On the viscous flows of leak-out and spherical cap natation

Abstract

This paper deals with the hydrodynamics of a viscous liquid passing through the hole in a deflating hollow sphere. I employ the method of complementary integrals and calculate in closed form the pressure and streamfunction for the axisymmetric, creeping motion coming from changes in radius. The resulting flow fields describe the motion of a deformable spherical cap in a viscous environment, where the deformations include changes in the size of the spherical cap, the size of the hole and translation of the body along the axis of symmetry. The calculations yield explicit expressions for the jumps in pressure and resistance coefficients for the combined deformations. The equation for the translation force shows that a freely suspended spherical cap is able to propel as an active swimmer. The expression for pressure contains the classic Sampson flow rate equation as a limiting case, but simulations show that the pressure must also account for the velocity of hole widening to correctly predict outflow rates in physiology. Movies based on the closed-form solutions visualize the flow fields and pressures as part of physical processes.

Hydrodynamics of a semipermeable inextensible membrane under flow and confinement

“…Such equilibrium shape of a semipermeable vesicle results from the balance between elastic stress and membrane tension. For an elastic membrane with a large pore, the equilibrium membrane (hemispherical) shape also results from such balance (59).…”

Solubilization kinetics determines the pulsatory dynamics of lipid vesicles exposed to surfactant

“…Noting that σ = ∂Vs/∂A, the conservative force becomes F (σ, r) = 2πσr − 2πγ. Finally, the geometric drag coefficient for a circular pore in a membrane of thickness h are [3,47,48] α1 = h and α2 = 2πr.…”

Preparation and In Vitro Cytotoxicity Assessments of Spherical Silica-Encapsulated Liposome Particles for Highly Efficient Drug Carriers

“…Figure b shows the SEM images and the particle size distribution of the SLPs as a function of the reaction temperature. The size of SLP particles is in the range of 1.78–3.15 μm as the reaction temperature increases, and the SLPs show an increase in particle size. , Wide-angle X-ray diffraction and Fourier transform infrared spectroscopy measurement (data not shown) of the SLPs were performed as a function of reaction temperature, and the results were almost the same as for the variation with TEOS concentration and reaction time process. In this case, the main XRD diffraction peak of silica was seen at 2θ = 20.11°, and several characteristic vibrations of FT-IR spectra were seen at 1215, 1749, and 2925 cm –1 , corresponding to Si–O–Si, CO, and C–H.…”

“…The size of SLP particles is in the range of 1.78−3.15 μm as the reaction temperature increases, and the SLPs show an increase in particle size. 31,32 Wide-angle X-ray diffraction and Fourier transform infrared spectroscopy measurement (data not shown) of the SLPs were performed as a function of reaction temperature, and the results were almost the same as for the variation with TEOS concentration and reaction time process. In this case, the main XRD 2.4.…”