Tube flow scaling laws

In a series of experiments on the flow of flocculated kaolin suspensions in laboratory and industrial scale pipelines(26-27-2Sl, measurements of pressure drop were made as a function of flowrate. Results were obtained using a laboratory capillary-tube viscometer, and pipelines of 42 mm and 205 mm diameter arranged in a recirculating loop. The rheology of all of the suspensions was described by the power-law model with a power law index less than unity, that is they were all shear-thinning. The behaviour in the laminar region can be described by the equation ... 

When trying to manipulate fluids on the micron scale, formidable problems have to be overcome [301], Miniature pumps, valves, switches, and new analytical tools have to be developed. To illustrate this we discuss the fundamental problem of transporting a liquid through a capillary tube. In the macroscopic world we would apply a pressure AP between the two ends. According to the law of Hagen-Poiseuille the volume of liquid V transported per time t is (assuming laminar flow)... 

We want to determine capillary flow dynamics m porous mcAa at Ae pore-scale. The Aeoretical basis of porosimetry is defined by Laplace s law which explained Aat Ae work reqmred to expand a non-wetting flmd surAce (mercury) of principal radii of curvature jRi and R2 is equal to the work done to Ae concave side of Ae surface. Washburn (1921) linked to Laplace s equation by using a c illary model where Ae porous meAum is assimilated to a bundle of cylindrical capillary tubes... 

A general scale-up equation for the laminar flow of a power-law fluid in cylindrical tubes may be written as... 

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