Dynamics of poroelastic filaments

Mahadevan, L.

doi:10.1098/rspa.2003.1270

Cited by 34 publications

(30 citation statements)

References 17 publications

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“…If l s ∼ H l , there is no relative motion between the fluid and the solid and the gel behaves as an incompressible elastic solid [11,12], with shear modulus G. From (20) and (21) we see that the effective modulus is…”

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confidence: 95%

Soft Lubrication

2004

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We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we show how the presence of a soft substrate leads to an increase in the physical separation between surfaces sliding past each other. By considering the model problem of a symmetric nonconforming contact moving tangentially to a thin elastic layer, we determine the normal force in the small and large deflection limit, and show that there is an optimal combination of material and geometric properties which maximizes the normal force. Our results can be generalized to a variety of other geometries which show the same qualitative behavior. Thus they are relevant in the elastohydrodynamic lubrication of soft elastic and poroelastic gels and shells, and in the context of bio-lubrication in cartilaginous joints.

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Soft Lubrication

2004

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“…As in the Venus flytrap, the timescale for this snapthrough transition is dictated by the smallest length scale in the system, in this case by the thickness of the shell. [1] The timescale for the snap-through of the Venus flytrap, s p ≈ 100 ms, is governed by: [1,21,22] …”

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confidence: 99%

Snapping Surfaces

2007

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The responsive mechanism of the Venus flytrap has captured the interest of scientists for centuries. Although a complete understanding of the mechanism controlling the Venus flytrap movement has yet to be determined, a recent publication by Forterre et al. [1] demonstrates the importance of geometry and material properties for this fast, stimuliresponsive movement. Specifically, the movement is attributed to a snapthrough elastic instability whose sensitivity is dictated by the length scale, geometry, and materials properties of the features.[2] Here, we use lessons from the Venus flytrap to design surfaces that dynamically modify their topography. We present a simple, robust, biomimetic responsive surface based on an array of microlens shells that snap from one curvature (e.g., concave) to another curvature (e.g., convex) ( Fig. 1) when a critical stress develops in the shell structure. This snap-transition is due to the onset of an elastic, snap-through instability similar to the capture mechanism of the Venus flytrap. The response rates can be over two orders of magnitude faster than the typical response of shape-memory polymers, and the sensitivity and rate of the response can be tuned with predictable geometric and/or material property changes. Based on materials choice, a wide variety of external stimuli can trigger this stress development, such as temperature, pH, solvent swelling, magnetism, electric current, and light. This strategy has great potential for the design of responsive surfaces, which will impact a variety of applications including: release-on-command coatings [3] and adhesives, [4][5][6][7] on-command frictional changes, [8,9] instant modification of optical properties at an interface, [10,11] rapid response drug delivery, [12][13][14] chemical sensing, [15][16][17] and antimicrobial devices. [18] To fabricate the active surface structures, we use the Euler buckling of plates to generate a controlled array of microlens shells under equibiaxial compressive stress (Fig. 2a). First, we pattern cylindrical posts of photoresist onto a silicon wafer and micromold poly(dimethyl siloxane) (PDMS) (Sylgard 184 TM ) elastomer onto it, creating an array of holes. This elastic, PDMS array of holes is then placed in equi-biaxial strain through a simple inflation procedure. A thin film of crosslinked PDMS (typically 15-60 lm in thickness) coated with a thin (∼ 1 lm) layer of uncured PDMS is placed on the surface of the strained holes. The assembly is heated to crosslink the uncured PDMS and bond the film to the array of holes while under equibiaxial tension. Releasing the tension causes an equibiaxial compressive strain to develop in the thin PDMS coating. The associated compressive stresses cause the circular plate of PDMS on the surface of each hole to buckle, thus creating an array of convex microlenses. This technique for microlens preparation is simple, robust, and should be scalable to much smaller length scales across a multitude of materials. COMMUNICATION

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“…To answer these questions, it is essential to accurately take into account the deformation-flow coupling as well the effects of anisotropy. A natural foundation underlying models of such soft, porous, fluid infiltrated composites is the theory of poroelasticity first proposed by Biot (1941Biot ( , 1955 more than half a century ago and put on a firm footing using both homogenization techniques and the intuitive mixture-theory formulation for bulk and low-dimensional objects (Bowen 1973;Rice & Cleary 1976;Burridge & Keller 1981;Mei & Auriault 1989;Wang 2000;Skotheim & Mahadevan 2004). Building on these studies, we describe and characterize carpet-like interfaces on length (spatial) scales that are large compared with the microscopic length scales characterizing the pore structure using an effective theory that takes into account the two-way coupling between fluid flow and elasticity and intrinsically anisotropic characteristics of the material.…”

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Elastohydrodynamics of wet bristles, carpets and brushes

Gopinath

Mahadevan

2011

Proc. R. Soc. A.

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Surfaces covered by bristles, hairs, polymers and other filamentous structures arise in a variety of natural settings in science such as the active lining of many biological organs, e.g. lungs, reproductive tracts, etc., and have increasingly begun to be used in technological applications. We derive an effective field theory for the elastohydrodynamics of ordered brushes and disordered carpets that are made of a large number of elastic filaments grafted on to a substrate and interspersed in a fluid. Our formulation for the elastohydrodynamic response of these materials leads naturally to a set of constitutive equations coupling bed deformation to fluid flow, accounts for the anisotropic properties of the medium, and generalizes the theory of poroelasticity to these systems. We use the effective medium equations to study three canonical problems-the normal settling of a rigid sphere onto a carpet, the squeeze flow in a carpet and the tangential shearing motion of a rigid sphere over the carpet, all problems of relevance in mechanosensation in biology with implications for biomimetic devices.

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Dynamics of poroelastic filaments

Cited by 34 publications

References 17 publications

Soft Lubrication

Soft Lubrication

Snapping Surfaces

Elastohydrodynamics of wet bristles, carpets and brushes

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