Rates and Patterns of Capillary Flow

Although it is important to analyze a capillary system with respect to the various factors affecting Pcap in order to understand liquid flow patterns, the effects of various fluid dynamic effects must also be kept in mind. While a thorough discussion of the topic is beyond the scope of this work, it may be useful to introduce a few simple ideas that can be applied in many situations. 

When one considers the smooth, uniform (laminar) flow of a fluid in a narrow cylindrical tube, which is the classical model of a capillary, one can employ PoiseuiUe s equation to relate the volume rate of flow to various characteristics of the fluid and capillary system. The volume rate of flow, dv/ dt (mL s ) is given by 

In practice, unfortunately, most capillary systems do not involve nicely uniform cylindrical tubes, so the preceding analysis will not apply in a quantitative way. In not overly complicated systems, reasonable, and useful results can be obtained if r is replaced by a so-called hydraulic radius given by the volume of the liquid in the capillary section being considered, V, divided by the solid-liquid interfacial area. A, in the same section. In systems of still higher complexity calculation of a hypothetical value for r, or of a resistance 

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