Flow characteristics of liquid with pressure-dependent viscosities in microtubes

It is obvious that the pressure gradient along the axial direction in a pipe flow keeps constant according to the Hagen-Poiseuille equation. However, recent experiments indicated that the distribution of the pressure seemed no longer linear for liquid flows in microtubes driven by high pressure (1-30MPa). Based on H-P equation with slip boundary condition and Bridgman’s relation of viscosity vs. static pressure, the nonlinear distribution of pressure along the axial direction is analyzed in this paper. The revised standard Poiseuille number with the effect of pressure-dependent viscosity taken into account agrees well with the experimental results. Therefore, the dependence of the viscosity on the pressure is one of the dominating factors under high driven pressure, and is represented by an important property coefficient α of the liquid.