Newtonian fluid flow through Microfabricated Hyperbolic

Contractions

Mónica S. Neves Oliveira^{1, 2}, Manuel A. Alves¹,

Fernando T. Pinho^{3, 4}, Gareth H. McKinley²

1: Departamento de Engenharia Química, CEFT, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, monica.oliveira@fe.up.pt, mmalves@fe.up.pt

2: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA 02139, USA, gareth@mit.edu

3: CEFT, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, fpinho@fe.up.pt

4: Universidade do Minho, Braga, Portugal, fpinho@dem.uminho.pt

Abstract

We study the flow of a Newtonian fluid through microfabricated hyperbolic contractions in detail. A set of planar converging geometries, with total Hencky strains ranging from 1 to 3.7, have been fabricated in order to produce a homogeneous extensional flow field within the contraction. The kinematics in the contraction region are investigated experimentally by means of micro particle image velocimetry (µPIV). Using this laser based technique, we are able to characterize quantitatively the velocity field at a given plane in the hyperbolic contraction region. The pressure drop across the converging geometry was also measured and was found to vary approximately linearly with the flow rate. Additionally, an extensive range of numerical calculations was carried out using a finite-volume method. The experimental results of velocity fields in the contraction and associated pressure drops compare very well with those predicted numerically. For the typical dimensions used in microfluidics, the flow is shown to be three-dimensional. Furthermore, we demonstrate that regions with nearly constant strain rate can only be achieved using geometries with large total Hencky strains under Hele-Shaw (potential-like) flow conditions.