  We study experimentally the motion and deformation of individual capsules
transported by a constant volume-flux flow of low Reynolds number, through the
T-junction of a channel with rectangular cross-section. We use millimetric
ovalbumin-alginate capsules which we manufacture and characterise independently
of the flow experiment. Centred capsules travel at constant velocity down the
straight channel leading to the T-junction where they decelerate and expand in
the spanwise direction before turning into one of the two identical daughter
channels. There, non-inertial lift forces act to re-centre them and relax their
shape until they reach a steady state of propagation. We find that the dynamics
of fixed-size capsules within our channel geometry are governed by a capillary
number Ca defined as the ratio of viscous shear forces to elastic restoring
forces. We quantify the elastic forces by statically compressing the capsule to
50% of its initial diameter between parallel plates rather than by the Young's
modulus of the encapsulating membrane, in order to account for different
membrane thickness, pre-inflation and non-linear elastic deformation. We show
that the maximum extension in the T-junction of capsules of different stiffness
collapses onto a master curve in Ca. Thus, it provides a sensitive measure of
the relative stiffness of capsules at constant flow rate, particularly for
softer capsules. We also find that the T-junction can sort fixed-size capsules
according to their stiffness because the position in the T-junction from which
capsules are entrained into the daughter channel depends uniquely on Ca. We
demonstrate that a T-junction can be used as a sorting device by enhancing this
initial capsule separation through a diffuser.
