RESEARCH ARTICLE Micro-scale and millimeter-scale rotating disk couette flows, experiments and analysis Danny Blanchard Æ Phillip M. Ligrani Received: 28 May 2006 / Revised: 12 September 2006 / Accepted: 14 September 2006 / Published online: 10 October 2006 Ó Springer-Verlag 2006 Abstract Experimental results are presented for rotating Couette flows with and without circumferen- tial pressure gradients between a rotating disk and a stationary fluid chamber. The spinning disk and the top of the C-shaped fluid chamber are separated by a l- scale gap that forms the fluid chamber passage with inner and outer radii of 1.19 and 2.38 mm, respectively. Ranges of experimental conditions are presented to demonstrate the fluid dynamics of the test arrange- ment, and for determination of fluid viscosity, and gas slip flow accommodation coefficients. As such, the test arrangement provides means to determine such fluid and flow properties using microliter sample sizes, with relatively low magnitudes of experimental uncertainty. List of symbols h gap height of the fluid chamber Kn Knudsen number p 1 static pressure at pressure port 1 p 2 static pressure at pressure port 2 P* normalized pressure rise, DP measured / DP max DP 2–1 pressure rise between pressure ports (p 2 – p 1 ) DP max maximum pressure rise, Eqn. (3) DP measured measured pressure rise between pressure ports (p 2 – p 1 ) Q volumetric flow rate Q* normalized volumetric flow rate, Q measured /Q max Q max maximum volumetric flow rate, Eq. 2 Q measured measured volumetric flow rate r radial location R 1 inner radius of the fluid chamber R 2 outer radius of the fluid chamber Re Reynolds number v s slip velocity v h fluid velocity in the circumferential direction z direction normal to disk surface Greek symbols b v slip parameter, 2r v r v h circumferential angle D h circumferential angle between pressure ports k molecular mean free path l absolute viscosity q fluid density r v tangential momentum accommodation coefficient x angular velocity of the spinning disk W dimensional rotational speed 1 Introduction Couette flow, or shear flow between surfaces in relative motion, and Poiseuille flow or pressure driven flow, are D. Blanchard Convective Heat Transfer Laboratory, Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112-9208, USA P. M. Ligrani (&) Department of Engineering Science, Oxford University, Parks Road, Oxford OX1 3PJ, England, UK e-mail: phil.ligrani@eng.ox.ac.uk Exp Fluids (2006) 41:893–903 DOI 10.1007/s00348-006-0208-8 123