## 1 Introduction  
Black liquor is a major by-product of chemical pulp production [1]. It helps to establish economically effective pulp mills, because during the chemical recovery cycle, black liquor is used as an energy source for the pulp mills, as well as the source for inorganic process chemical recovery and reuse [1; 2; 3; 4]. In the case of the kraft process of turning wood into wood pulp, the cellulose fibers are separated from other components during digestion in aqueous solutions of sodium hydroxide and sodium sulfide at elevated temperatures and pressure [1; 2]. Expanded cooking liquor is called black liquor, and it contains organic and inorganic compounds, as well as water [1; 5; 6]. The organic part is characterized by the degradation products of wood, such as lignin, polysaccharides (mainly hemicelluloses and carboxylic acids), and extractives (i.e., resins and fatty acids) [1; 5]. The inorganic part is mainly composed of soluble sodium salts [6]. There are also non-processing elements, which include, for example, potassium, chlorine, calcium, aluminum, silicon and iron ions, and these may originate from the initial raw materials, process water, make-up chemicals, waste streams, and/or equipment corrosion [1; 4; 7]. The chemical composition of black liquor is dependent on the origin of the raw fiber material and thus determines its physical properties. These properties include density, viscosity, rheological behavior, calorific heating value, and boiling point rise [1]. Understanding the physical properties of black liquor helps in predicting its behavior in the subsequent recovery processing [1]. The solids content (SC), or total SC, is one of the key parameters used to control the evaporation process, and it is used to estimate its efficiency. The analytical techniques of the process can be characterized by the method of measurement as off-line, at-line, in-line, or online types [8; 9]. In the off-line methods, the samples are collected from the process and are analyzed in the laboratory. For the at-line techniques, the analyses are made in close proximity to the process. Whilst for the online processes, the analytical equipment is connected to the process line, for example, using a bypass loop [9]. The sample is automatically delivered to the probe. Finally, using the in-line techniques, the analytical instruments do not require any sampling or connecting lines to transfer the sample [9]. These probes can be directly immersed into the process, wherein optical probes are typically used in the in-line techniques [9]. Traditionally, measurement of the SC is performed gravimetrically by drying at 105 \({}^{\circ}\)C [10] until a constant weight is reached. Although the technique is simple and robust, it is also time-consuming [2] and requires several sample preparation steps [2], such as the dilution of concentrated liquors and the addition of sand to the samples. Consequently, this gravimetric method is rarely automated or implemented in the online monitoring. Other methods, such as thermogravimetric analysis, differential scanning calorimetry, and multiple headspace extraction gas chromatography, have shown reliable results and were proposed as alternatives to the traditional methods of SC measurement [2; 11]. Despite allowing much shorter analysis times, these off-line techniques are considered costly. Online and in-line measurements of the physical properties of different constituents in the kraft pulping process can be performed using optical methods, such as refracometry [12] and Fourier transform near-infrared spectroscopy (FT-NIRS) [13; 14]. The main disadvantage of such methods is that the probes of the optical devices require regular cleaning. Fouling and a consequent reduction in the efficiency of the evaporators and the measuring equipment may occur due to scaling formation [2; 6]. Another way to control the process of evaporation online is to measure the density or viscosity of the black liquor.