Small-amplitude Deformations Research Articles

Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments

We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the “Stokes problems” in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.

Surface Waves on Polymer Brushes

We present a simple analytical method to study the deformation behavior of a grafted melt polymer brush. We calculate the change in the free energy associated with (1) small-amplitude deformations of the free surface, (2) nonuniformity in the areal density of grafted chains, and (3) deformations of the grafting surface. We obtain the same results as Fredrickson et al.4 for long-wavelength surface modes of melt brushes if we make their approximation that all the chain free ends reside at the surface. Our method can be applied to a wide range of problems, such as the deformation of cylindrical or spherical micelles.

The mechanism of the viscoelastic behaviour of electrorheological suspensions

Experimental results are presented for the rheology of dielectric silica suspensions in the presence of d.c. electric fields, both for uniaxial continuous shear and small-amplitude periodic deformations. All electrorheological suspensions (ERS) are grouped into three structural-rheological categories in dependence on an influence of the main composition factors (especially solid-phase concentration), electric intensity and mechanical load on the electrorheological effect magnitude. Each category exhibits specific features, typical of media with variable viscosity, of viscoplastic and elastoviscous behaviour, which provides a wide scope of ERS applications in different spheres of technology, e.g. in hydraulics, robotics and mechanical engineering.

Viscoelastic properties of thermotropic liquid crystal polymers from analysis of dynamical characteristics

The rheological properties of liquid-crystal polymers with side-chain mesogenic groups are studied by means of small-amplitude periodic deformations in the mesophase and in the isotropic melt.

Use of Clemmow functions in the study of an acoustic pulse generated by a deformable sphere

In this paper use is made of Clemmow's representation of solutions of Legendre's equation to consider the sound pulses generated in a fluid by axisymmetrical small amplitude deformations of a spherical boundary. The expansions and approximations derived yield more information about the structure and nature of the pulses than do solutions previously obtained.