arXiv subjects

Zahir A. Daya

Publications and source records attributed to Zahir A. Daya.

10 recordsLinked to original sources

arXiv2008

Localized states in sheared electroconvection

Electroconvection in a thin, sheared fluid film displays a rich sequence of bifurcations between different flow states as the driving voltage is increased. We present a numerical study of an annular film in which a radial potential difference acts on induced surface charges to drive convection. The film is also sheared by independently rotating the inner edge of the annulus. This simulation models laboratory experiments on electroconvection in sheared smectic liquid crystal films. The applied shear competes with the electrical forces, resulting in oscillatory and strongly subcritical bifurcations between localized vortex states close to onset. At higher forcing, the flow becomes chaotic via a Ruelle-Takens-Newhouse scenario. The simulation allows flow visualization not available in the physical experiments, and sheds light on previously observed transitions in the current-voltage characteristics of electroconvecting smectic films.

nlin.PS↗

arXiv2005

Charge Transport Scalings in Turbulent Electroconvection

We describe a local-power law scaling theory for the mean dimensionless electric current $Nu$ in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron thick liquid crystal film supported in the annulus between concentric circular electrodes. It is driven into electroconvection by an applied voltage between its inner and outer edges. At sufficiently large voltage differences, the flow is unsteady and electric charge is turbulently transported between the electrodes. Our theoretical development, which closely parallels the Grossmann-Lohse model for turbulent thermal convection, predicts the local-power law $Nu \sim F(Γ) {\cal R}^γ {\cal P}^δ$. ${\cal R}$ and ${\cal P}$ are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function $F(Γ)$, which is specified by the model, describes the dependence of $Nu$ on the aspect ratio $Γ$. We find that measurements of $Nu$ are consistent with the theoretical model.

physics.flu-dyn↗

arXiv2004

Codimension-two points in annular electroconvection as a function of aspect ratio

We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting, submicron thick liquid crystal film suspended between concentric circular electrodes and driven by an applied voltage between its inner and outer edges. We explicitly calculate the coefficient $g$ of the leading cubic nonlinearity and systematically study its dependence on the system's geometrical and material parameters. The radius ratio $α$ quantifies the film's geometry while a dimensionless group ${\cal P}$, similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed $α$, $g$ is a decreasing function of ${\cal P}$, as ${\cal P}$ becomes smaller, and is nearly constant for ${\cal P} \gtrsim 1$. As ${\cal P} \to 0$, $g \to \infty$. We find that $g$ is a nontrivial and discontinuous function of $α$. We show that the discontinuities occur at codimension-two points that are accessed by varying $α$.

nlin.PS↗

arXiv2003

Aspect ratio dependence of charge transport in turbulent electroconvection

We present measurements of the normalized charge transport or Nusselt number $\rm Nu$ as a function of the aspect ratio $Γ$ for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-B{é}nard convection, we develop the relevant theoretical framework in which we discuss the local-power-law-scaling of $\rm Nu$ with a dimensionless electrical forcing parameter $\cal R$. For these experiments where $10^4 \lesssim {\cal R} \lesssim 2 \times 10^5$ we find that ${\rm Nu} \sim {\rm F}(Γ){\cal R}^γ$ with $γ$ either $ = 0.26 (\pm 0.02)$ or $0.20 (\pm 0.03)$, in excellent agreement with the theoretical predictions of $γ= 1/4$ and 1/5. Our measurements of the aspect ratio-dependence of ${\rm Nu}$ for $0.3 \leq Γ\leq 17$ compares favorably with the function ${\rm F}(Γ)$ from the scaling theory.

cond-mat↗

arXiv2001

Sequential Bifurcations in Sheared Annular Electroconvection

A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number ${\cal R}$ and a shear Reynolds number ${\rm Re}$. The pattern is an azimuthally periodic array of traveling vortices with integer mode number $m$. Varying ${\cal R}$ and ${\rm Re}$ permits the passage through several codimension-two points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the codimension-two points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which $m \to m+1$ when ${\cal R}$ is increased at constant ${\rm Re}$.

nlin.PS↗

arXiv2001

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 $α$, 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 $α$, ${\cal P}$ 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 $α$ and ${\cal R}e$.

nlin.PS↗

arXiv2000

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 $α$ and Reynolds number ${{\cal R} e}$ of the shear flow, and obtain the critical control parameter ${\cal R}_c (α, {{\cal R} e})$ and the critical azimuthal mode number ${m_c (α, {{\cal R} e})}$. The Couette flow suppresses the onset of electroconvection, so that ${\cal R}_c (α, {{\cal R} e}) > {\cal R}_c (α,0)$. The calculated suppression is compared with experiments performed at $α= 0.56 $ and $0 \leq {{\cal R} e} \leq 0.22 $.

patt-sol↗

arXiv1997

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 $η\sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.

patt-sol↗

arXiv1997

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.

patt-sol↗

arXiv1996

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 Bénard 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 $κ$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${κ_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${ξ_0}$. The characteristic time scale ${τ_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${ξ_0}$ and ${τ_0}$ 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.

patt-sol↗