Some exact solutions of problems of laminar jets of immiscible fluids

Burde, Georgy I.

doi:10.1007/bf00853488

Cited by 2 publications

(2 citation statements)

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“…14 In the present study we investigate yet another class of laminar boundary-layer flows referred to as two-fluid jets and wakes. Like the problems 13,14 described above, these are not locally driven flows; rather, they owe their existence to a source ͑jet͒ or a sink ͑wake͒ of momentum upstream of the spatially developing flow. In the quiescent state, the two immiscible fluids are separated by a horizontal flat interface, with the heavier fluid residing below the lighter fluid to ensure hydrostatic stability.…”

Section: Introductionmentioning

confidence: 97%

“…This problem has attracted the interest of many researchers because of its practical importance, particularly when gravitational effects are included. Here we only cite the work of Burde, 13 who, with gravity excluded, found an explicit boundary layer solution for penetrating free jet flow in the special case ϭ1 with the aid of von Mises variables. This restricted case was further exploited to determine analytical boundary-layer solutions for the wall jet and a weakly swirling free fan jet of fluid 1, in each case penetrating into the quiescent domain of immiscible fluid 2.…”

Section: Introductionmentioning

confidence: 99%

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Two-fluid jets and wakes

2004

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Similarity solutions for laminar two-fluid jets and wakes are derived in the boundary-layer approximation. Planar and axisymmetric fan jets as well as classical and momentumless planar wakes are considered. The interface between the immiscible fluids is stabilized by the action of gravity, with the heavier fluid, taken to be a liquid, placed beneath the lighter fluid. Velocity profiles for the jets and the classical wake depend intimately, but differently, on the parameter ϭ 1 1 / 2 2 , where i and i are, respectively, the density and absolute viscosity of the fluid in the upper (iϭ1) and lower (iϭ2) fluid domains, while the momentumless wake profile depends on the parameter ⍀ϭ 1 2 3 / 2 1 3. Generally, all interfaces deflect from horizontal except the fan jet. However, while the interface for the classical planar two-fluid wake is never flat, the interfaces for the planar jet and the momentumless wake become flat in the particular case 1 ϭ 2. Velocity profiles illustrating the strongly asymmetrical jet and wake profiles that arise in air-over-water, oil-over-water, and air-over-oil flows are presented.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%