Intermediate regime and a phase diagram of red blood cell dynamics in a linear flow

In this paper we investigate the in vitro dynamics of a single rabbit red blood cell (RBC) in a planar linear flow as a function of a shear stress σ and the dynamic viscosity of outer fluid η_{o}. A linear flow is a generalization of previous studies dynamics of soft objects including RBC in shear flow and is realized in the experiment in a microfluidic four-roll mill device. We verify that the RBC stable orientation dynamics is found in the experiment being the in-shear-plane orientation and the RBC dynamics is characterized by observed three RBC dynamical states, namely tumbling (TU), intermediate (INT), and swinging (SW) [or tank-treading (TT)] on a single RBC. The main results of these studies are the following. (i) We completely characterize the RBC dynamical states and reconstruct their phase diagram in the case of the RBC in-shear-plane orientation in a planar linear flow and find it in a good agreement with that obtained in early experiments in a shear flow for human RBCs. (ii) The value of the critical shear stress σ_{c} of the TU-TT(SW) transition surprisingly coincides with that found in early experiments in spite of a significant difference in the degree of RBC shape deformations in both the SW and INT states. (iii) We describe the INT regime, which is stationary, characterized by strong RBC shape deformations and observed in a wide range of the shear stresses. We argue that our observations cast doubts on the main claim of the recent numerical simulations that the only RBC spheroidal stress-free shape is capable to explain the early experimental data. Finally, we suggest that the amplitude dependence of both θ and the shape deformation parameter D on σ can be used as the quantitative criterion to determine the RBC stress-free shape.