Biomedical subjects

V B Deyirmenjian

Publications and source records attributed to V B Deyirmenjian.

3 recordsLinked to original sources

PubMed2005

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 alpha quantifies the film's geometry while a dimensionless number P , similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed alpha, g is a decreasing function of P , as P becomes smaller, and is nearly constant for P> or =1 . As P-->0, g-->infinity. We find that g is a nontrivial and discontinuous function of alpha. We show that the discontinuities occur at codimension-two points that are accessed by varying alpha.

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PubMed2002

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 R and a shear Reynolds number Re. The pattern is an azimuthally periodic array of traveling vortices with integer mode number m. Varying R and Re permits the passage through several codimension-two (CoD2) points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the CoD2 points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which m-->m+1 when R is increased at constant Re.

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PubMed2001

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 R, analogous to the Rayleigh number, which is ~V2 and the Reynolds number Re of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio alpha, and a dimensionless number P, analogous to the Prandtl number. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of alpha, P, and Re. 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 Re.

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