From the biological side, the microcirculatory network is made of many capillary bifurcations. Indeed, a number of microfluidic devices consisting of a main channel with several side branches, aimed at separating particles with different size, has been proposed. The flow of suspensions through channel bifurcations is a relevant topic in several applications such as microfluidics and biology. The results illustrated here show the feasibility to efficiently separate/fractionate particles by size, through the use of viscoelastic suspending liquids. Such effect is more pronounced for larger particles and inlet flow rates. On the other hand, fluid elasticity strongly alters the fraction of particles exiting the two outlets as compared to the inlet. The results show that shear-thinning does not have a relevant effect as compared to the equivalent Newtonian case, i.e., with the same choice of the relative outlet flow rates. For each condition, the fluxes of particles through the two outflow channels are computed. Simulations are carried out by varying the confinement, the inlet flow rate and the relative weight of the two outlet flow rates. Specifically, an inelastic shear-thinning (Bird-Carreau) and a viscoelastic shear-thinning (Giesekus) models have been chosen the results are also compared with the case of a Newtonian suspending liquid. The effect of fluid rheology on the partitioning of particles between the two outlets is investigated by selecting different constitutive equations to model the suspending liquid. A fictitious domain method combined with a grid deformation procedure is used. We adopt a flow configuration such that the two outlets are orthogonal, and their flow rates can be tuned. In this work, we study through 2D direct numerical simulations the partitioning of particles suspended in non-Newtonian fluids flowing in a T-junction. Previous works have mainly investigated the dynamics of particles suspended in Newtonian liquids. It is known that the partitioning of particles at a bifurcation is different from the partitioning of the suspending fluid, which allows particle separation and fractionation. To accomplish this goal, Equation I.5 may be rewritten as: Φ Φ O * O i O O i O O G 2 2 2 2 2 2 p - p + p - p = K 1 I.11 Substituting Equations I.8 and I.10 into Equation I.11 yields: Φ Φ O * O i O O l O g O G 2 2 2 2 p - p + p - p = K 1 2 2 I.12 Substituting Equations I.3 and I.4 into Equation I.12 yields: k m + k 1 = K 1 L G G I.The flow of suspensions through bifurcations is encountered in several applications. The theoretical partial pressure of oxygen (p * O2 ) in equilibrium with the bulk liquid phase oxygen concentration may now be related to the bulk liquid phase oxygen concentration (c l O2 ) by: I.8 c m = p l O O * O 2 2 2 Also, the theoretical liquid phase oxygen concentration (c * O2 ) in equilibrium with the bulk gas phase oxygen concentration may now be related to the bulk liquid phase oxygen concentration (p g O2 ) by: c I.9 m = p * O O g O 2 2 2 Of course, the liquid phase oxygen concentration at the interface is in equilibrium with the gas phase oxygen concentration at the interface: I.10 c m = p i O O i O 2 2 2 We would like to find the relationship between K G, k G and k L. I.7 c m = p i j j i j If the species is oxygen, then Equation I.7 essentially becomes Equation I.2, with a conversion being necessary to relate mole fraction and concentration. For mass transport between other types of phases, a similar assumption may often be made.
This assumption is Henry's Law, and it is valid in the case where the transporting species is present in dilute concentration. Let us first make the simplification that the equilibrium relationship between the gas phase partial pressure and the liquid phase concentration of the transporting species at the interface is proportional.
The overall mass transfer coefficients may be related to the individual mass transfer coefficients.
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