The purpose of this research is to study the instability of a slightly conducting fluid layer with adverse temperature gradient under a vertical electric field.
A gradient in electric conductivity resulting from the temperature gradient causes free charges to accumulate in the fluid when the electric field is applied, and the interaction of the charges with the electric field creates a destabilizing electric force in the bulk of the fluid.
Taking into account the viscosity and thermal diffusivity of the fluid, the threshold conditions for the instability are predicted using linearized hydrodynamic stability theory.
The marginal stability curves are drawn in the plane of dimensionless electric force VS. dimensionless wave number. The stability domains are also drawn for the bounding surfaces are both free, and both rigid. It is proved, in the stability problem, that the principle of exchange of stability does not hold.
It is shown that the fluid becomes more unstable for larger relaxation times, and more stable for larger Prandtl numbers.
And it is also shown that the angular frequency of the disturbance increases monotonically as the dimensionless wave number increases.
Using Mazola corn oil as a test fluid, the threshold values for instability determined by Schlieren optical device are in good agreement with the theoretical results.
본연구는 저전도성 유체층의 역온도구배하에서 $R_c$보다 적은 R값에 대해서 수직 d-c 전장에 의한 불안정을 연구하는 것이다. 온도구배에 의해서 유기되는 전기전도도의 구배는 저전도성유체에 전장을 가할때 유체내에 진전하를 축적시킬 수 있고, 전장하에서 전하들의 상호작용으로 유체내에 불안정을 일으키는 전기적 체적력을 발생시킨다.
유체의 점성과 열확산을 고려하고, 불안정의 임계조건은 선형안정 이론을 이용하여 기술하였다.
불안정은 항상 overstability로 나타남을 보였으며, relaxation time이 클수록 유체는 불안정한 경향을 나타내고, prandtl number가 커질수록 안정화하려는 경향을 보인다. 또한 angular frequency ($w_i$)는 무차원파수의 증가에 따라 monotonic하게 증가함을 나타내었다.
시험유체로 Mazola corn oil을 사용하고, schlieren광학장치에 의한 임계값 측정결과는 이론의 타당성을 보인다.
