Hans O. Åkerstedt

Respiratory Deposition of Fibers in the Non-Inertial Regime—Development and Application of a Semi-Analytical Model

A semi-analytical model describing the motion of fibrous particles ranging from nano- to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10–100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range.

Electromagnetic braking of the flow of a liquid metal with a free surface

Abstract The electromagnetic braking of liquid metal flowing over a moving boundary is considered. The flow is two dimensional and the upper boundary is a free surface. The main interest of this flow originates from the application of horizontal belt strip casting. In this process, the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The bottom of the belt is cooled by water and the liquid is fed onto the belt through a slit. This results in a flow that can be modelled as a flat free jet impinging onto a horizontally moving boundary. The flow after the impingement region is analysed using the boundary layer equations. Here, the flow depends on the Reynolds number R, the Froude number F, the Hartman number M, and the ratio of the belt velocity to jet velocity, β. For β F−2/3, there is no hydraulic jump and the film thickness grows smoothly into the final state with constant thickness and uniform velocity. The braking length for the case without hydraulic jump is shown to be of order O(F2/3Ra/2) without magnetic field and of order O(M−2Ra/2) with magnetic field, where a is the jet width. Thus, the magnetic field decreases the braking distance considerably. This result is favourable for both the stability of the flow and for the solidification process in the horizontal belt strip casting process.

A three-dimensional analysis of the flow past an open terrestrial magnetopause

We present a three-dimensional analysis covering an investigation of the behavior of the magnetosheath plasma velocity and the magnetic field during the transfer from the magnetosheath to the magnetosphere. Magnetic reconnection is assumed to occur at an arbitrary line parallel to the y-axis, located in a region along the magnetopause stretching from the sub-solar point to the north. We do not focus on the process itself, but on its implications for the plasma flow and the magnetic field outside the diffusion region. Viscosity and resistivity are included in the magnetohydrodynamic equation of motion as non-ideal effects. The governing equations are solved approximately using the method of asymptotic expansions, with expansion in orders of large Reynolds and Lundquist numbers. We present two classes of solutions describing the properties north and south of the reconnection line, respectively. Results are presented for two locations of the reconnection line at distances of two and seven Earth radii from the sub-solar point correspondingly. It is shown that the velocity increases faster north of the reconnection line, and that the effect intensifies as the location of the reconnection line moves further away from the sub-solar point. It is also shown for this case, that there is less variation of the magnetic field and an increase in the field strength.

Damping mechanisms of perturbations in electromagnetically braked horizontal film flows

The stability of shear and surface modes in an electromagnetically braked free surface liquid metal flow over a horizontally moving boundary is considered. The main objective is to investigate the stabilizing effect of a transverse magnetic field of the film flow appearing in connection with the horizontal belt strip casting. The flow is two-dimensional and the upper boundary is a free surface. In the stability analysis the film flow is approximated as parallel and is therefore based on the MHD-modified Orr–Sommerfeld equation. Numerical calculations present the linear growth rate for shear and surface mode instabilities. A transverse magnetic field is found to have two damping mechanisms. For low Hartmann numbers the main mechanism is due to the braking of the flow, reducing the shear stress. The other mechanism is due to dissipation by the Joule effect.

Three‐dimensional stability of drift vortices

The three‐dimensional stability of drift vortices that are two‐dimensionally stable in the framework of the Hasegawa–Mima equation is studied. The three‐dimensionality is caused by a coupling of the vortex to ion‐acoustic waves that propagate along the magnetic field. It is concluded that this coupling does not significantly destabilize the vortex. A general stability criterion is derived that guarantees stability if the ratio between the parallel wave number k and the azimuthal mode number m is large enough. It is also found that no instability exists in the limit k→0 if the potential vorticity is a strictly decreasing function of r. Such profiles are typical for vortices that are two‐dimensionally stable. Some particular profiles where the potential vorticity vanishes outside some radius are also examined. In one case an instability with m=1 is found, but a numerical solution of the eigenvalue problem shows that the maximum growth rate is very small, three orders of magnitude smaller than the angular ve...

Three-dimensional flow near a reconnection site at the dayside magnetopause: analytical solutions coupled with MHD simulations

We present a coupling between an analytical three-dimensional model covering the plasma flow behaviour through the magnetopause transition layer near a reconnection site, with results from a global MHD simulation describing the plasma flow in the magnetosheath. The structure of the plasma flow near a reconnection site at the dayside terrestrial magnetopause is investigated, together with the development of the magnetopause transition region.

Initial solidification in liquid metal film flow over a moving boundary

The initial solidification problem of a two-dimensional liquid metal film flow over a heat extracting moving boundary is studied. Analytical solutions in the limit of large Peclet numbers are found. It is shown that the point of initial solidification depends on the Peclet number, the Biot number and the superheat. The initial growth of the solidified phase is found to have a quadratic dependence of the distance from the point of initial solidification. The results are applicable to continuous strip casters.

Time-Dependent Deposition of Micro- and Nanofibers in Straight Model Airways

In this paper, we increase the understanding of the influence of the breathing pattern on the fate of inhaled non-spherical micro and nanoparticles and examine the accuracy of replacing the cyclic ...

Solar wind flow near a reconnection site at the dayside magnetopause : development of an existing three-dimensional model

An improvement of an existing three-dimensional analytical model describing the solar wind flow near a reconnection site at the dayside magnetopause is reported. Introducing an arbitrary orientation of the reconnection line, general solutions for the plasma velocity and magnetic field during the transition of the magnetopause are presented, together with the development of the magnetopause transition layer away from the reconnection site.

A two-dimensional analysis of the compressible flow near a reconnection site at the dayside magnetopause

An improvement of an existing three-dimensional analytical model describing the solar wind flow near a reconnection site at the dayside magnetopause is reported. Introducing an arbitrary orientatio ...