View source for Biomimetic ratcheting motion of a soft, slender, sessile gel

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. 
 

[[Image:Elastic_rod.jpg|thumb|center|400px|
Figure 1. A schematic illustration of the elastic and frictional forces on an infinitesimal axial segment of the gel.]]

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. The hydrogel is also slitted in different angles to mimic the insects' scales and skin texture. 


[[Image:Periodicwave.jpg|thumb|center|400px|
Figure 2. Snapshots of a polyacrylamide hydrogel rod on a thin elastomeric film of polydimethylsiloxane, which is
subject to harmonic longitudinal vibrations.]]

==Results & Discussion==
The axial snail-like motion loses stability to snake-like and inchwormlike motions when the geometry of the scales of the hydrogels and or vibration is varied. As shown in the figure 3 below. In-plane bending deformations arise when the scales are inclined at a varying angle to the axis of the filament. These deformations lead to an anisotropic friction; thus, sideways oscillations cause the filament to bend and slither along. Out-of plane bending deformations arise when the filament is subjected to small-amplitude vertical oscillations. These deformations cause the filament to buckle out of the plane and then slip in one direction due to the presence of the scales, as shown

[[Image:Wormmotion.jpg|thumb|center|400px|
Figure 3. In plane and out-plane bending deformations of the hydrogels mimicking the worm's motion.]]

==Thin Film Relevance==

By considering the dynamical interaction of a soft, slender filament with a substrate, it is possible to mimic a number of different modes of motion seen in biological locomotion at interfaces such as creeping, crawling, inching, reptating, and slithering. At a purely physical level, this leads to a unified view wherein these modes arise naturally as symmetry breaking bifurcation transitions of slender bodies when the muscular forces exceed the buckling load. By using a soft, sessile gel filament on an elastic substrate as a model system, it is shown that these gaits can all be easily realized experimentally by using an external source of vibration coupled to the asymmetric interfacial interaction between the gel and the substrate.

An important aspect of these biomimetic gaits is that the motion of the gel is not prescribed a necessary aspect; instead, it arises from the interaction between the body and the environment once a periodic forcing is applied and is thus similar to biological reality. On the technological side, the externally applied vibration is one way to generate periodic pulses; artificially actuated gels that respond to various stimuli such as electromagnetic fields, temperature, and chemical oscillations point toward applications to situations requiring the autonomous motion of soft solids on surfaces.