Interface Fluctuations under Shear

Coarsening systems under uniform shear display a long time regime characterized by the presence of highly stretched and thin domains. The question then arises whether thermal fluctuations may actually destroy this layered structure. To address this problem in the case of non-conserved dynamics we study an anisotropic version of the Burgers equation, constructed to describe thermal fluctuations of an interface in the presence of a uniform shear flow. As a result, we find that stretched domains are only marginally stable against thermal fluctuations in $d=2$, whereas they are stable in $d=3$.Comment: 3 pages, shorter version, additional reference

Two-scale competition in phase separation with shear

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth $R(t) \sim t^{\alpha}$ of the average domain size, with $\alpha =4/3$ and $\alpha = 1/3$ in the flow and shear direction respectively, is shown to be obeyed.Comment: 5 Revtex pages, 4 figure

Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids

We perform a linear stability analysis of extended domains in phase-separating fluids of equal viscosity, in two dimensions. Using the coupled Cahn-Hilliard and Stokes equations, we derive analytically the stability eigenvalues for long wavelength fluctuations. In the quiescent state we find an unstable varicose mode which corresponds to an instability towards coarsening. This mode is stabilized when an external shear flow is imposed on the fluid. The effect of the shear is seen to be qualitatively similar to that found in experiments.Comment: 13 pages, RevTeX, 8 eps figures included. Submitted to Phys. Rev.

Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics

We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the parameters corresponding to the weak and strong segregation limits. For deep quenches we identify a complex structure of intermediate regimes and crossovers characterized by the existence of a time domain such that phase separation is pinned, followed by a preasymptotic regime which in the scalar case corresponds to surface diffusion. The duration of the pinning is analytically computed and diverges in the strong segregation limit. Eventually a late stage dynamics sets in, described by scaling laws and exponents analogous to those of the corresponding small molecule systems.Comment: 16 pages, 5 figures. Submitted to Phys. Rev.

Phase separation in an homogeneous shear flow: Morphology, growth laws and dynamic scaling

We investigate numerically the influence of an homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are clarified. Our numerical data show unambiguously that, in the shear flow, the domains have on average an elliptic shape. The time evolution of the three parameters describing this ellipse are obtained for a wide range of shear rates. For the lowest shear rates investigated, we find the growth laws for the two principal axis $R_\perp (t) \sim constant$, $R_\parallel(t) \sim t$, while the mean orientation of the domains with respect to the flow is inversely proportional to the strain. This implies that when hydrodynamics is neglected a shear flow does not stop the domain growth process. We investigate also the possibility of dynamic scaling, and show that only a non trivial form of scaling holds, as predicted by a recent analytical approach to the case of a non-conserved order parameter. We show that a simple physical argument may account for these results.Comment: Version accepted for publication - Physical Review

Ohta-Jasnow-Kawasaki Approximation for Nonconserved Coarsening under Shear

We analytically study coarsening dynamics in a system with nonconserved scalar order parameter, when a uniform time-independent shear flow is present. We use an anisotropic version of the Ohta-Jasnow-Kawasaki approximation to calculate the growth exponents in two and three dimensions: for d=3 the exponents we find are the same as expected on the basis of simple scaling arguments, that is 3/2 in the flow direction and 1/2 in all the other directions, while for d=2 we find an unusual behavior, in that the domains experience an unlimited narrowing for very large times and a nontrivial dynamical scaling appears. In addition, we consider the case where an oscillatory shear is applied to a two-dimensional system, finding in this case a standard t^1/2 growth, modulated by periodic oscillations. We support our two-dimensional results by means of numerical simulations and we propose to test our predictions by experiments on twisted nematic liquid crystals.Comment: 25 RevTeX pages, 7 EPS figures. To be published in Phys. Rev.

The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit

The effect of shear on the ordering-kinetics of a conserved order-parameter system with O(n) symmetry and order-parameter-dependent mobility \Gamma({\vec\phi}) \propto (1- {\vec\phi} ^2/n)^\alpha is studied analytically within the large-n limit. In the late stage, the structure factor becomes anisotropic and exhibits multiscaling behavior with characteristic length scales (t^{2\alpha+5}/\ln t)^{1/2(\alpha+2)} in the flow direction and (t/\ln t)^{1/2(\alpha+2)} in directions perpendicular to the flow. As in the \alpha=0 case, the structure factor in the shear-flow plane has two parallel ridges.Comment: 6 pages, 2 figure

Phase-separation of binary fluids in shear flow: a numerical study

The phase-separation kinetics of binary fluids in shear flow is studied numerically in the framework of the continuum convection-diffusion equation based on a Ginzburg-Landau free energy. Simulations are carried out for different temperatures both in d=2 and in d=3. Our results confirm the qualitative picture put forward by the large-N limit equations studied in \cite{noi}. In particular, the structure factor is characterized by the presence of four peaks whose relative oscillations give rise to a periodic modulation of the behavior of the rheological indicators and of the average domains sizes. This peculiar pattern of the structure factor corresponds to the presence of domains with two characteristic thicknesses whose relative abundance changes with time.Comment: 6 pages, 11 figures in .gif forma

Mechanical characterization of multilayered hydrogels: a rheological study for 3D-printed systems

We describe rheological protocols to study layered and three-dimensional (3D)-printed gels. Our methods allow us to measure the properties at different depths and determine the contribution of each layer to the resulting combined properties of the gels. We show that there are differences when using different measuring systems for rheological measurement, which directly affects the resulting properties being measured. These methods allow us to measure the gel properties after printing, rather than having to rely on the assumption that there is no change in properties from a preprinted gel. We show that the rheological properties of fluorenylmethoxycarbonyl-diphenylalanine (FmocFF) gels are heavily influenced by the printing process

Control of Gastric H,K-ATPase Activity by Cations, Voltage and Intracellular pH Analyzed by Voltage Clamp Fluorometry in Xenopus Oocytes

Whereas electrogenic partial reactions of the Na,K-ATPase have been studied in depth, much less is known about the influence of the membrane potential on the electroneutrally operating gastric H,K-ATPase. In this work, we investigated site-specifically fluorescence-labeled H,K-ATPase expressed in Xenopus oocytes by voltage clamp fluorometry to monitor the voltage-dependent distribution between E1P and E2P states and measured Rb+ uptake under various ionic and pH conditions. The steady-state E1P/E2P distribution, as indicated by the voltage-dependent fluorescence amplitudes and the Rb+ uptake activity were highly sensitive to small changes in intracellular pH, whereas even large extracellular pH changes affected neither the E1P/E2P distribution nor transport activity. Notably, intracellular acidification by approximately 0.5 pH units shifted V0.5, the voltage, at which the E1P/E2P ratio is 50∶50, by −100 mV. This was paralleled by an approximately two-fold acceleration of the forward rate constant of the E1P→E2P transition and a similar increase in the rate of steady-state cation transport. The temperature dependence of Rb+ uptake yielded an activation energy of ∼90 kJ/mol, suggesting that ion transport is rate-limited by a major conformational transition. The pronounced sensitivity towards intracellular pH suggests that proton uptake from the cytoplasmic side controls the level of phosphoenzyme entering the E1P→E2P conformational transition, thus limiting ion transport of the gastric H,K-ATPase. These findings highlight the significance of cellular mechanisms contributing to increased proton availability in the cytoplasm of gastric parietal cells. Furthermore, we show that extracellular Na+ profoundly alters the voltage-dependent E1P/E2P distribution indicating that Na+ ions can act as surrogates for protons regarding the E2P→E1P transition. The complexity of the intra- and extracellular cation effects can be rationalized by a kinetic model suggesting that cations reach the binding sites through a rather high-field intra- and a rather low-field extracellular access channel, with fractional electrical distances of ∼0.5 and ∼0.2, respectively