Shear flow effects on phase separation of entangled polymer blends

We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components

Kramers rate theory of ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We solve this classical problem by accounting for entropic memory at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

The Johnson-Segalman model with a diffusion term in Couette flow

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog

Muscle ‘regenerative potential’ determines physical recovery following total knee replacement

ObjectivesLower limb muscle power is thought to influence outcome following total knee replacement (TKR). Post-operative deficits in muscle strength are commonly reported, although not explained. We hypothesised that post-operative recovery of lower limb muscle power would be influenced by the number of satellite cells in the quadriceps muscle at time of surgery.MethodsBiopsies were obtained from 29 patients undergoing TKR. Power output was assessed pre-operatively and at six and 26 weeks post-operatively with a Leg Extensor Power Rig and data were scaled for body weight. Satellite cell content was assessed in two separate analyses, the first cohort (n = 18) using immunohistochemistry and the second (n = 11) by a new quantitative polymerase chain reaction (q-PCR) protocol for Pax-7 (generic satellite cell marker) and Neural Cell Adhesion Molecule (NCAM; marker of activated cells).ResultsA significant improvement in power output was observed post-operatively with a mean improvement of 19.7 W (95% confidence interval (CI) 14.43 to 30.07; p < 0.001) in the first cohort and 27.5 W (95% CI 13.2 to 41.9; p = 0.002) in the second. A strong correlation was noted between satellite cell number (immunohistochemistry) and improvement in patient power output (r = 0.64, p = 0.008). Strong correlation was also observed between the expression of Pax-7 and power output (r = 0.79, p = 0.004), and the expression of NCAM and power output (r = 0.84, p = 0.001). The generic marker explained 58% of the variation in power output, and the marker of activated cells 67%.ConclusionsMuscle satellite cell content may determine improvement in lower limb power generation (and thus function) following TKR

Spinodal-assisted crystallization in polymer melts

Recent experiments in some polymer melts quenched below the melting temperature have reported spinodal kinetics in small-angle x-ray scattering before the emergence of a crystalline structure. To explain these observations we propose that the coupling between density and chain conformation induces a liquid-liquid binodal within the equilibrium liquid-crystalline solid coexistence region. A simple phenomenological theory is developed to illustrate this idea, and several experimentally testable consequences are discussed. Shear is shown to enhance the kinetic role of the hidden binodal

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress \sigma is driven at a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate \lambda\sigma_2. Here \sigma_{1,2}(t) = \tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when \tau_2>\tau_1 and 0>R'(\sigma)>-\lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case \tau_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com

Coexistence and Phase Separation in Sheared Complex Fluids

We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are coupled to shear rate. Our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. We use the (generalized) Doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non-local effects are included.Comment: 4 pages REVTEX, 5 figures using epsf macros. To appear in Physical Review E (Rapid Communications