual sliding action of hundreds of dyneins into a regular overall beating pattern leading to propulsion. We developed a computational model based on a minimal representation of the axoneme consisting of two representative doublet microtubules connected by nexin links. The relative sliding of the microtubules is incorporated by modeling two groups of ATP-powered dyneins, each responsible for sliding in opposite directions. A time-delayed switching mechanism is postulated, which is key in converting the local individual sliding action of multiple dyneins into global beating. Our results demonstrate that an overall nonreciprocal beating pattern can emerge with time due to the spatial and temporal coordination of the individual dyneins. These findings provide insights in the fundamental working mechanism of axonemal dyneins and could possibly open new research directions in the field of flagellar motility.

Numerical modelling of chirality-induced bi-directional swimming of artificial flagella.

Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chirality-induced) swimmer whose chiral shape and rotational velocity can be controlled by an external magnetic field. In our model, we numerically solve the coupled governing equations that describe the system dynamics (i.e. solid mechanics, fluid dynamics and magnetostatics). We explore the swimming response as a function of the characteristic dimensionless parameters and put special emphasis on controlling the swimming direction. Our results provide fundamental physical insight on the chirality-induced propulsion, and it provides guidelines for the design of magnetic bi-directional micro-swimmers.

Swimming dynamics of bidirectional artificial flagella.

We study magnetic artificial flagella whose swimming speed and direction can be controlled using light and magnetic field as external triggers. The dependence of the swimming velocity on the system parameters (e.g., length, stiffness, fluid viscosity, and magnetic field) is explored using a computational framework in which the magnetostatic, fluid dynamic, and solid mechanics equations are solved simultaneously. A dimensionless analysis is carried out to obtain an optimal combination of system parameters for which the swimming velocity is maximal. The swimming direction reversal is addressed by incorporating photoresponsive materials, which in the photoactuated state can mimic natural mastigonemes.

Fluid flow due to collective non-reciprocal motion of symmetrically-beating artificial cilia.

Using a magneto-mechanical solid-fluid numerical model for permanently magnetic artificial cilia, we show that the metachronal motion of symmetrically beating cilia establishes a net pressure gradient in the direction of the metachronal wave, which creates a unidirectional flow. The flow generated is characterised as a function of the cilia spacing, the length of the metachronal wave, and a dimensionless parameter that characterises the relative importance of the viscous forces over the elastic forces in the cilia.

Swimming direction reversal of flagella through ciliary motion of mastigonemes.

Bio-inspired designs can provide an answer to engineering problems such as swimming strategies at the micron or nano-scale. Scientists are now designing artificial micro-swimmers that can mimic flagella-powered swimming of micro-organisms. In an application such as lab-on-a-chip in which micro-object manipulation in small flow geometries could be achieved by micro-swimmers, control of the swimming direction becomes an important aspect for retrieval and control of the micro-swimmer. A bio-inspired approach for swimming direction reversal (a flagellum bearing mastigonemes) can be used to design such a system and is being explored in the present work. We analyze the system using a computational framework in which the equations of solid mechanics and fluid dynamics are solved simultaneously. The fluid dynamics of Stokes flow is represented by a 2D Stokeslets approach while the solid mechanics behavior is realized using Euler-Bernoulli beam elements. The working principle of a flagellum bearing mastigonemes can be broken up into two parts: (1) the contribution of the base flagellum and (2) the contribution of mastigonemes, which act like cilia. These contributions are counteractive, and the net motion (velocity and direction) is a superposition of the two. In the present work, we also perform a dimensional analysis to understand the underlying physics associated with the system parameters such as the height of the mastigonemes, the number of mastigonemes, the flagellar wave length and amplitude, the flagellum length, and mastigonemes rigidity. Our results provide fundamental physical insight on the swimming of a flagellum with mastigonemes, and it provides guidelines for the design of artificial flagellar systems.

Magnetically-actuated artificial cilia for microfluidic propulsion.

In this paper we quantitatively analyse the performance of magnetically-driven artificial cilia for lab-on-a-chip applications. The artificial cilia are fabricated using thin polymer films with embedded magnetic nano-particles and their deformation is studied under different external magnetic fields and flows. A coupled magneto-mechanical solid-fluid model that accurately captures the interaction between the magnetic field, cilia and fluid is used to simulate the cilia motion. The elastic and magnetic properties of the cilia are obtained by fitting the results of the computational model to the experimental data. The performance of the artificial cilia with a non-uniform cross-section is characterised using the numerical model for two channel configurations that are of practical importance: an open-loop and a closed-loop channel. We predict that the flow and pressure head generated by the artificial cilia can be as high as 18 microlitres per minute and 3 mm of water, respectively. We also study the effect of metachronal waves on the flow generated and show that the fluid propelled increases drastically compared to synchronously beating cilia, and is unidirectional. This increase is significant even when the phase difference between adjacent cilia is small. The obtained results provide guidelines for the optimal design of magnetically-driven artificial cilia for microfluidic propulsion.

Breaking of symmetry in microfluidic propulsion driven by artificial cilia.

In this Brief Report we investigate biomimetic fluid propulsion due to an array of periodically beating artificial cilia. A generic model system is defined in which the effects of inertial fluid forces and the spatial, temporal, and orientational asymmetries of the ciliary motion can be individually controlled. We demonstrate that the so-far unexplored orientational asymmetry plays an important role in generating flow and that the flow increases sharply with Reynolds number and eventually becomes unidirectional. We introduce the concept of configurational symmetry that unifies the spatial, temporal, and orientational symmetries. The breaking of configurational symmetry leads to fluid propulsion in microfluidic channels.

Three-dimensional cross-linked F-actin networks: relation between network architecture and mechanical behavior.

Numerical simulations are reported for the response of three-dimensional cross-linked F-actin networks when subjected to large deformations. In addition to the physiological parameters such as actin and cross-linker concentration, the model explicitly accounts for filament properties and network architecture. Complementary to two-dimensional studies, we find that the strain-stiffening characteristics depend on network architecture through the local topology around cross-links.

Alternative explanation of stiffening in cross-linked semiflexible networks.

Strain stiffening of filamentous protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by nonaffine network rearrangements that govern a transition from a bending-dominated response at small strains to a stretching-dominated response at large strains. Filament undulations, which are key in the existing explanation of stiffening, merely postpone the transition.