Starting from the basic thermodynamic principles, we derive equations of micropolar Bingham fluids allowing for the variable concentration of polar particles. On the one hand, such fluids exhibit couple stresses, a non-symmetrical stress tensor, microrotations, and microinertia. On the other hand, the fluids support a yield stress. It was proved earlier that a micropolar fluid model can reproduce the Segre-Silberberg effect. Here, we study how the yield stress impacts this effect. (C) 2016 Published by Elsevier B.V.