# Deformation and sorting of capsules in a T-junction

## TL;DR

This study investigates how individual capsules deform and are sorted in a T-junction flow, revealing that capsule stiffness influences their trajectory and deformation, enabling potential sorting applications based on mechanical properties.

## Contribution

The paper introduces a capillary number based on static compression to quantify capsule stiffness and demonstrates its effectiveness in predicting capsule behavior and sorting in a T-junction.

## Key findings

- Capsule deformation correlates with a master curve in Ca.
- Capsule position in the T-junction depends on Ca, enabling sorting.
- A diffuser enhances capsule separation based on stiffness.

## Abstract

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.