Suspension Of Capsules Research Articles

Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids

Motivated by observations of the effects of drag-reducing polymer additives on various aspects of blood flow, suspensions of fluid-filled elastic capsules in Newtonian fluids and dilute solutions of high molecular weight (drag-reducing) polymers are investigated during plane Couette flow in a slit geometry. A simple model is presented to describe the cross-stream distribution of capsules as a balance of shear-induced diffusion and wall-induced migration due to capsule deformability. The model provides a theoretical prediction of the dependence of capsule-depleted layer thickness on the capillary number. A computational approach is then used to directly study the motion of elastic capsules in a Newtonian fluid and in polymer solutions. Capsule membranes are modeled using a neo-Hookean constitutive model and polymer molecules are modeled as bead-spring chains with finitely extensible nonlinearly elastic springs, with parameters chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. Results for an isolated capsule near a wall indicate that the wall-induced migration depends on the capillary number and is strongly reduced by addition of polymer. Numerical simulations of suspensions of capsules in Newtonian fluid illustrate the formation of a capsule-depleted layer near the walls. The thickness of this layer is found to be strongly dependent on the capillary number. The shear-induced diffusivity of the capsules, on the other hand, shows only a weak dependence on capillary number. These results thus indicate that the mechanism of wall-induced migration is the primary source for determining the capillary number dependence of the depletion layer thickness. Both the wall-induced migration and the shear-induced diffusive motion of the capsules are attenuated under the influence of polymer; reduction of migration dominates, however, so the net effect of polymers on the capsule suspension is to reduce the thickness of the capsule-depleted layer. This prediction is in qualitative agreement with experimental observations.

Hydrodynamic diffusion of a suspension of elastic capsules in bounded simple shear flow

A suspension of red blood cells in a flow undergoes hydrodynamic or shear-induced diffusion. It is known from experiments that deoxygenated or stiffer red blood cells have a lower hydrodynamic diffusion coefficient compared to oxygenated or softer red blood cells. In this paper, we numerically calculate the hydrodynamic diffusion coefficients of a suspension of elastic capsules of viscosity ratio unity and as a function of volume fraction, elastic capillary number and channel height in a bounded simple shear flow. We show that the time required for the suspension to reach the diffusive regime in the direction perpendicular to the shear plane decreases with channel height. In a narrow channel, the effect of capsule elasticity is to delay the approach to a diffusive regime. However, the motion in the direction parallel to the velocity gradient is always subdiffusive. We show that the hydrodynamic diffusion coefficient in the direction perpendicular to the shear plane varies linearly with capsule volume fraction up to about 25%. In addition, it does not increase monotonously with elastic capillary number but drops when the capsules become sufficiently soft. Finally, it displays a weak dependence on the channel height.

Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and number fraction of the more floppy particle Xf in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced toward the walls with increasing Xf, while the floppy particles were found to increasingly accumulate near the centerline with decreasing Xf. This segregation behavior was universally observed independent of the parameters. The origin of this segregation is traced to the effect of the number fraction Xf on the localization of the stiff and the floppy particles in the near wall region--the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing Xf, while the exact opposite trend is observed for a floppy particle with decreasing Xf. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain the contrasting effect of Xf on the near wall localization of the two species. The key observation in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles away from the wall and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.

The rheology and microstructure of concentrated non-colloidal suspensions of deformable capsules

AbstractA detailed study into the rheology and microstructure of dense suspensions of initially spherical capsules is presented, where capsules are composed of a fluid-filled interior surrounded by an elastic membrane. This study couples a lattice-Boltzmann fluid solver to a finite-element membrane model creating a robust and scalable method for the simulation of these suspensions. A Lees–Edwards boundary condition is used to simulate periodic simple shear to obtain bulk rheological properties, and three-dimensional results are presented for capsules in the regime of negligible inertia, Brownian motion and colloidal interparticle forces. The simulation results focus on describing the suspension rheology as a function of the particle concentration and deformability, and relating these macroscopic rheological findings to changes at the particle level, i.e. the suspension microstructure. Several important findings are made: suspensions of deformable capsules are found to be shear thinning, and the initially compressive normal stresses associated with rigid spherical suspensions undergo rapid changes with moderate levels of particle deformation. These normal stress changes are particularly evident in the first normal stress difference, which undergoes a sign change at fairly minor levels of deformation, and the particle pressure, which decreases rapidly with increasing particle deformability. Changes in the microstructure as quantified by the single-body microstructure and the pair distribution function are reported. Also, results calculating particle self-diffusion are presented and related to changes in the normal stresses.

Dynamic rheology of a dilute suspension of elastic capsules: effect of capsule tank-treading, swinging and tumbling

Three-dimensional numerical simulations are used to study the effect of unsteady swinging and tumbling motion on the rheology of a dilute suspension of oblate-shaped elastic capsules. Unlike a suspension of initially spherical capsules undergoing the steady tank-treading motion for which the rheology is constant in time, the suspension of non-spherical capsules is time-dependent due to the unsteady capsule motion. In a simple shear flow, the non-spherical capsules undergo a transition from the tank-treading/swinging to the tumbling motion with a reduction in the shear rate or an increase in the ratio of the internal to external fluid viscosities. We find that the time-averaged rheology obtained for the non-spherical capsules undergoing the unsteady motion is qualitatively similar to that obtained for the spherical capsules undergoing the steady tank-treading motion, and that the tank-treading-to-tumbling transition has only a marginal effect. The time-averaged rheology exhibits a shear viscosity minimum when the capsules are in a swinging motion at high shear rates but not at low shear rates. This is a remarkable departure from the behaviour of a vesicle suspension which exhibits a shear viscosity minimum at the point of transition. We find that the shear viscosity in a capsule suspension can decrease as well as increase with increasing viscosity ratio during both tank-treading and tumbling motions, while that of a vesicle suspension always decreases in tank-treading motion and increases in tumbling motion. We then seek to connect the time-dependent rheology with the time-dependent membrane tension, capsule orientation, deformation and tank-treading velocity. At low shear rates, the numerical results exhibit a similar trend to that predicted by analytical theory for rigid ellipsoids undergoing tumbling motion. The trend differs during swinging motion due to the periodic deformation and time-dependent variation of the membrane stress. The elastic component of the shear stress is minimum when the capsules are maximally compressed, and is maximum when the capsules are maximally elongated. In contrast, the viscous component is related to the periodic variation of the tank-treading velocity synchronized with the swinging motion, and the rate of capsule elongation or compression. The swinging or tumbling velocity makes no contribution to the time-dependent rheology.

Rheology of a dilute suspension of liquid-filled elastic capsules

Rheology of a dilute suspension of liquid-filled elastic capsules in linear shear flow is studied by three-dimensional numerical simulations using a front-tracking method. This study is motivated by a recent discovery that a suspension of viscous vesicles exhibits a shear viscosity minimum when the vesicles undergo an unsteady vacillating-breathing dynamics at the threshold of a transition between the tank-treading and tumbling motions. Here we consider capsules of spherical resting shape for which only a steady tank-treading motion is observed. A comprehensive analysis of the suspension rheology is presented over a broad range of viscosity ratio (ratio of internal-to-external fluid viscosity), shear rate (or, capillary number), and capsule surface-area dilatation. We find a result that the capsule suspension exhibits a shear viscosity minimum at moderate values of the viscosity ratio, and high capillary numbers, even when the capsules are in a steady tank-treading motion. It is further observed that the shear viscosity minimum exists for capsules with area-dilating membranes but not for those with nearly incompressible membranes. Nontrivial results are also observed for the normal stress differences which are shown to decrease with increasing capillary number at high viscosity ratios. Such nontrivial results neither can be predicted by the small-deformation theory nor can be explained by the capsule geometry alone. Physical mechanisms underlying these results are studied by decomposing the particle stress tensor into a contribution due to the elastic stresses in the capsule membrane and a contribution due to the viscosity differences between the internal and suspending fluids. It is shown that the elastic contribution is shear-thinning, but the viscous contribution is shear thickening. The coupling between the capsule geometry and the elastic and viscous contributions is analyzed to explain the observed trends in the bulk rheology.

P.094 Auricles' defects elimination using silicone implants

In this work bleached E. globulus kraft pulp was doped with polyhexamethylene biguanide (PHMB) from an aqueous solution or from a suspension of silica capsules ([email protected]) by impregnation under atmospheric or ultra-high pressure (UHP) conditions (500 MPa). The antimicrobial properties of pulps were evaluated towards gram-negative E. coli and gram-positive L. innocua bacteria. PHMB loads below 500 mg per kg of pulp revealed negligible bacteriostatic properties, whereas PHMB loads of ca 3000–4000 mg per kg demonstrated bactericidal properties of pulp without significant deterioration of its mechanical strength. The UHP impregnation allowed significant improvement of PHMB uptake. Thus, under equal conditions, PHMB uptake was ca 25% greater under UHP than under atmospheric pressure impregnation, whereas the leachable amounts of PHMB in both pulps were comparable. The sorption of [email protected] on pulp in suspension under UHP conditions was ca 17% greater than under atmospheric pressure with almost 70% increase of leachable PHMB.

Pairwise interaction of capsules in simple shear flow: Three-dimensional effects

We use a boundary integral formulation to investigate the collision of two identical capsules in simple shear flow. Each capsule consists of a viscous liquid drop enclosed by an elastic membrane. The hydrodynamic interaction is characterized by an irreversible cross-flow displacement after the capsules have crossed each other, as also observed for rough spheres or drops. This deflection would cause a shear-induced dispersion in a dilute suspension of capsules. After a previous work devoted to the interaction of two capsules located in the same shear plane, here, we focus on the more general case of capsules also shifted in the vorticity direction. For sufficiently spaced trajectories, the capsules exhibit negative deflections which displace them to closer streamlines after they have crossed. Furthermore, the cross-flow displacement occurs mainly in the vorticity direction. Both phenomena are in contradiction with the conclusions drawn for a pair of drops, and are, therefore, attributed to the elastic nature of the capsule interface.

簡易懸濁法による経管投与に対応した調剤支援システムの構築と運用

A simple method for making suspensions of tablets and capsules for administration via a feeding tube has been developed.It involves allowing tablets or capsules to disintegrate in hot water (55°C) without grinding.When this method was introduced for administration by feeding tube at the Japanese Red Cross Kumamoto Hospital in October,2006,we developed a dispensing support system for it.Our system enables us to verify whether medicines are appropriate for administration by feeding tube or not.It also raises efficiency in drug dispensing and facilitates the recording of drug information for the use of nurses at the time of administration.We feel that it is a useful and effective system for the administration of medicines by feeding tube.

Surface properties and implantation site affect the capsular fibrotic overgrowth

Transplantation of encapsulated pancreatic islets is a promising approach for the treatment of type 1 diabetes. Large-scale application of this technique, however, is hampered by insufficient biocompatibility of the capsules. In this study, we have evaluated the biocompatibility of a new synthetic material with six different chemical groups on their surface (amino, carboxy-sulfate, carboxylate, hydroxylate, sulfate, and PMMA) used for the fabrication of the microcapsules. Eight Lewis rats were inoculated with a suspension of empty capsules made for each candidate material in the retroperitoneal ileopsoas muscle and renal subcapsular space. Four weeks later kidney and muscle containing the capsules were explanted, paraffin embedded, sectioned and stained with Sirius Red and Masson's Trichrome for histological analysis. The amount of fibrosis was also ultrastructurally evaluated with scanning electron microscopy. The samples were then subjected to digitalized quantitative analysis using specific software to determine the degree of fibrotic overgrowth. The quantification of collagen deposition, calculated in proximity of the microcapsules, was expressed as a percentage of the total area and can be considered a good index for the biocompatibility, an essential prerequisite for functional pancreatic islet transplantation. The results show that subcapsular renal space is the best implantation site and the positive surface charge induces a more intense collagen synthesis.

Rheology of dilute suspensions of red blood cells: experimental and theoretical approaches

Shear viscosity measurements with dilute suspensions of red blood cells are interpreted using a microrheological model that relates the bulk measurements to the physical properties of the suspended cells. It is thus possible to quantify the average deformability of a RBC population in terms of a mean value of the membrane shear elastic modulus E s . The values obtained for normal cells are in good agreement with those given in the literature. The method allows to discriminate between normal and altered (diamide or glutaraldehyde treated) cells or pathological cells (scleroderma). The predictions of the microrheological model, based on analytic calculations, are also compared with the numerical results of Ramanujan and Pozrikidis (JFM 361, 1998) for dilute suspensions of capsules in simple shear flow.

Simple Shear Flow of Suspensions of Elastic Capsules

The simple shear flow of homogeneous suspensions of two-dimensional capsules enclosed by elastic membranes is studied in the limit of vanishing Reynolds number, in the special case where the viscosity of the fluid enclosed by the capsules is equal to the viscosity of the ambient fluid. The deformation of capsules with circular, elliptical, and biconcave unstressed shapes, and the rheological and statistical properties of their infinitely dilute and moderately dense suspensions are investigated by dynamical simulation using the method of interfacial dynamics for Stokes flow. In a preliminary investigation, the behavior of solitary capsules suspended in an infinite fluid is studied as a function of the dimensionless membrane elasticity number expressing the capsule deformability or the strength of the shear flow. It is found that a critical elasticity number above which a capsule exhibits continued elongation does not exist, and an equilibrium configuration is reached no matter how large the shear rate, in agreement with previous results for three-dimensional flow. A correspondence is established between the elasticity numbers for two- and three-dimensional flow at which the capsules undergo the same degree of deformation. Simulations of pairwise capsule interceptions reveal behavior similar to that exhibited by liquid drops with uniform surface tension. Because of strong hydrodynamic interactions in two-dimensional Stokes flow, the concept of hydrodynamic diffusivity in the limit of infinite dilution is ill-defined in the absence of fluid inertia. Dynamical simulations of doubly periodic monodisperse suspensions with up to 50 capsules distributed in each periodic cell at areal fractions of 0.25 and 0.40 provide information on the effective rheological properties of the suspension and on the nature of the statistical properties of the particle motion. The character of the flow is found to be intermediate between that of liquid drops and rigid particles, and this is attributed to the membrane deformability and to the ability of the interfaces to perform tank-treading motion. The results are compared with rheological measurements of blood flow with good agreement.

Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow

The transient deformation of liquid capsules enclosed by elastic membranes subject to simple shear flow is studied numerically using a new implementation of the boundary element method. The numerical results for capsules with spherical unstressed shapes and varying degrees of surface elasticity are compared with the predictions of an asymptotic theory for small deformations due to Barthès-Biesel and coworkers, and the significance of nonlinear effects due to finite deformation is assessed. It is found that the capsules exhibit continuous elongation when the dimensionless shear rate becomes larger than a critical threshold, in agreement with recent experimental observations of capsules with polymerized interfaces. Membrane failure at large deformations is discussed with respect to membrane thinning and development of excessive elastic tensions, and it is argued that the location where the membrane is likely to rupture due to continued deformation is insensitive to the precise mechanism of rupture. The numerical results suggest that a dilute suspension of capsules behaves like shear-thinning medium with some elastic properties. Results of oblate spheroidal capsules suggest that the points of maximum membrane thinning and tension coincide but their location depends upon the unstressed capsule shape.

Encapsulation of magnetic fluids

Encapsulation of non-aqueous magnetic fluids is described. The magnetic capsules thus obtained have a diameter of the order of a micron and are dispersed in water. The magnetization curves of the suspensions of magnetic capsules have been compared to the magnetization curves of the initial magnetic fluid to determine stability of this ferrofluid in the encapsulated droplets.

Theoretical Modelling of the Motion and Deformation of Capsules in Shear Flows

Mechanical models for capsules freely suspended in another liquid, are devised to predict the deformation, motion, breakup of one particle and also the rheological flow behaviour of a suspension. The capsule is filled with a newtonian liquid, and is surrounded by a thin deformable membrane having otherwise arbitrary mechanical properties. Initially spherical capsules in simple shear flow, are found to deform and orient with respect to streamlines, while their membrane is continuously rotating around the internal liquid. A dilute suspension of such capsules has a viscoelastic constitutive law which depends on the particle physical properties. It is then possible to use such models to interpret experiments in terms of the mean intrinsic properties of a capsule population.

Determination of the Red Blood Cell Apparent Membrane Elastic Modulus From Viscometric Measurements

Rhelogical measurements on a dilute suspension of red blood cells (RBCs) are interpreted by means of a microheological model that relates the shear evolution of the apparent viscosity to the intrinsic properties of the suspended particles. It is then possible to quantify the average deformability of a RBC population in terms of a mean value of the membrane shear elastic modulus, Es. Dilute suspensions of erthrocytes exhibit shear-thinning behavior with a constant high shear viscosity. This behavior is identical to the one predicted for a suspension of spherical capsules where the same phenomena of deformation and orientation prevail. A comparison between theoretical and experimental curves yields a mean value of Es, assuming all other cell properties--internal viscosity, geometry--to be otherwise equal. In Dextran, the values of Es for normal RBCs are found to be of order 3.10(-6) N/m. For erythrocytes hardened by heat exposure for 15 minutes at 48 degrees C, the increase in Es reaches 45 percent. This procedure of shear elastic modulus determination is easy to perform and seems to give a good discrimination between normal and altered erythrocytes.

Model suspension of spherical capsules: Physical and rheological properties

Oil-in-water dispersions stabilized by interfacial cross-linking polymerization are discussed. Two physical properties of this system are measured: the permeability of the membrane surrounding each oil droplet, and the shear viscosity of the suspension in the dilute regime. Using a microrheological model of a suspension of capsules, it is possible to relate the observed non-Newtonian behavior to the physical state of the microstructure. In particular, an evolution of the membrane properties with the degree of cross-linking polymerization is put in evidence.

The time-dependent deformation of a capsule freely suspended in a linear shear flow

An analysis is presented of the dynamics of a small deformable capsule freely suspended in a viscous fluid undergoing shear. The capsule consists of an elastic membrane which encloses another viscous fluid, and it deforms in response to the applied external stresses and the elastic forces generated within the membrane. Equations are derived which give its time-dependent deformation in the limit that the departure of the shape from sphericity is small. The form of the shear flow is arbitrary and a general (two-dimensional) elastic material is considered. Limiting forms are obtained for highly viscous capsules and for membranes which are area-preserving, and earlier results for surface tension droplets and incompressible isotropic membranes are derived as particular cases. Results for the viscosity of a dilute suspension of capsules are also given.The theoretical prediction for the relaxation rate of the shape is derived for an interface which has elastic properties appropriate for a red-blood-cell membrane, and is compared with experimental observations of erythrocytes.