Capillary rheometer Poiseuille flow

The capillary viscometer. The most common and simplest device for measuring viscosity is the capillary viscometer. Its main component is a straight tube or capillary, and it was first used to measure the viscosity of water by Hagen [28] and Poiseuille [60], A capillary rheometer has a pressure driven flow for which the velocity gradient or strain rate and also the shear rate will be maximum at the wall and zero at the center of the flow, making it a non-homogeneous flow. 

One of the most widely used rheometer configurations is a simple variant of the capillary flow viscometer. In this device, a concentrated polymer solution or melt undergoes Poiseuille flow in a narrow capillary, length L and internal radius R, under the action of an external pressure P. The capillary exit is typically open to the atmosphere, such that a pressure difference Ap = P - produces the driving force that leads to fluid flow (Figure 8.3). If the volumetric flow rate of fluid through the capillary Q is known (measured), Poiseuille s equation can be used to determine the fluid s viscosity if the fluid is Newtonian. 

Capillary Flow Rheometry Next we examine the experimentally obtained results with the capillary flow rheometer shown in Fig. 3.1, which are directly relevant to polymer processing flows, since the attainable shear rate values are in the range encountered in polymer processing. The required pressure drop AP does not increase linearly with increases in the volumetric flow rate Q, as is the case with Newtonian fluids. Rather, increasingly smaller increments of AP are needed for the same increases in Q. The Newtonian Poiseuille equation, relating flow rate to pressure drop in a tube, is linear and given by... 

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