Electrically driven convection in a thin annular film undergoing circular Couette flow

We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio $\alpha$ and Reynolds number ${{\cal R} e}$ of the shear flow, and obtain the critical control parameter ${\cal R}_c (\alpha, {{\cal R} e})$ and the critical azimuthal mode number ${m_c (\alpha, {{\cal R} e})}$. The Couette flow suppresses the onset of electroconvection, so that ${\cal R}_c (\alpha, {{\cal R} e}) > {\cal R}_c (\alpha,0)$. The calculated suppression is compared with experiments performed at $\alpha = 0.56$ and $0 \leq {{\cal R} e} \leq 0.22$.Comment: 17 pages, 2 column with 9 included eps figures. See also http://mobydick.physics.utoronto.c

Case report on peripartum cardiomyopathy in a patient with Schmidt syndrome with twin pregnancy for emergency lower segment cesarean section

Peripartum and autoimmune cardiomyopathy is an uncommon rare disorder associated with pregnancy. When it occurs association with autoimmune thyroid disorder and autoimmune adrenal insufficiency, it is eponymously referred to as Schmidt syndrome or autoimmune polyendocrine syndrome type 2 (APS type 2). Peripartum cardiomyopathy (PPCM) can be difficult to diagnose as the symptoms can be masked or misinterpreted due to the normal physiological changes during pregnancy, as the symptoms of heart failure can mimic those of pregnancy. PPCM is associated with considerable morbidity and mortality and so should not be underestimated. In this report, we are discussing the management of 32-years-old female with hypothyroidism and Addison’s disease (polyglandular syndrome type 2- Schmidt syndrome) who came for emergency lower segment cesarean section (LSCS) due to twin pregnancy (abnormal doppler of the second twin) and during the period developed pulmonary edema and was diagnosed as peripartum cardiomyopathy.

Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film

It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very simple convection pattern and exhibit a variety of interesting nonlinear effects. The linear stability problem for this system has recently been solved. The convection mechanism, which involves charge separation at the free surfaces of the film, is applicable to any sufficiently two-dimensional fluid. In this paper, we derive an amplitude equation which describes the weakly nonlinear regime, by starting from the basic electrohydrodynamic equations. This regime has been the subject of several recent experimental studies. The lowest order amplitude equation we derive is of the Ginzburg-Landau form, and describes a forward bifurcation as is observed experimentally. The coefficients of the amplitude equation are calculated and compared with the values independently deduced from the linear stability calculation.Comment: 26 pages, 2 included eps figures, submitted to Phys Rev E. For more information, see http://mobydick.physics.utoronto.c

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Bifurcations in annular electroconvection with an imposed shear

We report an experimental study of the primary bifurcation in electrically-driven convection in a freely suspended film. A weakly conducting, submicron thick smectic liquid crystal film was supported by concentric circular electrodes. It electroconvected when a sufficiently large voltage $V$ was applied between its inner and outer edges. The film could sustain rapid flows and yet remain strictly two-dimensional. By rotation of the inner electrode, a circular Couette shear could be independently imposed. The control parameters were a dimensionless number ${\cal R}$, analogous to the Rayleigh number, which is $\propto V^2$ and the Reynolds number ${\cal R}e$ of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio $\alpha$, and a Prandtl-like number ${\cal P}$. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of $\alpha$, ${\cal P}$ and ${\cal R}e$. We compared this data quantitatively to the results of linear stability theory. This could be done with essentially no adjustable parameters. The current-voltage data above onset were then used to infer the amplitude of electroconvection in the weakly nonlinear regime by fitting them to a steady-state amplitude equation of the Landau form. We show how the primary bifurcation can be tuned between supercritical and subcritical by changing $\alpha$ and ${\cal R}e$.Comment: 17 pages, 12 figures. Submitted to Phys. Rev. E. Minor changes after refereeing. See also http://mobydick.physics.utoronto.c

3D Topological Semimetal Phases of Strained α\alpha-Sn on Insulating Substrate

$\alpha$-Sn is an elemental topological material, whose topological phases can be tuned by strain and magnetic field. Such tunability offers a substantial potential for topological electronics. However, InSb substrates, commonly used to stabilize $\alpha$-Sn allotrope, suffer from parallel conduction, restricting transport investigations and potential applications. Here, the successful MBE growth of high-quality $\alpha$-Sn layers on insulating, hybrid CdTe/GaAs(001) substrates, with bulk electron mobility approaching 20000 cm$^2$V$^{-1}$s$^{-1}$ is reported. The electronic properties of the samples are systematically investigated by independent complementary techniques, enabling thorough characterization of the 3D Dirac (DSM) and Weyl (WSM) semimetal phases induced by the strains and magnetic field, respectively. Magneto-optical experiments, corroborated with band structure modeling, provide an exhaustive description of the bulk states in the DSM phase. The modeled electronic structure is directly observed in angle-resolved photoemission spectroscopy, which reveals linearly dispersing bands near the Fermi level. The first detailed study of negative longitudinal magnetoresistance relates this effect to the chiral anomaly and, consequently, to the presence of WSM. Observation of the $\pi$ Berry phase in Shubnikov-de Haas oscillations agrees with the topologically non-trivial nature of the investigated samples. Our findings establish $\alpha$-Sn as an attractive topological material for exploring relativistic physics and future applications.Comment: Main text: 35 pages, 7 figures; Supplementary Materials: 22 pages, 12 figure