Displacement flow of yield stress materials in annular spaces of variable cross section

We conducted an experimental study of a yield stress material being displaced upwardly at controlled flow rate by a Newtonian fluid in an annular space whose external wall consists of a sudden expansion–contraction. This system is a simplified representation of the primary cementing process of an oil well, whose bore diameter may present variations. In the experiments, different pairs of fluids were employed. The yield stress materials were Carbopol aqueous solutions at three different weight concentrations, with Herschel–Bulkley viscosity behavior. The Newtonian liquid was a glycerin/water mixture. A wide range of flow rates were explored, varying the dimensionless cavity depth and cavity axial length. A non-monotonic behavior is observed for the dimensionless volume of yield stress material displaced from the cavity by the Newtonian fluid flow. In addition, the rheological properties and geometrical parameters were seen to have a strong influence on the displaced volume.