The transient behavior of a leaky dielectric liquid drop under a uniform electric field of small strength is investigated. It is shown that for small distortion from a spherical shape, the drop deforms to an ellipsoid, and the deformation time history is represented by D=D(∞)[1-exp(-t/τ)], where D(∞) is the steady-state deformation and τ=(aμ(o)/γ)(19μ+16)(2μ+3)/(40μ+40)is the characteristic time, a, γ, μ(o) and μ being the drop radius, the surface tension, the viscosity of ambient fluid, and ratio of the drop viscosity to that of the ambient fluid, respectively. The contributions of the net normal and tangential electrical stresses in the degree of deformation and fluid flow strength are also determined.
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L – t1/2. Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric “off-centered PMS” and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
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