Motion and Deformation of Elastic Capsules and Vesicles in Flow

Barthès-Biesel, Dominique

doi:10.1146/annurev-fluid-122414-034345

Cited by 175 publications

(192 citation statements)

References 99 publications

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“…The thickness of the capsule wall is assumed to be infinitely small. A very thin hyperelastic membrane can be modelled as a zero-thickness elastic surface, with different possible constitutive laws (Barthès-Biesel 2016). Among those, the Skalak's (SK) law (Skalak et al 1973), which was originally proposed to describe the membrane of a RBC, assumes a strain energy function of the form…”

Section: Problem Descriptionmentioning

confidence: 99%

Motion of a spherical capsule in branched tube flow with finite inertia

et al. 2016

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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.

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Section: Problem Descriptionmentioning

confidence: 99%

Motion of a spherical capsule in branched tube flow with finite inertia

et al. 2016

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“…Since both the particle and the suspending medium are inertialess, no initial conditions on the velocities are required, whereas an initial condition is needed on the extra-stress tensor. We assume that the particle (and the matrix, in case it is viscoelastic) is initially stress-free, which means: τ| t=0 = 0 (14) The above listed equations are made dimensionless by choosing the channel diameter D c as the characteristic length, the unperturbed average velocity of the fluid u av = 4 Q/π D 2 c as the characteristic velocity, the ratio between the characteristic length and the characteristic velocity D c / u av as the characteristic time, μu av / D c (or μ 0 u av /D c ) as the characteristic stress in the matrix, and the shear modulus of the elastic material G p as the characteristic stress in the particle. All the variables appearing in the following Sections are made dimensionless through such characteristic quantities.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Very recently, Villone et al [12] studied through direct numerical simulations the deformation and cross-streamline migration of an initially spherical elastic particle in confined shear flow of both Newtonian and viscoelastic fluids. It was demonstrated that, at variance with rigid particles, elastic particles migrate orthogonally to the flow direction even in inertialess flows of Newtonian fluids; notice that such a migration was already known to occur also for other deformable particles, like Red Blood Cells (see, for example, the review by Geislinger and Franke [13] and the references therein), and vesicles or capsules (see the review by Barthès-Biesel [14] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of deformable particle lateral migration in tube flow of Newtonian and viscoelastic media

Villone

Greco

Hulsen

et al. 2016

Journal of Non-Newtonian Fluid Mechanics

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“…For example, a capsule in shear flow is a fundamental process that is related to erythrocytes (or red blood cells), leukocytes (or white blood cells), and platelets in blood flow [1–6]. Deformation is essential for red blood cells to perform their physiological functions in the circulation of capillary blood vessels and thus affects the rheology of the blood [6–8]. The deformations of white blood cells and red blood cells can, respectively, affect the immune response and the oxygen load release [9, 10].…”

Section: Introductionmentioning

confidence: 99%

“…The synthetic microcapsules with polymerized interfaces are designed for drug delivery, cosmetic production, and other technical usages [11, 12]. Therefore, great effort has been made to study this problem (e.g., [1, 4, 6, 8, 10, 12–14]).…”

Section: Introductionmentioning

confidence: 99%

Deformation of a Capsule in a Power-Law Shear Flow

Tian

2016

Computational and Mathematical Methods in Medicine

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An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

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Motion and Deformation of Elastic Capsules and Vesicles in Flow

Cited by 175 publications

References 99 publications

Motion of a spherical capsule in branched tube flow with finite inertia

Motion of a spherical capsule in branched tube flow with finite inertia

Numerical simulations of deformable particle lateral migration in tube flow of Newtonian and viscoelastic media

Deformation of a Capsule in a Power-Law Shear Flow

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