Biomimetic ratcheting motion of a soft, slender, sessile gel

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L. Mahadevan, S. Daniel, and M. K. Chaudhury

" Biomimetic ratcheting motion of a soft, slender, sessile gel"

Entry by Fei Pu, AP 225, Fall 2012


Keywords: hydrogel, inchworm, [[ratcheting motion]


Summary

Inspired by the locomotion of terrestrial limbless animals, the motion of a lubricated rod of a hydrogel on a soft substrate is studied. It's shown that it's possible to mimic observed biological gaits by vibrating the substrate and by using a variety of mechanisms to break longitudinal and lateral symmetry.The simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcations of a simple periodic longitudinal oscillations by using a slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on substrates.

Materials and Methods

The experiment is done using a long cylindrical filament (length, l, and area of cross-section, a) on a substrate, with a thin film of intercalating liquid at the interface. The deformation can be characterized by a displacement field, where the local strain and stress are approximated by linear Hookean Law. The interaction of the gel with the substrate is modeled by means of a simple dynamic friction law so that the resisting force per unit area. In the absence of inertia and any other body forces (due to muscular movement, etc.), the forces are balanced by the segment's elastic force and the gel's frictional force.


Figure 1. A schematic illustration of the elastic and frictional forces on an infinitesimal axial segment of the gel.
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To test these ideas experimentally, an artificial snail is prepared, which is a long cylindrical hydrogel rod with a radius of 2 mm and a length of 2 cm lying on a thin film of silicon rubber bonded to a glass plate. The hydrogel is liquid-volume fraction of 80%. This preparation leads naturally to the presence of an intercalating liquid layer that separates the hydrogel from the elastic substrate, otherwise the soft gel will adhere strongly to the substrate. To mimic the muscular contractions of a real snail, an induced periodic vibrations of the soft filament by using an external source is implemented; the glass plate itself is clamped to a vibrating table driven by a pattern generator. When the hydrogel rod is aligned with the direction of vibration and the table is subject to asymmetric vibrations, the gel rod glides on the thin water film, consistent with a simple ratchet driven by an asymmetric waveform. Figure 2 shows the periodic motion.


Figure 2. Snapshots of a polyacrylamide hydrogel rod on a thin elastomeric film of polydimethylsiloxane, which is subject to harmonic longitudinal vibrations.
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Results & Discussion

When two colloids overlap each other, the depletion entropy increases, and such phenomenon makes the colloids attract more closely. The effect of rough particles interacting with smooth particles and other rough particles was recorded and analyzed. At higher concentrations and thus stronger attractions, the roughness anisotropic colloidal particles spontaneously organized into clusters, in which the attractive parts constitute the core of the aggregate and the non-attractive rough sides are located at the outside. These structures look like micelles, as shown below in Figure 1.


Monte Carlo simulation was further done on the smooth and rough colloids, shown in Figure 2. As time went on, it seems like smooth particles attracted into clusters and formed the core of the micelles and that the rough particles stayed outside and surrounded the core.

Figure 2. Smooth particles clustered on the inside of the micelles while the rough particles surrounded the outside.

Finally,cluster size distributions changed as interactions increased and geometry overlapped more. From Figure 3, it's clear that as density, p, increased, clusters were more prone and easily formed. When density was low at the beginning, the particles flowed freely and even repelled. Only when density reached a threshold that the surface energy and forces favored clustering.

Figure 3. As density of particles increased, they overlapped more and formed clusters.

Soft Matter Applications

Due to the available variety of colloids and their straightforward assembly even between different patch sizes, it is expected that these soft colloidal particles with smooth and rough surfaces could self-assemble in a controlled manner into superstructures with desired topology and properties. This has significant applications. For example, the virus macromolecules, protein subunits, and building cell blocks in our body are often complex and challenging to identify key elements for self-assembly processes. By mimicking such self-assembly processes on a colloidal scale, insights into the paramount elements that control the assembly can be obtained in situ and applied to build up superstructures with new and desirable properties. The findings in this article have fundamental and practical importance in the field of colloidal and macromolecular self assembly.