Experimental study of the flow of a yield stress fluid in a 4:1 planar contraction

The flow of viscoplastic fluids is often encountered in several industrial sectors, such as food pumping, polymer formatting processes, and others. Understanding their behavior and flow in different geometries is of major importance. The rheological characterization of these fluids is complex due to their intrinsic characteristics, notably the slip effect, as well as the inert unyieldedzones that form at the corners of the contraction when flowing through a rectangular pipe with an abrupt contraction. The main objective of this study is to analyze, firstly, the rheological behavior of Carbopol solutions using laser Doppler velocimetry (LDV) as a non-intrusive, in-situ method. By measuring velocity profiles and associated pressure drops, the analysis of flow curves will enable us to characterize the rheology of the fluids studied. Two approaches are used. The first involves fitting the analytical profile to the experimental profile obtained by laser Doppler velocimetry (LDV), while the second involves converting local velocity profiles into local shear rate profiles, and pressure drops into local shear stress profiles.The flow of this fluid in the rectangular channel was analyzed using LDV, taking into account the associated head losses. Velocity profiles revealed the presence of a moving zone at constant velocity, called 'plug', in the center of the channel, as well as the formation of inert dead zones at the corners of the contraction. The impact of contraction and inertia on flow structure was examined first, highlighting the influence of both factors. The interface between the static dead zone and the fluid zone was identified and characterized for various flow rates. Velocity profiles revealed the existence of a line known as the 'slip line', where all profiles intersect at a single point. The position of this line is found to be independent of flow rate, while its velocity varies with flow rate, for which a correlation has been proposed. This slip line coincides with the contraction height. Local shear rate profiles are provided for each flow rate. These profiles show a non-monotonic evolution: they increase from zero at the solid-liquid interface to reach a peak, then decrease again to zero in the 'plug' region at the center of the pipe. This variation suggests the presence of different layers between the solid -liquid interface and the slip line. The position of the maximum shear rate line remains constant irrespective of flow rate, suggesting that the width of the zone between the slip line and this line remains constant for all flow rates. In addition, the study includes an analysis of head losses upstream, downstream and at the contraction, for which correlations have been proposed concerning the friction factor f and the Euler number Eu as a function of the generalized Reynolds number Regen.