Flow of Stokesian fluids through conical ducts

Pressure-Driven Nanoparticle Transport across Glass Membranes Containing a Conical-Shaped Nanopore

“…The GNM consists of a cylindrical capillary and a conical nanopore in series. The flow rate Q (m 3 /s) is readily derived in terms of the solution viscosity, η, (see ref and the Supporting Information for details) Q = normalΔ P ( 3 π 8 η ) false[ 3 L R 3 − 4 + cot nobreak.25em normalθ false( R 1 − 3 − R 2 − 3 false) false] − 1 where Δ P = P 3 – P 1 , L is the height of the solution in the cylindrical capillary, R 1 and R 2 are the small and large orifice radii of the nanopore, θ is the half-cone angle of the nanopore, and R 3 is the capillary radius.…”

Fluid dynamics in conically tapered microneedles

“…The three theoretical approaches showed varying levels of agreement with our experimental measurements. Kemblowski and Kiljanski24 modeled fluid flow through a conical geometry by assuming that the axial velocity profile at each axial location was similar to the Poiseuille velocity profile for flow in a circular tube. This model is most valid in the slow‐flow limit, where Re < 1, and for small cone half‐angles.…”

“…These theoretical approaches have been validated macroscopically using only limited or no data and have not been validated at microscopic dimensions. The experimental data that do exist,24 as well as the more extensive numerical analysis of fluids in conical channels,25, 26 is almost exclusively at low Reynolds numbers, where viscous effects dominate inertial effects. For this reason, our data can also be used to validate previous analytical and numerical predictions from the literature.…”

Hyperbaric Swimming Simulator

“…Two phenomena are similar when some dimensionless units of physical parameters characterizing these phenomena are both equal. These dimensionless parameters are called modules, numbers of criteria Φ [2].…”