For accurate density measurements of fluids in the homogeneous gas and liquid region, a novel single-sinker densimeter was developed in the early 1990s [68, 76, 109]. It covers a temperature range from 233 K to 523 K, a pressure range from 0.1 to 30 MPa, and a density range from 10 kg/m³ to 2000 kg/m³. This densimeter complements our approved two-sinker densimeter in the pρT region at higher temperatures and pressures. The total uncertainty in the density measurement, including the uncertainty in temperature and pressure measurement, is ≤0.02% for the most regions of the fluid state, except for the low gas-density region below about 40 kg/m³. The following figure shows a photo of the densimeter in our laboratory.

The principle of the novel single-sinker densimeter is presented in the second figure. The method for density measurement is based on the Arichimeds' buoyancy principle applied in a special way with a magnetic suspension coupling and compensation weights on the balance. The sinker, a cylinder of quartz glass (V_S ≈  26,5 cm³; m_S ≈ 60 g; ρ_S =  2200 kg/m³), is contained in a pressure-proof measuring cell. For density measurements, the sinker can be connected with a commercial analytical balance (Mettler AT 201, weighing range 205 g, resolution 10 μg) via a magnetic suspension coupling in combination with a sinker coupling and decoupling device. Thus, the density of a sample fluid in the measuring cell can be determined by the simple relation: ρ = (m_S − m_S* )/ V_S, where m_S is the “true” mass of the sinker, m_S* is the “apparent” mass of the sinker, when surrounded by the sample fluid, and V_S is its volume. The mass, m_S, of the sinker is accurately determined by weighing in the evacuated measuring cell. The volume of the sinker is calibrated with water at reference conditions (T = 293.15 K, p = 0.1 MPa) with an uncertainty of ≤0.004%; the dependence of the volume of the quartz-glass sinker on temperature and pressure can be calculated very accurately. (In the temperature range from 233 K to 533 K at pressures up to 30 MPa the uncertainty of the sinker volume is ≤0.010 %.) The uncertainty in the density measurement is ≤(0.015% + 0.002 kg/m³).

The main component of the single-sinker densimeter is a new type of a magnetic suspension coupling. By means of this coupling, the suspension force is contactlessly transmitted from the pressurized measuring cell to the balance at ambient atmosphere. The coupling consists of an electromagnet, a permanent magnet, a position sensor and a control system. The electromagnet is attached to the underfloor weighing hook of the analytical balance and the permanent magnet is connected to the sinker in the measuring cell by means of the sinker coupling and decoupling device. The pressure-proof coupling housing, which separates the two magnets and also the pressure region from ambient atmosphere, is made of beryllium copper, a magnetically neutral metal. To achieve a freely suspended state of the permanent magnet, its position is controlled by a direct analog control circuit (PID controller and position sensor). By means of a superimposed microcontroller driven digital set-point controller, several vertical motions of the permanent magnet can be generated. In this way, soft up- and downward movements of the permanent magnet can be achieved and via the sinker coupling and decoupling device the sinker can be coupled and decoupled with the permanent magnet. In the tare position, the permanent magnet is suspended at a relatively large distance (about 6 mm) from the top of the coupling housing; see the drawing on the left-hand side in the figure. In this position, the sinker is decoupled from the permanent magnet and the balance can be tared to zero. In order to achieve the measuring position (see the drawing on the right-hand side in the figure), the permanent magnet is gently moved upwards (up to about 5 mm) and lifts the sinker by means of the coupling device. In this way, the sinker is coupled to the balance and can be weighed. (The weighing pan and the weighing hook of the analytical balance are controlled at a constant vertical position over the entire weighing range by the balance itself.) To improve the accuracy of the measured values m_S or m_S* (mass and apparent mass of the sinker, respectively), the sinker can be coupled and decoupled several times and an average value can be used; the scatter only amounts to a few digits. Moreover, due to the differential weighing between the tare position and measuring position the zero-point drift of the balance is compensated. After switching on the coupling, a few seconds are required to reach a stable tare or measuring position. Both positions are stable in a way that the performance of the analytical balance (resolution 10 μg) is not adversely affected by the magnetic suspension coupling. Moreover, in both positions of the permanent magnet, the distance between the two magnets is controlled in such a way that the current through the electromagnet (with its soft iron core) is zero on average and the suspension force is then completely transmitted by the permanent magnet. This avoids self-heating of the electromagnet and its surroundings that would produce convection flows. This new type of a magnectic suspension coupling was especially developed in the early 1990s to improve the density measurement technique [71].

In order to achieve high accuracy by using the single-sinker densimeter even at relatively low densities, the analytical balance is operated only near its tare point by means of a basic load compensation mechanism (see figure). In the tare position a tantalum weight (m_Ta ≈ 82 g, V_Ta ≈ 4.9 cm³, ρ_Ta ≈ 16700 kg/m³) is placed on the balance. When switching to the measuring position, the tantalum weight is automatically exchanged with a titanium weight (m_Ti ≈ 22 g, V_Ti ≈ 4.9 cm³, ρ_Ti ≈ 4500 kg/m³). Since in this position the sinker (m_S ≈ 60 g) is coupled with the balance, the total load on the balance is again about 82 g as in the tare position. In this way, errors of the balance due to changes in the slope of the characteristic line are drastically reduced. Since both weights have the same volume, the buoyancy effect of the ambient air on the weights is compensated.

The basic design of the single-sinker densimeter is shown in the third figure. It consists of the measuring cell containing the sinker, the magnetic suspension coupling, the analytical balance, an inner and outer double-wall thermostat, and a vacuum vessel for insulation of the two-stage thermostat. Depending on the temperature range, methanol or heat transfer oil are used as thermostating liquids which are prethermostated outside the vacuum vessel by a special thermostat (Huber Unistat 380 W HT, Germany). The measuring cell can be evacuated and filled with the sample fluid via two tubes which also allow the entire system to be flushed. The temperature is measured with a 25 W platinum resistance thermometer (Rosemount 162 D, USA) in conjunction with an accurate resistance measuring bridge (ASL F700A, UK); the uncertainty in the temperature measurement is between ≤0.008 K, including local and temporal temperature gradients. The pressure is measured with a relative dead weight gauge and the atmospheric pressure is measured with an absolute dead weight gauge (Desgranges et Huot 5200S² and 2171, France) via a differential pressure indicator (Rosemount G 1151 HP, USA); the uncertainty in the pressure measurement is ≤0.006 % or ≤50 Pa, whichever is greater.

Up to now, many technically and scientifically important pure fluids have been measured by using this single-sinker densimeter, for more information see pρT measurements.

The single-sinker densimeter is comprehensively described in [68] and the present state is summarized in two recent review articles [141, 143]. The application of the single-sinker method by other research and metrology laboratories is also briefly described in these articles.

In order to simplify further the single-sinker densimeter, a compact version was developed in the 1990s [96, 112, 76, 141, 143]. The next figure shows the basic design of this compact single-sinker densimeter. In this version, the measuring cell and the coupling housing of the magnetic suspension coupling have been unified, yielding a very compact design requiring only small amounts of sample fluid. Owing to its compact design this version is also suitable for pressures up to 200 MPa and temperatures up to 773 K. The cylindrical sinker, with a hole in its centre, is made of titanium (ρ_Ti ≈ 4500 kg/m³), quartz glass (ρ_Q ≈ 2200 kg/m³), or single-crystal silicon (ρ_S ≈ 2329 kg/m³); its volume is about 20 cm³.

On the basis of this compact version of the single-sinker densimeter, a new apparatus for combined measurements of the viscosity and the density of fluids was also developed in the late 1990s; for more information see combined viscometer-densimeter.

In the meantime, compact versions of the single-sinker densimeter are also commercially available (Rubotherm Präzisionsmesstechnik, Germany, www.rubotherm.de); such densimeters can be designed for pressures up to 200 MPa and temperatures up to 773 K.