Page 251 - Gas Adsorption Equilibria

5. Oscillometry 237

2. MEASUREMENT OF PURE GAS ADSORPTION
EQUILIBRIA (N=1) BY SLOW OSCILLATIONS OF
A ROTATIONAL PENDULUM

2.1 Experimental

Pure gas adsorption equilibria can be measured by observing slow
oscillations of a rotational pendulum bearing the sorbent material. An
instrument of this type has been designed and built at the author’s institute
*)
during (1995-1997), Fig. 5.1. It basically consists of a disk bearing a ring slit
filled with homogeneously distributed sorbent material (pellets, powder etc.),
fixed to a torsional wire and stabilized by a stem bearing a small mirror to
reflect a laser beam, Fig. 5.2. The pendulum is placed in a vessel (adsorption
chamber) which can be filled with sorptive gas. The adsorption chamber
should be placed within a thermostat and equipped with manometer(s) and
thermometer(s).

To observe the motion of the pendulum a laser beam is sent to the mirror,
the reflected beam crossing during its motion in radial direction within a
horizontal plane 2 diodes placed at known angles Fig. 5.2. The diodes
of a couple produce by photo effect electric signals of opposite signs, hence
the time when the reflected beam is crossing the area between the two diodes
can be detected very accurately, cp. signal sample given in Fig. 5.3. The series
of time signals produced in this way by a slow damped oscillation of the
pendulum in the gas provides the basis to fit an ideal damped harmonic
motion, Eq. (5.7) to it and to calculate the respective angular frequency and
logarithmic decrement by a Gaussian minimization procedure. To start the
motion of the pendulum, the instrument is based on a ball bearing allowing to
rotate it by an arbitrary angle, cp. Fig. 5.1. Choosing this at about 90 ° and
**)
keeping the instrument in this position for a while , the pendulum inside the
instrument starts to move due to the retarding moment of the torsional wire.
Returning then the whole instrument to its original position will maintain
motion of the pendulum, this procedure resulting now in an oscillation. This
however will fade away slowly due to internal friction of the wire and the
flow of gas surrounding the pendulum.

* ) The instrument meanwhile has been transferred to the Institute of Thermodynamics, Dept.
Chem. Engineering, University of Dortmund, Dortmund (2003).
** )
The time interval to be chosen for this distorted position of the pendulum depends on its
design parameters, especially its mass and may vary from a few seconds up to a minute.