Response of a polymer network to the motion of a rigid sphere

Abstract

Abstract. In view of recent microrheology experiments we re-examine the problem of a rigid sphere oscillating inside a dilute polymer network. The network and its solvent are treated using the two-fluid model. We show that the dynamics of the medium can be decomposed into two independent incompressible flows. The first, dominant at large distances and obeying the Stokes equation, corresponds to the collective flow of the two components as a whole. The other, governing the dynamics over an intermediate range of distances and following the Brinkman equation, describes the flow of the network and solvent relative to one another. The crossover between these two regions occurs at a dynamic length scale which is much larger than the network's mesh size. The analysis focuses on the spatial structure of the medium's response and the role played by the dynamic crossover length. We examine different boundary conditions at the sphere surface. The large-distance collective flow is shown to be independent of boundary conditions and network compressibility, establishing the robustness of two-point microrheology at large separations. The boundary conditions that fit the experimental results for inert spheres in entangled F-actin networks are those of a free network, which does not interact directly with the sphere. Closed-form expressions and scaling relations are derived, allowing for the extraction of material parameters from a combination of one-and two-point microrheology. We discuss a basic deficiency of the two-fluid model and a way to bypass it when analyzing microrheological data.

Localization and diffusion of tracer particles in viscoelastic media with active force dipoles

“…It should be stressed that this is a simplification and the situation for real tracers can be much more complicated (see, e.g., ref. [11]). Interactions between a tracer and the elastic network depend on the ratio between the size of the tracers and the mesh size of the polymer network.…”

“…The dynamics of such particles inside a gel is itself a complicated problem; it depends on the mechanical properties of such particles and on their interactions with the polymer network [11].…”

Anomalous diffusion in viscoelastic media with active force dipoles

“…(35)]. (b) The case when the time correlation of the force dipole decays exponentially with a characteristic relaxation time τ d [see Eq (39)…”

Surface Response of a Polymer Network: Semi-infinite Network

“…This modulus has eluded measurement, because decoupling it from the total compression modulus of the medium (which is governed by the solvent's very large modulus) is hard. 18 The dispersion relation of eq 15 is relevant to low frequencies where inertia is negligible. Comparison with refs 10,11, which included inertial effects, reveals that this requirement is fulfilled for ω min( γq 3 /ρ m , η b q 2 /ρ m ), where ρ m ∼ 1 gr/cm 3 is the medium's mass density.…”