In the present study we investigate computationally the steady-state motion of an elastic capsule along the centerline of a square microfluidic channel and compare it with that in a cylindrical tube. In particular, we consider a slightly over-inflated elastic capsule made of a strain-hardening membrane with comparable shearing and area-dilatation resistance. Under the conditions studied in this paper (i.e. small, moderate and large capsules at low and moderate flow rates), the capsule motion in a square channel is similar to, and thus governed by the same scaling laws with the capsule motion in a cylindrical tube, even though in the channel the cross-section in the upstream portion of large capsules is non-axisymmetric (i.e. square-like with rounded corners). When the hydrodynamic forces on the membrane increase, the capsule develops a pointed downstream edge and a flattened rear (possibly with a negative curvature) so that the restoring tension forces are increased as also happens with droplets. Membrane tensions increase significantly with the capsule size while the area near the downstream tip is the most probable to rupture when a capsule flows in a microchannel. Because the membrane tensions increase with the interfacial deformation, a suitable Landau-Levich-Derjaguin-Bretherton analysis reveals that the lubrication film thickness h for large capsules depends on both the capillary number Ca and the capsule size a; our computations determine the latter dependence to be (in dimensionless form) h ~ a−2 for the large capsules studied in this work. For small and moderate capsule sizes a, the capsule velocity Ux and additional pressure drop ΔP+ are governed by the same scaling laws as for high-viscosity droplets. The velocity and additional pressure drop of large thick capsules also follow the dynamics of high-viscosity droplets, and are affected by the lubrication film thickness. The motion of our large thick capsules is characterized by a Ux−u~h~a−2 approach to the undisturbed average duct velocity and an additional pressure drop ΔP+ ~ a3/h ~ a5. By combining basic physical principles and geometric properties, we develop a theoretical analysis that explains the power laws we found for large capsules.

The optimal parameters affecting the adsorption of arsenic ions As(III) on iron oxide impregnated activated alumina (IOIAA) were determined by conducting batch and column experiments. The adsorption of As(III) was strongly dependent on pH, temperature and initial adsorbate concentration. The adsorption process satisfied the Langmuir and Freundlich isotherms. Equilibrium studies were conducted to obtain the thermodynamic parameters and data showed the endothermic nature of adsorption. Kinetics studies showed that a pseudo first-order rate equation successfully described the adsorption process. Equilibrium was attained within 10 h and the time taken to attain equilibrium was independent of initial arsenite concentration. Column studies showed that adsorption was strongly dependent on empty bed contact time. Column design parameters such as the time taken for the establishment of primary adsorption zone, fractional capacity, length of primary adsorption zone and the percentage saturation at breakpoint were calculated to be in the range of 18.3 to 70.4 h, 0.39 to 0.63, 3.0 to 3.85 cm and 69.6 to 81.5%, respectively. The observations mentioned above provide a direct relationship between the length of the adsorption zone (δ) and percent saturation at break point.

In the present study we investigate computationally the deformation of an elastic capsule in a rectangular microfluidic channel and compare it with that of a droplet. In contrast to the bullet or parachute shape in a square or cylindrical channel where the capsule extends along the flow direction, in a rectangular channel the capsule extends mainly along the less-confined lateral direction of the channel cross-section (i.e. the channel width), obtaining a pebble-like shape. The different shape evolution in these two types of solid channels results from the different tension development on the capsule membrane required for interfacial stability. Furthermore, in asymmetric channel flows, capsules show a different deformation compared to droplets with constant surface tension (which extend mainly along the flow direction) and to vesicles which extend along the more-confined channel height. Therefore, our study highlights the different stability dynamics associated with these three types of interfaces. Our findings suggest that the erythrocyte deformation in asymmetric vessels (which is similar to that of capsules) results from the erythrocyte’s inner spectrin skeleton rather than from its outer lipid bilayer.

Determination of the elastic properties of the membrane of artificial capsules is essential for the better design of the various devices that are utilized in their engineering and biomedical applications. However this task is complicated owing to the combined effects of the shear and area-dilatation moduli on the capsule deformation. Based on computational investigation, we propose a new methodology to determine a membrane's shear modulus, independent of its area-dilatation modulus, by flowing strain-hardening capsules in a converging micro-capillary of comparable size under Stokes flow conditions, and comparing the experimental measurements of the capsule elongation overshooting with computational data. The capsule prestress, if any, can also be determined with the same methodology. The elongation overshooting is practically independent of the viscosity ratio for low and moderate viscosity ratios, and thus a wide range of capsule fluids can be employed. Our proposed experimental device can be readily produced via glass fabrication while owing to the continuous flow in the micro-capillary, the characterization of a large number of artificial capsules is possible.