Pressure Flow of Two Immiscible Fluids with Different Viscosities

4 Pressure Flow of Two Immiscible Fluids with Different Viscosities 

Pressure flow of two immiscible fluids with different viscosities that flow as separate layers between parallel plates are often encountered inside dies during co-extrusion when producing multi-layer films. Such a system is schematically depicted in Fig. 6.16, which presents two layers of thickness h/2 and viscosities m and //,2, respectively. 

When solving this problem, we first assume that the melts are both Newtonian fluids and that there is no velocity component in the -direction. If we also assume that d/dx = 0, the continuity equation reduces to 

Furthermore, assuming negligible surface tension, we can assume that the stresses match at the melt-melt interface, y = h/2, 

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