Session E25: Microscale Flows: Locomotion

Around a camphoric-acid boat, is the surfactant adsorbed on to the interface or dissolved in the bulk?

A camphoric-acid boat (c-boat for short), a cylindrical gel tablet infused with camphoric acid, moves spontaneously when placed on an air-water interface. This system is a classic example of propulsion driven by Marangoni forces. Despite rich history on particles propelled by Marangoni forces, including contributions by figures such as Benjamin Franklin, Allesandro Volta, and Giovanni Venturi, the underlying fluid dynamics remains poorly understood. A key missing piece is the nature of the surfactant; in our case, the question is whether the camphoric acid is dissolved in the bulk or adsorbed on to the interface. We gain insight into this piece by holding the c-boat stationary and measuring the surrounding axisymmetric flow velocity to a precision needed to distinguish between the two possibilities. For soluble surfactants, it is known that the velocity field decays as $r^{-2/3}$, where $r$ is the distance from the center of the c-boat. Whereas, for surfactant adsorbed on to the air-water interface, we derive that the surrounding velocity fields decays as $r^{-3/5}$. Based on our measurements we deduce that, even though soluble in water, the Marangoni flow results from a layer of camphoric acid adsorbed to the air-water interface.   

Steering artificial nanoscale swimmers using teardrop shaped posts

Microorganisms use various strategies to bias their swimming to achieve long-time directed motion against a flow, against gravity, or up a chemical gradient. To make use of artificial swimmers for transporting cargo, to separate swimming particles from diffusing ones, or to concentrate a solution of motile particles, ways of steering such swimmers are required. We make use of the attraction of artificial bi-metallic swimmers to vertical walls to direct their long-time motion. We will describe how these swimmers are attracted to the surface of teardrop-shaped posts and leave preferentially at regions of higher curvature. We use this understanding to interpret their behavior when interacting with arrays of teardrop-shaped posts.   

Convective self-propulsion of chemically active particles

A mechanism of particle self-propulsion activated by transduction of chemical energy into convective motion of fluid that drags microscale particles is proposed. The convection is generated by an active spherical particle located on the bottom of a microchannel and coated with a catalyst that decomposes reagent dissolved in the solution into less dense products and gives rise to a buoyancy force. The symmetry of the flow generated around the active particle can be broken if a passive spherical particle, which does not produce the flow, is present in the vicinity of the first one. The generated flow drags the passive particle toward the active one along the bottom wall until they form a dimer. The resulting asymmetric fluid flow, which is generated by only one of the particles, imposes a different drag on the different sides on the dimer. The net force causes the dimer to translate along the bottom wall. By varying numbers of active and passive particles, as well as their positions within a group, one can control the structure of the generated convective flow and, therefore, design clusters with different mobile properties. The proposed mechanism can be harnessed to transport cargo in microchannels.   

Wall-induced self-diffusiophoresis of active isotropic colloids

While chemically-active homogeneous spherical particles do not undergo self-diffusiophoresis in free solution, they may do so when suspended in the vicinity of a solid boundary. We explore this possibility using a first-order kinetic model of solute absorption, where the relative magnitude of reaction to diffusion is characterized by the Damkohler number Da. When the particle is remote from the wall, it is repelled from it with a velocity that scales inversely with the square of distance. The opposite extreme, when the ratio $\delta$ of separation distance to particle size is small, results in the anomalous scaling $\delta^{\frac{\sqrt{1+2\mathrm{Da}}-1}{2}}$ of the solute concentration in the narrow gap separating the particle and wall. This irrational power may only be obtained by asymptotic matching with solute transport outside the gap. For Da$<4$ the self-propulsion speed possesses the same scaling, being set by the large pressures forming in the gap through a lubrication-type mechanism. For Da$>4$ the particle velocity is $O(\delta)$, set by the flow in the region outside outside the gap. Solute advection is subdominant to diffusion in both the remote and near-contact limits, and accordingly affects neither the above scaling nor the resulting approximations.   

Traction Reveals Nature of Wall-effects for Microswimmers near Boundaries

The flow field due to a low-Reynolds number swimmer swimming in the vicinity of a planar boundary has been frequently studied using image systems of flow singularities. However, it can also be represented by an integral of the traction on the boundary. We show that examining the traction pattern on the boundary caused by a swimmer provides insights into determining when far-field multipole models are accurate. We investigate the instantaneous swimming velocity and traction induced by a three-sphere swimmer placed near a solid planar wall quantitatively. When the swimmer is far from the wall, the effect of the wall can be accurately represented using the image of a force dipole, but near the wall, a system of singularities reflecting the internal structure of the swimmer is necessary. We find that the instantaneous traction reflects these limits, and furthermore can be used to determine the range of validity of the far-field approximation. We also investigate the time-averaged velocity and traction. In the far field, the image of a quadrupole accurately represents the effect of the boundary, and the traction is also quadrupolar, while in the near field, the traction shows the influence of the internal structure of the swimmer.   

Maximizing the propulsive thrust of a driven filament at low Reynolds number through non-uniform flexibility

In the low Reynolds number regime, periodic boundary actuation of a rigid filament leads to a reciprocal motion and hence produces zero propulsive thrust. Introducing flexibility into the filament results in filament deformation enabling propulsion in the absence of inertia. For a given actuation frequency and filament length, an optimal bending stiffness of the filament can be determined to produce the largest propulsive force. However, the possibility of further improving the propulsion by allowing variable flexibility along the filament remains largely unexplored. In this work, we perform a theoretical investigation of flexibility distributions that can maximize propulsive thrust of a driven filament at low Reynolds number.