SoluÃÃes exatas para arranjos periÃdicos de bolhas na cÃlula de Helen-Shaw

AUTOR(ES)

AntÃnio MÃrcio Pereira Silva

DATA DE PUBLICAÇÃO

2008

RESUMO

In this thesis exact solutions for the problem of multiple bubbles in a Hele-Shaw cell are presented for the case when surface tension effects are neglected. The solutions reported here describe a doubly-periodic array of bubbles that move with constant velocity in the x direction. In a reference frame that moves with the bubbles, the bubble centroids are located in a rectangular grid whose unit cell has width 2a and length 2L, and there can be any number N of bubbles per unit cell. The solutions described in the present work represent the most general family of solutions for the steady motion of bubbles in a Hele-Shaw cell in the sense that all previously known solutions for steady bubbles are particular cases of our generic solution. The solution is obtained via conformal mapping techniques, where we compute the appropriate mapping function from the upper half-plane of the auxiliary ζ plane onto the physical domain occupied by the fluid in the unit cell (the z plane). In its most general form, the solution is valid for an infinite Hele-Shaw cell, but of particular interest are the cases where we have a periodic array of bubbles in a Hele-Shaw channel. An analytical expression for the bubble velocity as a function of the volume fraction occupied by the bubbles is also obtained

ASSUNTO(S)

hele-shaw cell cÃlula de hele-shaw dinÃmica de interfaces mecanica dos fluidos fluid mechanics mecÃnica dos fluidos interface dynamics

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