Electrohydrodynamic convection in the nematic liquid crystal MBBA in the presence of a competing magnetic field produces disclination loops in the two dynamic scattering states DSM 1 and DSM 2. The convection and magnetic field bias this initial state so that the subsequent decay of the disclination loops does not obey dynamic scaling. We experimentally confirm this breakdown of dynamic scaling. [S0031-9007(97)04577-8] PACS numbers: 61.30.Gd, 47.65. + a, 61.30.Jf, 64.60.HtSystems quenched from a disordered to an ordered state often evolve patterns of some characteristic size as they return to equilibrium. The challenge is to describe the temporal evolution of these patterns, which can often be described by a scaling relation. The best known example of such a transition is phase separation in binary mixtures undergoing spinodal decomposition in which domains grow with a power law dependence. In this example the system has discrete symmetry and a conserved order parameter. More recently, attention has focused on systems with continuous symmetry and nonconserved order parameters in which line defects (strings or disclinations) form as a result of the quench. Such systems have been studied theoretically [1-4], numerically [5], and with computer simulations [6] which predict that the defect density scales as t 2f , where the exponent depends on details of the order parameter and the spatial dimensionality. Experimental realizations include liquid crystals undergoing a pressure quench [7-10] from the isotropic to nematic phase and coarsening of domains in twisted nematic films [11,12] under temperature quenches in which defect density exhibits the predicted dynamic scaling.Recent theoretical work [13] and computer simulations [14] have considered the evolution of defects resulting from a quench in which the disordered state is biased by some field which favors a particular state in the ordered phase. The bias causes the system's evolution to no longer be described by a simple power law. The length of the defects is instead predicted to behave as l͑t͒ ϳ ͑t͒ 2f exp͓2g͑t͒ d ͔, where the exponent f depends on the nature of the order parameter and d depends on the spatial dimensionality. The decay constant g is a nontrivial function of the bias field such that power law behavior is recovered when the bias is removed. An experiment [15] involving the relaxation of biased twist regions in nematic liquid crystals showed agreement with the functional form of the above equation but no values for exponents were reported.In this Letter, we report on an experimental study of the decay of disclination loops formed by a nematic liquid crystal undergoing electrohydrodynamic convection [16] with the convecting flow field acting as the bias field. These disclination loops, which are topological defects whose circumference is a disclination line that separates regions of opposite twist, do not obey dynamic scaling as they decay, in contrast to loops formed by pressure or temperature quenches from the isotropic to the nematic phase.These ...
The sedimentation dynamics of extremely low polydispersity, non-colloidal, particles are studied in a liquid fluidized bed at low Reynolds number, Re 1. When fluidized, the system reaches a steady state, defined where the local average volume fraction does not vary in time. In the steady state, the velocity fluctuations and the particle concentrations are found to strongly depend on height in the particle column. Using our results, we test a recently developed stability model (Segrè 2002 Phys. Rev. Lett. 89 254503) for steady state sedimentation. The model describes the data well, and shows that in the steady state there is a balancing of particle fluxes due to the fluctuations and the concentration gradient. Some results are also presented for the dependence of the concentration gradient in fluidized beds on particle size; the gradients become smaller as the particles become larger and fewer in number.
Many fluids appear white because refractive index differences lead to multiple scattering. In this paper, we use safe, low-cost commercial index matching fluids to quantitatively study light transmission as a function of index mismatch, reduce multiple scattering to allow single scattering probes, and to precisely determine the index of refraction of suspended material. The transmission profile is compared with Rayleigh-Gans and Mie theory predictions. The procedure is accessible as a student laboratory project, while providing advantages over other standard methods of measuring the refractive index of an unknown nanoparticle, making it valuable to researchers.
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