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. C 2012 American Institute of Physics. [http://dx.
The dynamics and pair collisions of fluid-filled elastic capsules during Couette flow in Newtonian fluids and dilute solutions of high-molecular weight (drag-reducing) polymers are investigated via direct simulation. Capsule membranes are modeled using either a neo-Hookean constitutive model or a model introduced by Skalak et al. [“Strain energy function of red blood-cell membranes,” Biophys. J. 13, 245 (1973)], which includes an energy penalty for area changes. This model was developed to capture the elastic properties of red blood cells. Polymer molecules are modeled as bead-spring trimers with finitely extensible nonlinearly elastic springs; parameters were chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a novel Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. The results for isolated capsules in shear indicate that at the very low concentrations considered here, polymers have a little effect on the capsule shape. In the case of pair collisions, the effect of polymer is strongly dependent on the elastic properties of the capsules’ membranes. For neo-Hookean capsules or for Skalak capsules with only a small penalty for area change, the net displacement in the gradient direction after collision is virtually unaffected by the polymer. For Skalak capsules with a large penalty for area change, polymers substantially decrease the net displacement when compared to the Newtonian case and the effect is enhanced upon increasing the polymer concentration. The differences between the polymer effects in the various cases are associated with the extensional flow generated in the region between the capsules as they leave the collision. The extension rate is highest when there is a strong resistance to a change in the membrane area and is substantially decreased in the presence of polymer.
Use of prefilled syringes (syringes prefilled with active drug) is becoming increasingly common for injectable drugs. Compared to vials, prefilled syringes offer higher dose accuracy and ease of use due to fewer steps required for dosage. Convenience to end users can be further enhanced through the use of prefilled syringes in combination with delivery devices such as autoinjectors. These devices allow patients to self-administer the drug by following simple steps such as pressing a button. These autoinjectors are often spring-loaded and are designed to keep the needle tip shielded prior to injection. Because the needle is not visible to the user, such autoinjectors are perceived to be less invasive than syringes and help the patient overcome the hesitation associated with self-administration. In order to successfully develop and market such delivery devices, we need to perform an in-depth analysis of the components that come into play during the activation of the device and dose delivery. Typically, an autoinjector is activated by the press of a button that releases a compressed spring; the spring relaxes and provides the driving force to push the drug out of the syringe and into the site of administration. Complete understanding of the spring force, syringe barrel dimensions, needle size, and drug product properties is essential for robust device design. It is equally important to estimate the extent of variability that exists in these components and the resulting impact it could have on the performance of the device. In this work, we studied the impact of variability in syringe and device components on the delivery forces associated with syringe injection. More specifically, the effect of barrel size, needle size, autoinjector spring force, and frictional forces has been evaluated. An analytical model based on underlying physics is developed that can be used to predict the functionality of the autoinjector.
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