Deformation of a biconcave-discoid capsule in extensional flow and electric field

Abstract

Biconcave-discoid (empirical shape of a red blood cell) capsule finds numerous applications in the field of bio-fluid dynamics and rheology, apart from understanding the behavior of red blood cells (RBC) in blood flow. A detailed analysis is, therefore, carried out to understand the effects of the uniaxial extensional flow and electric field on the deformation of a RBC and biconcave-discoid polymeric capsule in the axisymmetric regime. The transient deformation is computed numerically using axisymmetric boundary integral method for Stokes flow considering the Skalak membrane constitutive law as the model for the area incompressible RBC/biconcave-discoid capsule membrane. A remarkable biconcave-discoid to prolate spheroid transition is observed when the elastic energy is overcome by the viscous or Maxwell electric stresses. Moreover, the significance of membrane stresses developed during the deformation and at steady state and different modes of deformation are presented. This study should be useful in designing an artificial system involving biological cells under an electric field. arXiv:1801.01971v2 [cond-mat.soft]

Electrohydrodynamics of Vesicles and Capsules

“…Effective algorithms for such scenarios are necessary, as was demonstrated in one of our recent works, 110 and will be critical to the development of solvers for dielectrophoretic devices. 4.…”

“…There have been few studies to investigate RBCs (erythrocytes) subjected to an electric field with the aim of determining the elastic modulus, observing hemolysis, and estimating Maxwell stress. 109 An interesting possibility in the context of diagnosis is the possibility of a biconcave discoid− prolate shape transformation in an RBC, which we recently investigated and is discussed in detail 110 next. Moreover, the electrohydrodynamics of a discoid, including an estimation of the accurate transmembrane potential, remain a challenge due to the nontrivial shape of a biconcave discoid, 99 and simplified but inaccurate shapes such as oblate spheroids have been assumed in the literature.…”

“…Considering the parameters E s ≈ 0.1 N/m, μ e ≈ 0.1 Pa s, σ e ≈ 0.1 mS/m, and ϵ e ≈ 80, equivalent radius a ≈ 5 μm, , Ĝ m = 0, and a fairly high electric capillary number ( Ca el = 0.5), a biconcave-discoid capsule deforms into a series of cylindrical shapes (Figure a,b) and the high tensile Maxwell stress at the poles and the shoulders (Figure f,g) leads to positive curvature near the poles. For t < t m , due to the tensile electric stress (which is maximized near the poles, Figure h) the biconcave-discoid shape evolves into a cylindrical shape (Figure c).…”

“…Variations of meridional ( T s , red ), azimuthal ( T ϕ , blue ·), and mean ( T m , ) membrane tensions along the arc length are shown in the insets. Adapted with permission from ref . Copyright 2019 Cambridge University Press.…”

“…Transmembrane potential at the interface at (···) t = 10, (red ) t = 23, (blue ·) t = 29, (pink ··) t = 37, (green ·) t = 50, and (orange ) t = ∞ at electric Ca = 0.5 during the shape evolution of a biconcave-discoid capsule. Adapted with permission from ref . Copyright 2019 Cambridge University Press.…”