  The unique ability of a red blood cell to flow through extremely small
microcapillaries depends on the viscoelastic properties of its membrane. Here,
we study in vitro the response time upon flow startup exhibited by red blood
cells confined into microchannels. We show that the characteristic transient
time depends on the imposed flow strength, and that such a dependence gives
access to both the effective viscosity and the elastic modulus controlling the
temporal response of red cells. A simple theoretical analysis of our
experimental data, validated by numerical simulations, further allows us to
compute an estimate for the two-dimensional membrane viscosity of red blood
cells, $\eta_{mem}^{2D}\sim 10^{-7}$ N$\cdot$s$\cdot$m$^{-1}$. By comparing our
results with those from previous studies, we discuss and clarify the origin of
the discrepancies found in the literature regarding the determination of
$\eta_{mem}^{2D}$, and reconcile seemingly conflicting conclusions from
previous works.
