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 $Nu \sim F(\Gamma) {\cal R}^{\gamma} {\cal P}^{\delta}$. ${\cal R}$ and ${\cal P}$ are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function $F(\Gamma)$, which is specified by the model, describes the dependence of $Nu$ on the aspect ratio $\Gamma$. We find that measurements of $Nu$ are consistent with the theoretical model.Comment: 12 pages, 7 figures, Submitted to Phys. Rev. E. See also http://www.physics.utoronto.ca/nonlinea

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

Affinity resin screening for optimal DSP – application to rotavirus vaccine production.

A crucial step in the down-stream processing (DSP) of recombinant vaccine production is the correct choice of affinity chromatography resins for product purification. All too often vaccine DSP protocols are based on methodologies that worked to allow development of candidate products to proof of concept and clinical trial rather than being optimized for efficiency and cost. This “what worked” approach often leads to increased production costs. Our aim here, as part of a Bill and Melinda Gates funded ULTRA project, is a more systematic approach to resin choice and DSP development that will enable low cost of goods of 15cents/dose or less. Ideally, this approach should be incorporated into the early stages of vaccine development. To achieve this we have implemented a resin screening protocol based on the use of 96 well filter plates where each well contains chromatography resins. This approach allows for the rapid screening of large numbers of potential affinity resins and bind/elute conditions. It has the advantage that it can be operated either fully automated (using TECAN robotic platforms) or manually using relatively simple laboratory equipment. It is therefore quite feasible to incorporate such an approach into DSP development irrespective of whether development is being carried out in a well-funded or resource-limited environment. This approach allows for a saving of many months in process development time along with significant savings in resources compared to a conventional resin and bind/elute condition screening using individual columns. We have applied this approach to the screening of affinity chromatography resins for DSP of two non-replicative rotavirus (NRRV) vaccines. Bind/elute characteristics are determined by monitoring OD280nm for total protein levels, OD260nm for nucleic acid levels and specific product levels by antibody detection and finally SDS-PAGE. We have screened 19 potential resins for use in hydrophobic interaction (HIC), cation exchange (CIEX) and multimodal (MM) chromatography. Initial rounds of screening allowed exclusion of four HIC resins as completely unsuitable. Bind/elute conditions were further investigated for the remaining resins leading to the choice of optimal resin-bind-elution combination for each affinity class. These were scaled up to for use in column chromatography. Using the data from the 96 well plate studies it proved possible to predict DSP protocols that can be used in NRRV purification by HIC, CIEX or MM chromatograph. These results further demonstrate which of these can potentially be incorporated into an integrated production process

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

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