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Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis
patt-sol · Submitted 5 Jul 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. | background 1.00 | 0.11 | 0.17 | asserted 1.00 |
| s1 | We present a linear stability analysis for this system. | contribution 0.82 | 0.94 | 0.03 | asserted 0.93 |
| s2 | The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. | background 0.80 | 0.19 | 0.08 | asserted 1.00 |
| s3 | 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. | method 0.69 | 0.48 | 0.05 | asserted 1.00 |
| s4 | We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. | result 0.67 | 0.96 | 0.15 | asserted 1.00 |
| s5 | ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. | interpretation 0.63 | 0.62 | 0.07 | asserted 1.00 |
| s6 | 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 ${\xi_0}$. | result 0.65 | 0.95 | 0.17 | asserted 1.00 |
| s7 | 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. | result 0.79 | 0.93 | 0.08 | asserted 1.00 |
| s8 | ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. | interpretation 0.61 | 0.78 | 0.16 | asserted 1.00 |
| s9 | We compare our results to recent experiments. | contribution 0.70 | 0.86 | 0.04 | asserted 0.76 |
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The paper
Original abstract
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.
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