A simple capillary viscometer based on the ideal gas law

Abstract

We report a simple, inexpensive and user-friendly capillary viscometer based on the measurement of pressure drop in capillary tubing using the principle of ideal gas law. Viscosity is an important physical property of a fluid that provides molecular information of the fluid's behavior under flow conditions. Measuring viscosity, however, generally requires relatively large fluid volume samples and is expensive with commercial viscometers. Microfluidic viscometers at different levels of complexity can measure fluids at different flow rates with a small sample volume but the cost of commercially available microfluidic viscometers is still high. The reported capillary viscometer is cost-effective, uses small amounts of sample fluid and can measure viscosity under various shear rates. According to the Hagen–Poiseuille equation, the pressure drop of laminar flows in a capillary at a given flow rate is proportional to the viscosity of the fluid. When an enclosed air volume is connected to the upstream of the capillary, the pressure drop can be calculated with the change of the connected air volume, which is reflected by the displacement change of the air–liquid interface in the connecting capillary to the enclosed air volume. Based on these principles, the viscometer was assembled with readily accessible materials, and required no internal sensors or extensive programming. Measurements were successfully performed for five liquids including water, acetone, 2% fat milk, glycerin 30% and glycerin 40%. Except for acetone, the difference between measured and known viscosity was within 4% and highly consistent, well within the 13% uncertainty errors of readily accessible laboratory materials. Overall, the simple viscometer was easily assembled with low cost materials, was portable and accurate, and provided an alternative to expensive commercial viscometers. Finally, the simple capillary viscometer was a good outreach project for K-12 students to understand fluid behavior.