Nanochannel-Based Measurements of Apparent and Real Viscosity Effects

2 Nanochannel-Based Measurements of Apparent and Real Viscosity Effects  

4 The Flow of a Wetting Liquid along the Comers of a Noncircular Capillary 

If a cylindrical capillary is occupied by a wetting liquid and a gas, a thin film of the liquid is observed on the interior wall of the capillary in the regions occupied by the gas. In many cases of (micro-) capillaries, however, one has to deal with capillary cross sections that are noncircular, characteristic for underground porous media and microlabricated channels. A considerable amount of liquid flow occurs in these cases in the corner regions of the capillary tubes (see Fig. 11.15a). 

The problem of two-phase flow through noncircular ducts has received considerable attention in the last decades and was studied specifically by Ransohoff and Radke. They addressed the problem of the low Reynolds number wetting liquid flow in a noncircular capillary occupied predominantly by a nonwetting gas phase by presenting a solution in terms of a dimensionless flow resistance, fi, depending on corner geometry and fluid parameters. 

To understand the main steps of their approach, we consider the geometry depicted in Fig. 11.15b. 

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