Elasto-visco-plastic flows in benchmark geometries: II. Flow around a confined cylinder

We examine computationally the two-dimensional flow of elastoviscoplastic (EVP) fluids around a cylinder symmetrically placed between two plates parallel to its axis. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method using the OpenFOAM software. As in viscoplastic materials, unyielded regions arise around the plane of symmetry well ahead or behind the cylinder, as two small islands located above and below the cylinder and as polar caps at the two stagnation points on the cylinder. Most interestingly, under certain conditions, an elongated yielded area around the midplane is predicted downstream of the cylinder, sandwiched between two unyielded areas. This surprising result appears, for example, with Carbopol 0.1 % when considering a blockage ratio of 0.5 (the ratio of the cylinder's diameter to the channel's width) and above a critical elastic modulus ($G>30Pa$). An approximate semi-analytical solution using the same model, in the region mentioned above reveals that it is caused by the intense variation of the stress magnitude there, which may approach the yield stress asymptotically either from above or below, depending on material elasticity. The drag coefficient on the cylinder increases with yield stress and blockage ratio but decreases with material elasticity. The unyielded regions expand as the yield stress increases. They also expand when material elasticity increases because this allows the material to elastically deform more before yielding. Behind the cylinder, the so-called "negative wake" appears which becomes more intense as elasticity increases. Furthermore, by decreasing the elastic modulus or increasing the yield stress beyond a critical value, the yield surface may exhibit damped oscillations, or irregular shapes even without a plane of symmetry, all under creeping flow conditions. Both properties generate these patterns mainly behind the cylinder, because they increase the elastic stresses and the curvature of the streamlines triggering a purely elastic instability.