The Flow of Liquids in Micro-Capillary Tubes. Consideration to Application of the Navier-Stokes Equations.

Abstract

Designing the micro-fluid machines as micro-pumps and micro-valves requires the clarification of fluid dynamics on the order of 0.1-100m. This paper describes the flow of liquids in micro-capillary tubes and a method of measuring it. The method can precisely measure flow rates as small as 10 pl/s to 10 nl/s. The estimated measurement error of the method is less than 6 percent for flow rate, and less than 4 kPa for pressure loss. In 4.5 to 50.5 m diameter micro-capillary tubes,the flow rate and the pressure loss were measured for silicon oil of 2.6 x 10-6 to 4.3 x 10-4 m2/s kinematic viscosity. The measurement results showed that the flow rate is proportional to the pressure loss for a diameter of 11.2 pm and kinematic viscosity of 4.3 x 10-4 m2/s. The measured values are in agreement with the theoretical values calculated by the Navier-Stokes equations.