Current through a straight line
(proof of principle)

As a starting point, the principle of this manipulation technique is tested with the simplest setup. A single straight conducting line with two contact pads at both ends is patterned with optical lithography. Above the conducting line, a drop of water with magnetic markers is placed. A current through the line creates a magnetic gradient field, that magnetises the superparamagnetic markers, aligns them to the magnetic field and pulls the markers to the conducting line. Figure 3.6 shows 5 selected images of the video of this simple experiment.

Figure 3.6: A 5mA current through the straight conducting line (width = 3.8$\mu$m) attracts the magnetic marker. The images have a size of 63$\mu$m $\times$ 37.8$\mu$m. See the CD for the complete Video.

[0sec]     [10sec]     [20sec] [30sec]         [33sec]

A constant current of 5mA is already enough to attract a magnetic marker that is about 33$\mu$m away. Without the magnetic field, the marker just follows the brownian motion [78], but with the magnetic gradient field it slowly moves towards the conducting line. The marker accelerates towards the conducting line until it reaches the local field maxima on top of the line. Before it reaches the conducting line, the maximum velocity of the bead is about 6$\mu$m/sec.

In order to describe the forces that act on the magnetic marker, the friction of the marker in the fluid (STOKES' law) has to be subtracted from the magnetic force (see equation 1.10 on page ):

$$\vec{F} = \vec{F}_{\rm mag} - \vec{F}_{\rm friction}= \frac{m \cdot \mu_0 I}{2\pi R^2} - 6 \pi r \eta \vec{v}$$ (3.1)

Here we assume a spherically shaped marker with radius $r$, a viscosity $\eta$ of the water drop and an actual velocity $\vec{v}$ of the marker. Using equation 3.1, the maximum possible velocity can be calculated, when $\vec{F}_{\rm mag} = \vec{F}_{\rm friction}$. With a maximum current of $I=150$mA, a magnetic moment of $m=1.82$fAm$^2$ of the particle (see table 1.1), a distance $R = 2$$\mu$m, a radius of the marker $r=1$$\mu$m and a viscosity for water of $\eta = 1$mPasec at room temperature, the maximum possible velocity is:

$$\vec{v} = \frac{m \cdot \mu_0 I}{12\pi^2 r \eta R^2} = 7\cdot10^{-4} \frac{\rm m}{\rm sec}$$ (3.2)

This initial experiment proves that in principle the manipulation works well. Several more examples for particle manipulation are following.