The force acting on a levitating droplet/particle can be calibrated
by using gravity as in the Millikan experiment. It is convenient to
tilt the chip, i.e. to use "magnetic incline". We have used this
to achive femtonewton resolution in force. However, this resolution
can be improved by several orders of magnitude.
Consider typical, 3 micron in diameter droplet.
It has volume about 15 femtoliter and weight 150 femtonewtons.
By controlling tilt angle with resolution of 0.1 millirad, it is
feasible to calibrate force acting on the droplet with resolution
15 attonewtons. Typically droplet(s) are captured in a potential well.
Tilt means droplet shift in this well. The "force constant" in such
well in the direction parallel to the slit between the magnets
can be as small as 10 attonewton/micron. With video system
(microscope + camera) resolution of 0.1micron this provides possibility
to control force with attonewton resolution. Of course, with such
small value of force constant the amplitude of brownian motion (see next
movie) can reach 10 micron.
However, large enough statistic provides possibility
for accurate measurements (see
for more details).