For accurate measurements of saturated-liquid and saturated-vapour densities of pure fluids, a new type of a hydrostatic balance densimeter was developed in the early 1980s [27, 32]. Densities in the homogeneous gas and liquid region including the critical region can also be measured over wide ranges of temperature T, pressure p, and density ρ. At present, the densimeter covers a temperature range from 60 K to 340 K, a pressure range from 0.001 MPa to 12 MPa, and a density range from 1 kg/m³ to 2000  kg/m³ {Uncertainties: ΔT ≤3 mK; Δp/p ≤(0.004% + 30 Pa); Δρ/ρ ≤(0.010% + 0.001 kg/m³)}. The total uncertainty in the measured density, including the uncertainty in temperature and pressure measurement, is ≤0.02% to ≤0.01% for the most regions of the fluid state. The first figure shows a photo of the densimeter in our laboratory.

The principle of this two-sinker densimeter is illustrated in the second figure. The method used for density measurements is based on the Archimedes' buoyancy principle applied in a novel way as a differential method. Instead of the usual single sinker, two specially matched sinkers are used; one of the sinkers is a gold covered quartz-glass sphere (V_S ≈ 24.5 cm³; m_S ≈ 54 g; ρ_S ≈ 2200 kg/m³), and the other is a disk of solid gold (V_D ≈ 2.8 cm³; m_D ≈ 54 g; ρ_D ≈ 19300 kg/m³). Both sinkers have the same mass, the same surface area, and the same surface material, but a considerable difference in volume ((V_S − V_D) ≈ 21.7  cm³). For density measurements the sinkers can be put alternately on a sinker support, or lifted from it by means of a sinker-changing device. This sinker support is connected to a commercial analytical balance (Sartorius R 160 P, weighing range 160 g, resolution 10 μg) by a thin wire via a magnetic suspension coupling so that the “apparent mass difference” Δm* =  (m_D* − m_S*) of the sinkers, surrounded by the sample fluid, can be accurately measured. By means of the magnetic suspension coupling [71], the suspension force is contactlessly transmitted from the pressurized measuring cell to the balance at ambient conditions. Thus, the density ρ of the sample fluid in the measuring cell can be determined by the simple equation: ρ = (Δm* − Δm_Vac) / (V_S − V_D), where Δm_Vac = ( m_D − m_S) corresponds to the very small mass difference of the two sinkers which is accurately determined by weighing in the evacuated measuring cell. The volumes of the two sinkers are calibrated with water at reference conditions (T = 293.15 K, p = 0.1 MPa) with an uncertainty of 0.003%; the dependence of the volume of quartz glass and gold on temperature and pressure can be calculated very accurately [27]. (In the temperature range from 60 K to 340 K and at pressures up to 12 MPa, the uncertainty of the volume difference (V_S − V_D) is less than 0.008%.)

Owing to the rigorous application of the Archimedes' principle in a differential mode, all disturbing side effects which usually reduce the accuracy of such density measurements (e.g. buoyant forces on the sinker suspension, surface-tension forces between the sample liquid and the suspension wire, and a great part of the uncertainty of the weighing device) are automatically compensated. Even the adsorption of gas on the sinker surfaces is approximately compensated because both sinkers have the same surface area and the same surface material. Since the measured mass difference Δm*, is directly proportional to the density ρ of the sample fluid, even very low gas densities can be very accurately measured. To improve the accuracy of the measured value Δm*, the sinkers are changed several times and then an average value is used; the scatter only amounts to a few digits. Depending on the design and the operating range of individual densimeters, very small uncertainties in density of only a few 0.001 % and less are achievable by means of this two-sinker method.

A key component of the weighing system is the magnetic suspension coupling [71]. By means of this coupling, the suspension force is contactlessly transmitted from the pressurized measuring cell to the balance at ambient conditions. This coupling consists of an electromagnet, attached to the underfloor weighing hook of the analytical balance, and a permanent magnet connected by a thin wire to the sinker support. The permanent magnet is placed in a pressure-proof coupling housing that separates the pressure region from ambient atmosphere and the two magnets from each other. The coupling housing is made of beryllium copper, a nearly non-magnetic metal. When the coupling is switched on, the permanent magnet is gently attracted to the electromagnet by means of a position sensor and a control system. The distance between the two magnets is controlled in such a way that the current through the electromagnet (with 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. After switching on the coupling, it takes only a few seconds to reach a stable magnetically-suspended state.

The basic design of the two-sinker densimeter is shown in the next figure. The densimeter consists of a copper measuring cell, three copper radiation shields and a copper intermediate plate, a stainless-steel vacuum vessel, a magnetic suspension coupling, and a commercial analytical balance. The measuring cell and the intermediate plate are suspended by three thin stainless-steel tubes, which also serve for inlet and outlet of the cooling liquid. The temperature of the measuring cell can be accurately controlled by means of a cooling liquid (which is liquid nitrogen for T ≥ 84 K or liquid helium for T < 84 K) and an electrical heater in conjunction with a platinum resistance thermometer; the local and temporal temperature gradients of the measuring cell are less than 0.001 K. The pressure is measured with a relative dead weight gauge and the atmospheric pressure is measured with an absolute dead weight gauge.

The procedures to measure the saturated-liquid and saturated-vapour densities and the densities in the homogeneous liquid region at pressures below the critical pressure are not described here. For the measurement of these properties special devices (liquid-level indicator, reference cell, pressure adjusting cell [57], etc) have been integrated in the densimeter and different sophisticated procedures are applied (e.g., see [99]).

Up to now, the pρT behaviour of many technically and scientifically important pure fluids has been comprehensively measured by using the two-sinker densimeter; for more information see pρT measurements.

The two-sinker densimeter is comprehensively described in [27] and the present state is summarized in two recent review articles [141, 143]. The application of the two-sinker method by other research and metrology laboratories is also briefly described in theses articles.

A special two-sinker densimeter for accurate measurements of natural gas densities has also been developed for the gas industry; see research projects for industry, accurate gas densimeter.