Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth

An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding wave number for any combination of thickness and viscosity of the fluid. Applying this method to magnetic fluids of finite depth, these results are quantitatively compared to the wave number of the transient pattern observed experimentally after a jump--like increase of the field. The wave number grows linearly with increasing induction where the theoretical and the experimental data agree well. Thereby a long-standing controversy about the behaviour of the wave number above the critical magnetic field is tackled.Comment: 19 pages, 15 figures, RevTex; revised version with a new figure and references added. submitted to Phys Rev

Soft elasticity in biaxial smectic and smectic-C elastomers

Ideal (monodomain) smectic-$A$ elastomers crosslinked in the smectic-$A$ phase are simply uniaxial rubbers, provided deformations are small. From these materials smectic-$C$ elastomers are produced by a cooling through the smectic-$A$ to smectic-$C$ phase transition. At least in principle, biaxial smectic elastomers could also be produced via cooling from the smectic-$A$ to a biaxial smectic phase. These phase transitions, respectively from $D_{\infty h}$ to $C_{2h}$ and from $D_{\infty h}$ to $D_{2h}$ symmetry, spontaneously break the rotational symmetry in the smectic planes. We study the above transitions and the elasticity of the smectic-$C$ and biaxial phases in three different but related models: Landau-like phenomenological models as functions of the Cauchy--Saint-Laurent strain tensor for both the biaxial and the smectic-$C$ phases and a detailed model, including contributions from the elastic network, smectic layer compression, and smectic-$C$ tilt for the smectic-$C$ phase as a function of both strain and the $c$-director. We show that the emergent phases exhibit soft elasticity characterized by the vanishing of certain elastic moduli. We analyze in some detail the role of spontaneous symmetry breaking as the origin of soft elasticity and we discuss different manifestations of softness like the absence of restoring forces under certain shears and extensional strains.Comment: 26 pages, 6 figure

Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory

Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the non-equilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance namely a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.Comment: 14 pages, 2 figures, to appear in PR

Reply to Comment on “Director reorientation in nematic liquid-single-crystal elastomers by external mechanical stress”

In their comment E. M. Terentjev and M. Warner try to argue that the results we obtained in ref. [1] are physically incorrect. To do this they use estimates of the orders of magnitude, and their scaling with cross-linking density, of a number of elastic coefficients. We point out that their arguments are based on their misunderstanding of several basic concepts. First, they confuse the Landau model to describe phase transitions with a macroscopic description of the nematic phase. Second, they apply the technique of a linear stability analysis above the threshold of the instability, where this type of analysis is incorrect

Director reorientation in nematic-liquid-single-crystal elastomers by external mechanical stress

As has been shown recently by Kundler and Finkelmann, a sample of nematic-liquid-single-crystal elastomers subject to a mechanical stress perpendicular to the initial director orientation shows a reorientation of the director reminiscent of that observed in low-molecular-weight nematic liquid crystals in a magnetic field. Here we present a simple model, which captures all the essential features. We calculate the threshold stress and show that the director reorientation occurs over the entire sample. A weakly nonlinear analysis gives a forward bifurcation in agreement with the experimental results. We also discuss the origin of the domain walls in the director observed experimentally and give an expression for the thickness of these walls

Rheological properties of mono- and polydomain liquid crystalline elastomers exhibiting a broad smectic A phase

We investigate the rheological properties of polydomain smectic A Side-Chain Liquid Crystalline Elastomers (SCLCE) by dynamic shear and compression measurements and find a very similar behavior for both experiments. We show that the dynamic shear modulus G' is independent of a precompression applied to the sample. In addition, we present the first dynamic measurements of the anisotropy of G' observed for the corresponding Liquid Single Crystal Elastomers (LSCE). We find that these monodomains show dynamically a dramatic difference depending on whether the shear is in a plane parallel or perpendicular to the layer normal, demonstrating the in-plane fluidity of the smectic layering