Oblate Capsule Research Articles

Thermal Performance of Constrained Melting of PCM Inside an Elliptical Capsule of Two Orientations

The phase change material is deemed a hopeful method of saving a large quantity of thermal energy latently at an approximately low-temperature swing. A computational investigation to examine the thermal behavior of constrained phase change of paraffin wax inside an elliptical cell under the influence of different wall heat fluxes is presented. The impact of two orientations of the capsule (prolate and oblate) on the transient movement of the melting-front and liquid fraction is examined. The results exhibit that the imposed wall heat flux has an important influence on the melting characteristics, whereas a small effect on the melting process is exhibited by the orientation of the capsule. Nevertheless, the melting process is relatively faster and lower time is required in an oblate capsule than that experienced in the prolate capsule. The reduction in fusion time resulted from container orientation increases with the increase in supplied heat flux. The maximum reduction in the melting time of the oblate capsule is about 7.71% less than that of the prolate capsule for the same size. Besides, it is found that the time needed for complete melting in an elliptical cell is lower than that observed in spherical one for the same size, surface area and amount of heat flux.

Dynamics of capsules enclosing viscoelastic fluid in simple shear flow

Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.

Stable equilibrium configurations of an oblate capsule in simple shear flow

The objective of the paper is to determine the stable mechanical equilibrium states of an oblate capsule subjected to a simple shear flow, by positioning its revolution axis initially off the shear plane. We consider an oblate capsule with a strain-hardening membrane and investigate the influence of the initial orientation, capsule aspect ratio$a/b$, viscosity ratio${\it\lambda}$between the internal and external fluids and the capillary number$Ca$which compares the viscous to the elastic forces. A numerical model coupling the finite element and boundary integral methods is used to solve the three-dimensional fluid–structure interaction problem. For any initial orientation, the capsule converges towards the same mechanical equilibrium state, which is only a function of the capillary number and viscosity ratio. For$a/b=0.5$, only four regimes are stable when${\it\lambda}=1$: tumbling and swinging in the low and medium$Ca$range ($Ca\lesssim 1$), regimes for which the capsule revolution axis is contained within the shear plane; then wobbling during which the capsule experiences precession around the vorticity axis; and finally rolling along the vorticity axis at high capillary numbers. When${\it\lambda}$is increased, the tumbling-to-swinging transition occurs for higher$Ca$; the wobbling regime takes place at lower$Ca$values and within a narrower$Ca$range. For${\it\lambda}\gtrsim 3$, the swinging regime completely disappears, which indicates that the stable equilibrium states are mainly the tumbling and rolling regimes at higher viscosity ratios. We finally show that the$Ca$–${\it\lambda}$phase diagram is qualitatively similar for higher aspect ratio. Only the$Ca$-range over which wobbling is stable increases with$a/b$, restricting the stability ranges of in- and out-of-plane motions, although this phenomenon is mainly visible for viscosity ratios larger than 1.

Cross-type optical separation of elastic oblate capsules in a uniform flow

The dynamic behavior of an elastic capsule with an initially oblate spheroidal shape during cross-type optical separation was numerically investigated. The penalty immersed boundary method was adopted for the fluid-membrane interaction, and the optical force calculation was conducted by using the ray optics method including the ray-surface intersection algorithm. The oblate elastic capsule of b/a = 0.5 with different surface Young's moduli and different initial inclination angles was considered. The oblate capsule with higher surface Young's moduli was less deformed, and was more migrated for each initial inclination angle. Unlike the oblate rigid particle, the initially inclined capsules with moderate inclination angles were similarly migrated since the oblate elastic capsule was deformed during rotation near the laser beam axis. The oblate capsules can be separated according to the surface Young's modulus, except for nearly non-inclined capsules. As the fluid velocity decreased, the migration distance increased. The maximum deformation parameter was insensitive to the fluid velocity. Furthermore, a new dimensionless number (Sec) was introduced to predict the migration distance of the oblate elastic capsule.

Migration of Elastic Capsules by an Optical Force in a Uniform flow

The behavior of an elastic capsule by an optical force in a uniform flow is examined by using the penalty immersed boundary method. The elastic capsule is subjected to the laser beam with Gaussian distribution in the perpendicular direction to the fluid flow. The elastic capsule migrated by the optical force along the direction of the laser beam propagation, and the migration distance is dependent on its properties. The oblate capsule with b/a = 0.5 obeying the neo-Hookean constitutive law is first considered, and the effects of the surface Young's modulus and the initial inclination angle on the migration distance are studied. The migration distance of the oblate capsule is increased as the surface Young's modulus increases, and the non-inclined oblate capsule is more migrated than the differently inclined capsules. Then the spherical, oblate, and biconcave capsules obeying the Skalak constitutive law are considered. A comparison of the trajectories of the capsules indicates that the migration of the spherical capsule is the largest. Unlike the oblate capsule, the non-inclined biconcave capsule is less migrated than other inclination angles due to its initial shape.

Time required for an oblate capsule in flow to reach equilibrium

Blood is a concentrated suspension of cells composed of 45% in volume of red blood cells (RBCs). The RBC orientation relative to the flow direction and its deformation depend on the hydrodynamics s...

Three-dimensional dynamics of oblate and prolate capsules in shear flow

We study computationally the dynamics of oblate and prolate spheroidal capsules in simple shear flow with small inertia for a range of dimensionless shear rates. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane, and its equatorial plane is initially tilted out of the plane of shear. We find, at low shear rates, the well-accepted tumbling motion is not always stable for both oblate and prolate capsules. For an oblate capsule, the dominant stable modes for increasing dimensionless shear rate are as follows: rolling with the equatorial plane staying in the plane of shear, precessing following Jeffery's orbit [Proc. R. Soc. London A 102, 161 (1922)], and tumbling. Interestingly, the order of modes is reversed for a prolate capsule: tumbling, precessing, and rolling with increasing dimensionless shear rate. At transitional regimes, we find the stable motion of a capsule can depend on its initial titled angle, even at the same shear rate. At high dimensionless shear rates, a spheroidal capsule undergoes a complicated oscillating-swinging motion: Its major axis oscillates about the plane of shear in addition to the swinging about a mean angle with flow direction found previously, and the amplitudes of both oscillations decrease when increasing the dimensionless shear rate towards a steady tank treading motion asymptotically. We summarize the results in phase diagrams and discuss the reorientation of both oblate and prolate capsules in a wide range of dimensionless shear rates.

Off-plane motion of an oblate capsule in a simple shear flow

"Off-plane motion of an oblate capsule in a simple shear flow." Computer Methods in Biomechanics and Biomedical Engineering, 16(sup1), pp. 4–5Keywords:: oblate capsulefluid–structure interactionfinite-element methodboundary integral methodshear flow AcknowledgementsThis research was funded by the Conseil Régional de Picardie (MODCAP grant), by the French Ministère de la Recherche (Pilcam2 grant) and by the French Agence Nationale de la Recherche (CAPSHYDR grant no. ANR-11-BS09-013).

Influence of membrane viscosity on capsule dynamics in shear flow

AbstractMost previous numerical studies on capsule dynamics in shear flow have ignored the role of membrane viscosity. Here we present a numerical method for large deformation of capsules using a Kelvin–Voigt viscoelastic model for the membrane. After introducing the model and the related numerical implementation, we present a comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics. We observe that the membrane viscosity leads to buckling in the range of shear rate in which no buckling is observed for capsules with purely elastic membrane. For moderate to large shear rates, the wrinkles on the capsule surface appear in the same range of the membrane viscosity that was reported earlier for artificial capsules and red blood cells based on experimental measurements. In order to obtain stable shapes, it is necessary to introduce the bending stiffness. It is observed that the range of the bending stiffness required is also in the same range as that reported for the red blood cells, but considerably higher than that estimated for artificial capsules. Using the stable shapes obtained in the presence of bending stiffness, we analyse the influence of membrane viscosity on deformation, inclination and tank-treading frequency of initially spherical capsules. Membrane viscosity is observed to reduce the capsule deformation, and introduce a damped oscillation in time-dependent deformation and inclination. The time-averaged inclination angle shows a non-monotonic trend with an initial decrease reaching a minimum and a subsequent increase with increasing membrane viscosity. A similar non-monotonic trend is also observed in the tank-treading frequency. We then consider the influence of the membrane viscosity on the unsteady dynamics of an initially oblate capsule. The dynamics is observed to change from a swinging motion to a tumbling motion with increasing membrane viscosity. Further, a transient dynamics is also observed in which a capsule starts with one type of dynamics, but settles with a different dynamics over a long time.