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 0.1-100 μm. 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 μm diameter micro-capillary tubes, the flow rate and the pressure loss were measured for silicon oil of 2.6 × 10^-6 to 4.3 × 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 μm and kinematic viscosity of 4.3 × 10 ^-4 m²/s. The measured values are in agreement with the theoretical values calculated by the Navier-Stokes equations.