At the Chair of Thermodynamics a special measuring system was developed to measure the dynamic viscosity and the density of gases by a combined measuring procedure over large ranges of temperature and pressure. By carrying out the density and the viscosity measurement in the same compact measuring cell it is possible to measure the viscosity directly as a function of temperature and density. The density measurement is based on the buoyancy principle according to our single-sinker method [68, 76] and the viscosity measurement is a newly developed rotation procedure [133].

Principle of the combined viscometer and densimeter.

The figure above shows the principle of the combined viscosity and density measurement. The essential feature of the single-sinker method is that the forces acting upon the sinker are transferred without contact through the wall of the pressurized measuring cell by an electronically controlled magnetic suspension coupling [71, 76] to the balance, which is placed at ambient conditions. The electromagnet is arranged outside of the measuring cell and carries the permanent magnet as a component of the rotational body, which is placed in the measuring cell. Since this condition is physically not stable, the vertical position of the rotational body is controlled with an inductive sensor placed outside of the measuring cell and an electronic control unit, which causes a stable free suspension state of the rotating body.

The single-sinker densimeter is based on a buoyancy method according to the Archimedes principle, which is applied in a new way. The principle of this special single-sinker method is illustrated in the next figure. Thereby, the vertical position of the rotational body is detected by a position sensor and controlled in a direct and fast loop. Thus, several vertical motions of the permanent magnet (included inside the rotational body) are generated automatically. In this way, soft up- and downward movements of the permanent magnet can be realized, by these movements the cylindrical sinker (titanium based alloy) can be coupled (density measuring position) and decoupled (viscosity measuring position); this position is also called zero-point position. 

Density measurement principle.

With the single-sinker density measurement procedure the density is measured by weighting the sinker surrounded by the fluid. The electronically controlled magnetic suspension balance transfers without contact through the wall all vertical forces affecting the lowering body (weight force and buoyant force) to the analytical balance. By the separate arrangement of the force measuring instrument (environmental conditions) and the sinker (measuring cell) precise weighings can be realized by this procedure, even at high pressures and temperatures.

Viscosity measurement principle.

With the viscosity measuring procedure shown in the figure above, the dynamic viscosity of the measuring fluid is determined by the slow decrescence rotation speed of the free-floating and unpowered rotating body. Here, the magnetic suspension coupling serves as frictionless bearing so that the deceleration of the rotation is caused only by the viscous momentum produced by the fluid.

During the viscosity measurement the rotating body with the permanent magnet remains in the zero-point position mentioned before (see figure above). The freely suspended permanent magnet is embedded in the rotating body, which is immersed in the fluid. The rotating body has the shape of a slender cylinder, which is produced from an aluminium alloy with good electrical conductivity. It is surrounded concentrically by the sinker and the wall of the measuring cell. At the beginning of a viscosity measurement the rotating body is contactlessly accelerated from the resting position to a certain rotational speed by a cyclic electromagnetic field, which is generated by four induction coils placed outside the measuring cell [133]. When the desired rotational speed is reached, the driving currents are turned off so that no interaction between the rotating body and the drive remains. After shutting off the drive, the rotational speed starts to decrease because of the viscous momentum caused by the fluid.

A clock, similar to a frequency counter, measures the times t_i needed for each revolution n_i of the cylinder and transfers these data to a computer. The computer stores the periods t_i and calculates the absolute time t_n corresponding to the n-th revolution by adding up the periods t_i. By this procedure, data pairs (n, t) are generated which allow the analysis of the decay of the rotational speed due to the viscosity of the fluid. Theory predicts [133] that the number of revolutions of the cylinder n(t) varies exponentially with the time t to an asymptotic value n_∞: n(t)=n_∞⋅(1−e^−Dt).

The characteristic value is the so-called damping constant D, which can be interpreted as the relative decrease of the rotational speed. The damping constant D is the quantity calculated from the actual measuring signal n(t) of the viscometer since it is proportional to the viscosity, η=z⋅D−D_R⁄C. The damping constant D_R corrects the measured value of D for the residual drag. The factor C is the so-called apparatus coefficient and z is the nonstationary parameter, which interprets the nonstationary character of the flow as an increase in the moment of inertia of the cylinder due to the rotating fluid [133]. The values of the apparatus coefficient C and the nonstationary parameter z mainly depend on the geometric parameters of the measuring system and the mass of the rotating body. Moreover, the nonstationary parameter z depends also on the density of the surrounding fluid.

The combined viscometer-densimeter covers a viscosity range up to 150 µPa s and a density range up to 2000 kg⁄m³ at temperatures from 233 K to 523 K and pressures up to 30 MPa. Comprehensive measurements on nitrogen, argon, methane, helium, neon and krypton have been made on selected isotherms. All measurements show that the estimated total uncertainty of 0.15 % to 0.4 % in viscosity and of 0.02 % to 0.05 % in density is clearly met.

The following film clarifies the function mode of the measuring procedure: