Doubling particle capture from laminar flow requires quadruple force

Particle trajectories in a parabolic and constant velocity profile

Capturing particles or droplets from a flow is relevant for various applications like continuous separators, aerosol removal, and magnetic drug targeting. In a laminar flow, doubling the capturing of a small fraction of particles turns out to require a four times higher force or length of pipe or a four times lower flow velocity (Eq. 12). This is because particles from twice as far away have to be captured from a location where the flow velocity in a laminar flow is also twice as high. This simple scaling law, with an analytical correction for flow through cylindrical pipes (Eq. 35),  turns out to hold well for a wide range of different force fields.

Magnetic particle motion in a Poiseuille flow
J. W. Haverkort, S. Kenjeres, and C. R. Kleijn

Annals of Biomedical Engineering, vol. 37, nr. 12, p. 2436-2448
© 2009 DOI: 10.1007/s10439-009-9786-y

Magnetic drug targeting possible even in large arteries


By attaching drugs to magnetic nanoparticles, magnetic fields can concentrate them at the location in the body where they are needed. Pre-clinical trials have shown some potential for treatment of superficial cancer tumors. More applications could be envisioned when targets deeper in the body can be reached.

Our 2009 publication was perhaps the first three-dimensional simulation showing that it is possible to capture particles from the bloodstream of large arteries like the coronary and carotid artery. This opens up the possibility of applying the technique to combat also cardiovascular diseases.

Because of an old theorem, the drugs can only be held in a stable position deep inside the body using a dynamic magnetic field configuration or in a quasi-stable position using carefully tailored magnetic fields. Despite this fundamental complication, progress remains to be made today, particularly from the perspective of computational modeling.

Computational Simulations of Magnetic Particle Capture in Arterial Flows
J. W. Haverkort, S. Kenjeres, and C. R. Kleijn

Electrical charge can be sustained in a highly conducting fluid


Magnetohydrodynamics of insulating spheres
J. W. Haverkort, T. W. J. Peeters

A widespread notion in the field of ‘ideal’ magnetohydrodynamics describing highly conducting fluids there can be no electrical charge accumulation. Any nonzero charge will quickly redistribute over a short enough time-scale to be irrelevant. One can however easily show that in the presence of a magnetic field Lorentz forces can act to sustain a finite charge density, see equation 3.  This charge and the associated electric field have a distinct influence on the current distribution and the resulting forces on non-conducting inclusions and bubbles in a conducting fluid as shown in the above picture and explained in the paper.


Magnetic field shape forces bubbles out of liquid metals

In the industrial processing of metals, magnetic fields are often used to stir or break liquid metals, calm free surfaces, influence turbulence properties and remove unwanted inclusions.

Even though bubbles and solid inclusions in liquid metals may not conduct electricity themselves, because the surrounding metal does, some interesting magnetohydrodynamic effects arise, like the electromagnetic Archimedes force, and electromagnetically induced drag.

In a continuous caster, liquid steel enters a mold and slowly turns into a solid slab. Under the influence of unwanted flow patterns small bubbles or inclusions can be trapped into the steel, forming elongated ‘blowholes’ after rolling the steel slabs. To suppress unwanted liquid steel flows enormous electromagnets fully surrounding the casting mold. Currents induced by the flow though this magnetic field generate Lorentz forces that brake the flows.

Through computer simulations we discovered a new effect on gas bubbles in the submerged entry nozzle of a continuous caster. We show that, depending on the shape of the magnetic field, the so-called electromagnetic Archimedes force can force  Argon bubbles radially outwards. This effect may be used improving the anti-clogging capacity of gas.

Magnetohydrodynamic Effects on Insulating Bubbles and Inclusions in the Continuous Casting of Steel
J. W. Haverkort and T. Peeters