An approximate solution to flow through a contraction for high Trouton ratio fluids

Pressure-drop and kinematics of viscoelastic flow through an axisymmetric contraction–expansion geometry with various contraction-ratios

“…(3) and (4), it is assumed that in the contraction zone, the fluid reduces its velocity such that the velocity profile for a shear thinning fluid is nearly parabolic, as suggested by Cable and Boger [7]. The velocity reduction is caused by a minimization of energy through an increment in the pressure drop and/or vortex generation, as reported by Binding [4] and Lubansky et al [15], where the effects of the first and second normal stress differences are considered negligible. In this work, such effects are measured and considered in the evaluation of the excess pressure drop.…”

The extrusion of a model yield stress fluid imaged by MRI velocimetry

“…The second model follows a more realistic depiction of viscoplastic materials, proposing that the material behaves as a viscoelastic solid until the yield stress limit is surpassed at which point it behaves as a non-Newtonian fluid. The elastic stress of the incompressible solid is thus computed incrementally using Hookean theory such that the elastic stress at time t for a small yet finite material volume is calculated aṡ (9) in which G is the shear modulus. Additionally, the elastic stress tensor and this material volume translate and rotate within the deforming material.…”

“…The works examining the extrusion of viscoelastic fluids have largely focused on the addition of a non-reactive powdery substances to transparent materials which, when photographed with long exposure times, produce streaklines [8,9] exposing the relevant flow paths. Another technique, known as Particle Image Velocimetry (PIV) [10], is an approach capable of revealing local velocity fields through the addition of reflective 'tracer' particles, unfortunately, slightly affecting the material properties, and the velocity is then carefully determined from successive images.…”

Transient flow behavior of complex fluids in microfluidic channels

“…Recent studies show that the length of a constriction has even impact on the upstream flow kinematics (Rodd et al 2010). Although detailed studies on a single-molecule level have proven to be powerful in addressing the effect of elongation on the polymer configuration (Perkins 1997;Smith 1998;Larson et al 1999;Squires and Quake 2005;Steinhauser et al 2012) and efforts are made in simulating and calculating the flows of complex fluids on different length scales (Feigl 1996;Doyle et al 1998;Xue et al 1998;Lindner et al 2003;Kröger 2004;Lubansky et al 2007;Castillo-Tejas et al 2009), microscopic explanations for the observable macroscopic flow effects remain challenging. To this end, detailed studies on the flow behavior of these fluids in benchmark geometries and its relation to microscopic mechanisms are essential.…”