Journal of Biomechanics 38 (2005) 159–167 Short communication Dynamic shear stress in parallel-plate flow chambers Rommel G. Bacabac a, *, Theo H. Smit b , Stephen C. Cowin c , Jack J.W.A. Van Loon a,e , Frans T.M. Nieuwstadt d , Rob Heethaar b , Jenneke Klein-Nulend a a Department of Oral Cell Biology, Academic Centre for Dentistry Amsterdam-Vrije Universiteit, Van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands b Department of Physics and Medical Technology, Vrije Universiteit Medical Center, Amsterdam, The Netherlands c Departments of Biomedical and Mechanical Engineering, The City College of New York, New York, NY, USA d J.M. Burgers Centre, Delft University of Technology, Delft, The Netherlands e Dutch Experiment Support Center, Vrije Universiteit, Amsterdam, The Netherlands Accepted 24 March 2004 Abstract An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h=l v ; in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled bya shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h=l v o2; where h is the distance between the plates and l v is the viscous penetration depth; and (2) f 0 of c =m; where the critical frequency f c is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f 0 is the fundamental frequency of fluid flow. r 2004 Elsevier Ltd. All rights reserved. Keywords: Fluid flow; Dynamic shear stress; Parallel-plate flow chamber; Cells; Dynamic loading 1. Introduction The parallel-plate flow chamber (PPFC) is used for flow stimulation of various cell types, e.g., bone cells and endothelial cells (Brown, 2000). A cell monolayer attached to one of the internal plate surfaces is subjected to fluid flow by creating a pressure gradient along the chamber. To calculate the resulting shear stress on the cells, the mathematical model assumes a Newtonian fluid in which the shear tensor is proportional to the deformation tensor. For steady flow between infinitely wide parallel plates, wall shear stress t w is calculated as a function of the measured flow Q: t w ¼ 6mQ bh 2 ð1Þ with m ¼ fluid viscosity, b ¼ width of the chamber, h ¼ distance between plates. For finite chamber dimensions (finite b=h), the fluid velocity profile remains parabolic between the plates, but vanishes at the boundaries of the rectangular channel (Fig. 1a,b, Belansky and Wanser, 1993; Booij et al., 1995). The shear stress profile, calculated from the velocity gradient, has maximum magnitudes at the plate surfaces and vanishes at the corners of the channel (Fig. 1c). Less than 1% difference from a full parabolic velocity profile occurs after an entry length L entry ¼ 0:04 h Re (Schlichting, 1968; Reynolds number Re ¼ Qr=ðmbÞ). Practically, more than 85% of the surface is exposed to a homogenous wall shear stress for b=h > 20: ARTICLE IN PRESS *Corresponding author. Tel.: +31-(0)-20-444-8687; fax: +31-(0)-20-444-8683. E-mail address: rg.bacabac.ocb.acta@med.vu.nl (R.G. Bacabac). 0021-9290/$-see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2004.03.020