Session J09: Biofluids: Low Re Swimming II

Experimental and numerical study of untethered microswimmers with light-driven particle hinges

Light-driven microswimmers are studied numerically and experimentally in the forms of one-hinge "scallop" swimmers and two-hinge "Purcell" swimmers. Although the untethered microswimmers hold great potential in their applications, such as minimally invasive medicine and active environment monitoring, the study of microswimmers' locomotion on the length scale of mm to cm is often hindered by the availability of experimental techniques at microscale and the limited understanding of its flow physics. In this study, an electromicrofluidic (EMF) printing platform, that independently drives and assembles hydrogel droplets and suspended particles, is adapted to fabricate hydrogel scallop and Purcell swimmers with particle-embedded hinges driven by light. The response of the hinges, including folding angle, folding speed, and unfolding speed, are characterized. The locomotion trajectory and speed are characterized in experiments and compared with the numerical simulation. In particular, we studied numerically and experimentally the nonlinear impact to the flow dynamics and locomotion of microswimmers, since nonlinearity has been neglected in most of the previous studies based on Stokes flow assumption.   

Microswimming by odd elasticity

Microswimmers such as bacteria, sperm cells, and microalgae often generate a traveling wave to propel themselves at low Reynolds number. This non-reciprocal deformation is created by internal actuation within an elastic filament. In this talk, we introduce the concept of odd elasticity, which is a relatively new framework for describing the non-equilibrium state of matter and an extension of linear elasticity, to the field of microswimmer elastohydrodynamics. This provides a unified description of living materials in viscous fluids. We begin by presenting a minimal mathematical model known as Purcell's swimmer, being consisted of three rods connected by two hinges, and demonstrate that hinges with odd-elastic properties enable the swimmer to exhibit stable periodic locomotion without any controlled actuation. Furthermore, we formulate a general swimmer subjected to periodic deformations by extending the concept of odd elasticity into a non-linear regime. Through analyses of various simple mathematical models and experimental data, we introduce an extension of the elastic modulus to capture non-local, non-reciprocal interactions within the active filament.    

An entropic effect essential for surface entrapment of bacteria

The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is still not well understood. We demonstrate that it is crucial to include a commonly neglected entropic effect arising from the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α₁ the ratio of thermal energy to self-propulsion, and α₂ an intrinsic shape factor. For α₁ and α₂ that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α₁,α₂}.   

Swimming with deep learning

The study of micro-organisms' propulsion has intrinsic relevance for the development of micro-robots designed for targeted drug delivery and as a foundation for further studies on hydrodynamic interactions between micro-organisms in complex environments. Numerical simulations have been used extensively to investigate micro-organisms' locomotion. Recently, physics-informed neural networks (PINNs) have shown promise for approximating solutions to differential equations that govern various physical problems. In this talk, we evaluate the effectiveness of using PINNs to predict the low Reynolds dynamics that characterize the propulsion of micro-organisms.   

The effect of particle geometry on squirming in a heterogeneous medium

Micro-organisms encounter heterogeneous viscous environments due to networks of obstacles embedded into viscous fluid media. In this talk we present a numerical investigation of the effects of shape on swimming in such a heterogeneous medium. Specifically, we analyze the microorganism's propulsion speed as well as its energetic cost and swimming efficiency. The analysis allows us to probe the general characteristics of swimming in a heterogeneous viscous environment in comparison with the case in a purely viscous fluid.   

Exploring forward and backward swimming dynamics in bioinspired undulatory swimmers

This research devises a sophisticated numerical model for bioinspired underwater vehicles, drawing inspiration from the locomotion of natural aquatic creatures, including both forward and backward swimmers. This model features a rigid head equipped with a heave, pitch actuation, and a passive flexible tail, operating effectively under quiescent flow conditions at a Reynolds number of $Re=100$. An exhaustive exploration of different tail flexibility and head actuation parameters has been undertaken, leading to the observation of a diverse range of wake patterns, from a downward wake to an upward wake, and even revealing the formation of a unique bifurcated wake. The findings indicate that when tail rigidity is set at $gamma=1.0$ and head actuation parameters are defined with a pitching amplitude $Theta_0=pi/8$ and a heaving amplitude $h=0.3$, and vortices shed from the tail create a downward jet. In contrast, at $gamma=0.5$, vortices are released from both the head and tail, moving upward and downward trajectories. Decreasing the bending rigidity to $gamma=0.2$ with $Theta_0=pi/8$ and $h=0.1$ results in the creation of successive vortices on alternating sides of the mean swimming path, forming a single upward jet similar to the motion observed in backward swimmers. Intriguingly, at $gamma=0.2$ with $Theta_0=pi/8$ and $h=0.3$, a dipole couple is generated in each half cycle, moving towards the head at an inclined angle, thereby resulting in a distinctive bifurcated wake structure.   

Theoretical efficiency limits for microswimmer propulsion

As a microswimmer displaces the fluid it is moving through, it inevitably dissipates energy. The dissipation consists of two contributions. The external dissipation takes place in the viscous fluid surrounding the microswimmer. Internal dissipation takes place in the propulsive layer on the swimmer's surface and is often the dominant contribution. Here, we solve the combined minimum dissipation problem for different classes of swimmers including surface-driven viscous droplets, swimmers driven by tangential forces and swimmers driven by normal forces. We have previously shown that a lower bound on the external dissipation can be derived with the knowledge of drag coefficients of two bodies of the same shape, one with a no-slip and one with a perfect slip boundary condition [1]. We now generalize the approach to a number of models where the lower bound on the dissipation by the active swimmer can be expressed with two passive drag coefficients [2]. We thus provide an exact analytical solution to a class of problems that were previously only tractable by numerical optimization.

[1] B. Nasouri, A. Vilfan and R. Golestanian, Phys. Rev. Lett., 126, 034503 (2021).

[2] A. Daddi-Moussa-Ider, R. Golestanian, A. Vilfan, arXiv:2302.07711   

Efficient Blood Propulsion of Squirmer-Type Microrobots

Microrobots capable of navigating through the intricate network of blood vessels hold significant promise for various medical applications. Blood contains high volume fraction of blood cells, a microrobot must propel itself by rearranging the surrounding blood cells for navigation. However, the most effective swimming mechanism for propulsion in blood remains unknown. In this study, we numerically investigate two different microrobots: non-surface active and surface active microswimmers. We systematically vary parameters such as the capillary number, hematocrit, magnetic torque exerted on the microrobot, and microrobot to red blood cell (RBC) radius ratio to evaluate their impact on microrobot behavior in complex in vivo environments. Our findings reveal that a surface active microrobot is by far more efficient in moving through blood than a non-surface active microrobot.  When the microrobot size is comparable to a red blood cell, the puller microrobot swims faster than the pusher microrobot. When the microrobot size becomes much smaller, on the other hand, the pusher microrobot swims faster than the puller microrobot. The swimming speed is thus strongly dependent on the swimmer type and microrobot size as well as hematocrit and magnetic torque used to control the microrobot orientation. These results offer valuable insights into the design of microrobots that can efficiently navigate through blood, with implications for targeted drug delivery and minimally invasive medical procedures.   

Manufacturing and near wall swimming of helical thin magnetic ribbons

In this study, we employed micro manufacturing techniques to fabricate magnetic helical micro ribbons, which consist of a nickel layer sandwiched between two SiN layers. Then the ribbons are placed inside a chamber filled with isopropyl alcohol on top of a microscope glass. Three pairs of Helmholtz coils generated a rotating magnetic field around the chamber, exerting a magnetic torque on the ribbon, causing it to rotate synchronously with the field. Additionally, a piezo actuator was attached to the microscope glass and driven at frequencies of 1 and 10 kHz during the experiments. Forward and lateral velocities of the ribbons are obtained from recorded images. According to experimental results, lateral velocities of the ribbons decreased, and forward velocities improved when the vibration is induced by the piezo actuator. To analyze the swimming behavior, we also developed a three-dimensional CFD model, assuming steady Stokes flow around the swimmer due to both its rotation and translation. In the simulations, we varied the distance between the swimmer and the bottom wall. The CFD model provided valuable insights to understand the effect of vibration on the swimming behavior of the helical ribbons which exhibit sliding behavior near the wall when the gap between the swimmer and the wall is minimal. This sliding behavior is due to a large pressure gradient around the nip region when the swimmer almost touches the wall.