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We computationally study the transient motion of an initially spherical capsule flowing through a right-angled tube bifurcation, composed of tubes having the same diameter. The capsule motion and deformation is simulated using a three-dimensional immersed-boundary lattice Boltzmann method. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane following the Skalak’s law (Skalak et al., Biophys. J., vol. 13(3), 1973, pp. 245–264). The fluids inside and outside the capsule are assumed to have identical viscosity and density. We mainly focus on path selection of the capsule at the bifurcation as a function of the parameters of the problem: the flow split ratio, the background flow Reynolds number Re , the capsule-to-tube size ratio a/R and the capillary number Ca , which compares the viscous fluid force acting on the capsule to the membrane elastic force. For fixed physical properties of the capsule and of the tube flow, the ratio Ca/Re is constant. Two size ratios are considered: a/R=0.2 and 0.4. At low Re , the capsule favours the branch which receives most flow. Inertia significantly affects the background flow in the branched tube. As a consequence, at equal flow split, a capsule tends to flow straight into the main branch as Re is increased. Under significant inertial effects, the capsule can flow into the downstream main tube even when it receives much less flow than the side branch. Increasing Ca promotes cross-stream migration of the capsule towards the side branch. The results are summarized in a phase diagram, showing the critical flow split ratio for which the capsule flows into the side branch as a function of size ratio, Re and Ca/Re . We also provide a simplified model of the path selection of a slightly deformed capsule and explore its limits of validity. We finally discuss the experimental feasibility of the flow system and its applicability to capsule sorting.

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu. We used a microfluidic technique in order to study the mechanical properties of cross-linked albumin capsule membranes. The capsules were produced from aqueous human serum albumin (HSA) solutions with concentrations of 15%, 20%, 25% and 30% (w/v). The radii were in the range 55-80 m. We find that the capsules follow the neo-Hookean law, which is strain-softening and depends on one parameter, the surface shear modulus. A possible pre-inflation effect due to osmolarity is accounted for by imposing various values of pre-inflation. Small values of pre-inflation are sufficient to fit the data, which indicates that the capsule membrane is under small osmotic stress. Accounting for pre-inflation changes only slightly the surface shear elastic modulus of the membrane. Whatever the pre-inflation ratio, the shear modulus sharply increases with the HSA concentration from a low-value plateau.

International audience; We introduce a new numerical method to model the fluid-structure interaction between a microcapsule and an external flow. An explicit finite element method is used to model the large deformation of the capsule wall, which is treated as a bidimensional hyperelastic membrane. It is coupled with a boundary integral method to solve for the internal and external Stokes flows. Our results are compared with previous studies in two classical test cases: a capsule in a simple shear flow and in a planar hyperbolic flow. The method is found to be numerically stable, even when the membrane undergoes in-plane compression,which had been shown to be a destabilizing factor for other methods. The results are in very good agreement with the literature. When the viscous forces are increased with respect to the membrane elastic forces, three regimes are found for both flow cases. Our method allows a precise characterization of the critical parameters governing the transitions.

Bioartificial capsules consisting of an internal medium protected by a membrane are used for drugs or nutrients transport and can also be considered as models of cells. In microfluidic devices or in microcirculation, they flow through channels of different dimensions where they must adapt their motion and deformation. Membrane mechanics is then a key factor. An interesting situation is the flow of a capsule from a narrow to a wide channel. At the junction, the adverse pressure gradient compresses the particle in the streamwise direction and expands it crosswise. The distance between the capsule and the channel wall may become small, leading to contact and eventually adhesion. Cells clusters downstream of a sudden expansion (e.g. filter) has been observed. The aim of the present study is to analyze the dynamics of a bioartificial capsule when it exits a cylindrical pore as a function of different system parameters: size ratio between capsule and pore, membrane mechanical properties, initial osmotic pre-stress, internal viscosity, flow strength. We consider an initially spherical capsule consisting of a liquid droplet enclosed by a thin hyperelastic membrane and moving under imposed flow rate through a cylindrical pore. It is centred on the pore axis, so that the situation is axisymmetric. A numerical model based on the boundary integral method is used to follow the capsule motion and compute its deformation. When the cylindrical pore is long enough, the capsule reaches a stationary parachute shape that depends on the system parameters. When the membrane is strain-softening, a steady state may not exist and the capsule may break-up. The exit from the pore is a transient phenomenon that leads to increased tensions in the membrane and thin films between the pore wall and the capsule. We show how this process depends on membrane properties and internal viscosity.

Bioartificial capsules consisting of an internal liquid protected by a thin hyperelastic membrane are used in many applications (biomedical, cosmetic, pharmaceutical industries), where they are transported in small channels such as capillary vessels, cylindrical tubes or microfluidic channels. Such particles are quite fragile owing to the thinness of the membrane and it is important to verify that they will not break up unduly. When flowing in a channel, a capsule may deform but the stress level in the membrane is difficult if not impossible to measure. We have thus designed a numerical model of the flow of one or more capsules in a cylindrical pore. The situation is assumed to be axisymmetric and the boundary integral formulation of the Stokes equations is used. For an isolated capsule, the model shows how the shape and the elastic tensions in the membrane depend on flow strength, size ratio between the tube and the particle, membrane elastic constitutive behaviour. We find that when the membrane is strain-softening, the capsule does not always reach a steady shape and may elongate continuously until burst occurs. For two identical capsules, the hydrodynamic interaction is weak unless the particles almost touch. For a large capsule followed by a smaller faster one, the interaction can be quite strong and a capsule train can form. Experimental observations of capsules with a membrane made of cross-linked albumin (average diameter 45 µm) flowing inside small glass capillary tubes corroborates the predictions of the numerical model: capsule deformation and particle trains are observed, while burst cannot be achieved within the range of experimental flow rates.