Coexistence Curve, Density, and Viscosity for the Binary System of

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Coexistence Curve, Density, and Viscosity for the Binary System of Perfluorohexane + Silicone Oil Sergiy Ancherbak, Viktar Yasnou, Aliaksandr Mialdun, and Valentina Shevtsova*

Downloaded via UNIV OF SOUTH DAKOTA on July 6, 2018 at 06:25:29 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Microgravity Research Center, Université libre de Bruxelles, CP-165/62, Av. F.D. Roosevelt, 50, B-1050 Brussels, Belgium ABSTRACT: Mutual solubility (coexistence) curve, density, and dynamic viscosity data have been measured for the binary liquid system Fluorinert FC-72 + 1 cSt silicone oil. Liquid−liquid equilibrium (LLE) data have been obtained by the cloud-point technique with the use of the shadowgraph observation. The measurements of the dynamic viscosity and density of the mixtures have revealed a change in the slope in the temperature dependence at a temperature which corresponds to LLE. The solubility curve from density measurements is in excellent agreement with that estimated by the cloud-point technique. The experimental data along the binodal curve have been analyzed by the extended scaling theory using the mass fraction as the order parameter. The scaling expression for the diameter and width of the coexistence curve is consistent with the experimental data for t < 0.1, where t is the reduced temperature.

■

periodic vibrations.11 For the use of the same cell in the microgravity experiment, the transition from miscible to immiscible liquids will go through a temperature change in a way that the system crosses binodal back and forth with predictable change in physical-chemical properties. The mixture under investigation has been preselected as the best candidate for this test system. Therefore, the study of mutual solubility and density/viscosity data is necessary for the evaluation of the stability of the mixture FC-72 + silicone oil (1 cSt), careful planning and successful implementation of the space experiment, and its adequate numerical simulation. Information about the liquid−liquid phase diagram of the FC-72 + silicone oil (1 cSt) systems is absent in the literature. The lack of experimental data for this mixture has motivated our study. One of the goals of this work is to measure the liquid−liquid phase diagram for the binary system Fluorinert FC-72 + silicone oil (1 cSt) in a broad range of temperatures. Another objective is to determine the density and viscosity for pure FC-72 and silicone oil (1 cSt) and their mixtures, starting at a temperature of 318.15 K (single-phase) and descending to a two-phase region. Finally, we complement the coexistence curve obtained by the cloud-point detection method with the data from density and viscosity measurements.

INTRODUCTION Many sets of liquids important for industry have limited mutual solubilities. At the same time, information about mutual solubilities, as well as liquid−liquid equilibrium (LLE) data, is crucial for the simulation, design, and operation of different processes such as extraction, refining, separation, etc. Such data are also valuable in theoretical studies, for example, for the determination of activity coefficients with the subsequent purpose of calculating the diffusion coefficients.1,2 Fluorinert FC-72 (perfluorohexane) is a derivative of hexane in which all of the hydrogen atoms are replaced by fluorine atoms. Due to its thermal and chemical stability, FC-72 is an ideal choice for low temperature heat transfer applications.3 Its biological inertness together with its chemical stability also makes it attractive to medicine.4 The spectrum of silicone oils of different viscosities is often used in the experiments where the driving force depends on the surface tension, as the latter is stable with respect to the air pollution.5,6 Liquid mixtures with a miscibility gap exhibit two liquid phases with different compositions. These LLE compositions are represented by the binodal and can be measured experimentally. One of the commonly used methods for the estimation of the mutual solubilities of binary and ternary mixtures is the cloud-point detection method.7−10 The temperature at which a homogeneous mixture at slow cooling starts to phase separate and a number of phases appears, thus it becomes turbid, is denoted as the cloud-point temperature, Tcp. In this work, we used the cloud-point method in combination with shadowgraphy to accurately detect the appearance of turbidity. Our interest in the mixture of perfluorohexane/silicone oil is motivated by the preparation of the experiment VIPIL (VIbrational Phenomena In Liquids), which is supposed to be performed on the International Space Station (ISS) in the frame of European Space Agency (ESA) project. The VIPIL project focuses on the analysis of instabilities in systems composed of two layers of miscible/immiscible liquids under © XXXX American Chemical Society

■

EXPERIMENTAL SECTION

Materials. Fluorinert FC-72 (perfluoro-n-hexane, CAS: 355-42-0, Mw = 338.04 g/mol) was purchased from Acros Organics (98+%, lot: A0371455, Belgium), and silicone oil XIAMETER PMX-200 1 cSt (octamethyltrisiloxane, CAS: 107-51-7, Mw = 236.53 g/mol) was purchased from Dow Received: April 4, 2018 Accepted: June 12, 2018

A

DOI: 10.1021/acs.jced.8b00278 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

precision Pt resistance probe and a thermometer readout (Fluke, 1560 Black Stack, USA). The temperature was measured with an uncertainty of ±0.1 K. Experimental Procedure. At first, the prepared samples with a known mass fraction were heated to about 5 K above the critical temperature for about 1 h, homogenized using a magnetic stirrer, and intensively shaken. Then, the cell was cooled at a constant rate. The cooling rate was varied between 0.025, 0.05, 0.1, and 0.2 K/min starting from the highest one in order to establish the narrowest possible temperature interval at which the mixture becomes turbid. First-order phase transitions may occur under highly supersaturated conditions, especially at the wings of the phase diagram. The onset of phase separation depends on the speed of penetration into the metastable region. By varying the cooling rate, uncertainties in estimation of the cloud-point temperature related to kinetic effects and the appearance of metastable states are minimized.8 After each measurement, the temperature was increased again to the one-phase region. The measurements were repeated at least 3−4 times for each concentration at a certain cooling rate. The repeatability of the transition temperature detection was less than ±0.1 K. The measurements at different cooling rates were done both with and without activation of the magnetic stirrer during cooling. Optical Part. During the experiments, a monochromatic but noncoherent light from a red LED (LZ1-10R200, peak wavelength 655−670 nm, LED Engin, USA) is collimated by a telecentric back-light illuminator (part #62-760, Edmund Optics, United Kingdom) and after passing through the cell with the sample is registered by a CCD camera with a time interval between acquired images varying from 10 to 60 s depending on the cooling rate. The higher the cooling rate, the higher the acquisition frequency. When critical opalescence begins in the tested liquid, it causes strong refraction of the light on density fluctuations and microdroplets of another phase. It results in temporal darkening of the field of view corresponding to the liquid sample. The analysis of the images has been done as follows. First, a region of interest (ROI) was selected corresponding to a clear liquid phase (typically of 4 × 6 mm2 real size). Then, an average intensity of light was calculated over the ROI for all of the images of an experiment. Finally, the images were correlated to the temperature of the liquid in the respective time instant. A typical example of an experimental observation is shown in Figure 2. An average intensity of the light captured by the CCD camera in the very first image in the series is taken as 100% light transmittance through the sample; then, all of the following light reduction by turbidity is scaled in percentage of the initial transmittance. A cloud-point temperature, Tcp, was determined in the point corresponding to the largest drop in transmittance between two subsequent images.

Corning (99+%, lot: 0008288908, United Kingdom); both liquids were used as received. Sample Preparation. For cloud-point measurements, mixtures of FC-72 and silicone oil (1 cSt) of different compositions were prepared directly in a vertical cell of an inner size of 10 × 10 × 40 mm3. A transparent quartz cell of type 119.000-QS was purchased from Hellma (Germany). It features a closing cap of chemically inert polytetrafluoroethylene (PTFE) and a place for a PTFE-coated magnetic stirrer bar. The typical mass of the sample was about 3.5 g, and the volume was about 3 mL. The composition was determined gravimetrically by weighing each component into syringes before and after cell refilling with an accuracy of 10−5 g, which results in an overall uncertainty of the mass fraction of δc = 10−5. Density and Viscosity Measurements. A DMA 5000 density meter of Anton Paar (Austria) with an accuracy of 5 × 10−6 g/cm3 and temperature repeatability of 0.001 K was used for the determination of density. In combination with the density meter, dynamic viscosity measurements were performed by a Lovis 2000 M/ME rolling-ball viscometer (also of Anton Paar) on the basis of Hoeppler’s falling ball principle, with an accuracy of up to 0.5%. Its temperature is controlled by Peltier elements with an accuracy of 0.02 K. Density and dynamic viscosity measurements were done every 1 K at cooling. Cloud-Point Measurements. The transition temperatures defining the liquid−liquid phase diagrams of the FC-72 + 1 cSt silicone oil binary mixtures were determined by the cloudpoint method using a shadowgraph technique. The sketch of the experimental setup is shown in Figure 1. All of the

Figure 1. Sketch of the experimental setup: CSL - source of collimated light, MS - magnetic stirrer, MSB - magnetic stirring bar, TC - thermocouple, DL - data logger, CCD - camera CCD, PC personal computer, TB - thermal bath.

measurements were carried out at atmospheric pressure. The cloud-point temperature, Tcp, was estimated as a temperature at which, in a mixture of a known composition, the second phase appears. A mixture of a known composition was prepared in a thermostated transparent measurement cell. The cell with 10.0 mm light path was incorporated into a custom-made water jacket. The temperature inside the jacket was controlled by a programmable thermal bath Lauda Eco RE415S (Germany) with stability better than ±0.05 K. The temperature of the tested liquid was measured using a thermocouple placed inside the cell. The signal from the thermocouple was registered every 10 s by a data acquisition unit (Agilent, 34970A, Malaysia). The thermocouple was previously calibrated with a high-

■

RESULTS AND DISCUSSION Effect of the Cooling Rate. Foremost, we have performed studies on the effect of the cooling rate on the cloud-point temperature. As said above, the applied cooling rate was equal to 0.025, 0.05, 0.1, or 0.2 K/min. We have carried out three to four measurements for each case with and without a stirrer. The results obtained for the concentration of 95.75% are shown in Figure 3. We have found that the cooling rate below 0.1 K/min does not affect the results within experimental error. However, at a cooling rate equal to 0.2 K/min, a noticeable B



Article

Figure 2. Record of the cloud-point detection experiment with a mixture of FC-72 + silicon oil (1 cSt) when the mass fraction of FC72 is 0.7536 kg kg−1. The estimated cloud-point temperature is 315.05 K.

Figure 4. Coexistence (LLE) curve of the FC-72 + 1 cSt silicone oil binary mixture measured by the cloud-point method (filled circles) and by the change of slope in the temperature dependence of density and viscosity (triangles). The diameter of the coexistence curves from eq 3 is shown by crosses.

Table 1. Experimental Results for the Liquid−Liquid Phase Diagram of FC-72 + Silicon Oil (1 cSt) Mixturesa Measurements by cloud point

Figure 3. Effect of cooling rate on cloud-point temperature estimation in the FC-72 + 1 cSt silicone oil system when the concentration of FC-72 is 95.75 wt %.

by density-viscosity

Tcp (K)

c′

c″

Tdv (K)

c

286.21 287.00 297.36 298.95 299.49 308.30 310.40 313.55 313.85 315.05 315.20

0.1999 (0.2038) (0.2654) (0.2775) 0.2819 (0.3828) 0.4212 0.4989 (0.5109) (0.6107) 0.6460

(0.9592) 0.9575 0.9346 0.9299 (0.9282) 0.8866 (0.8710) (0.8393) 0.8329 0.7536 (0.7226)

282.15 298.15 305.15 305.15 298.15 287.15

0.9720 0.9299 0.8972 0.3455 0.2801 0.1999

a

Tcp is the cloud-point temperature, Tdv is the temperature at which density and viscosity dependence changes its slope, c″ and c′ are the mass fractions of FC-72 on the opposite branches of the coexistence curve, and c is the mass fraction of FC-72. Values in parentheses are obtained by interpolation.

increase of the estimated cloud-point temperature is observed. Note that the cloud-point temperatures estimated from the experiments when the stirrer was on are slightly less than those when the stirrer was off. Further, in this work, the measurements of the cloud-point temperature were done without a stirrer at a cooling rate of 0.025 K/min. Phase Diagram. The studied binary mixture reveals a phase diagram of an asymmetric shape with an upper critical solution temperature (UCST), Tc. The coexistence (binodal) curve given in Figure 4 denotes the condition at which two distinct phases may coexist. The binodal curve delineates the concentration range of the components, which form two immiscible liquid phases (i.e., below the curve) from that which will form one phase (i.e., above the curve). The binodal is rather steep at high concentrations of FC-72 (above 85 wt %). The critical temperature is the highest temperature of the phase diagrams and located on an almost flat curve in the concentration region 60% < c < 75%. In the vicinity of the binodal curve, the phenomenon of the critical opalescence (scattering of light on density fluctuations) in the whole volume of the cell was observed. The data of the phase diagram (mass fractions and cloud-point temperatures) are given in Table 1. Coexistence Curve Analysis. Order Parameter. The description of thermodynamic anomalies near critical points is

greatly facilitated by distinguishing between two classes of thermodynamic variables: “field variables” and “density variables”. Field variables are those thermodynamic variables which have equal values in coexisting phases at thermal equilibrium. Examples of field variables are temperature, pressure, and chemical potential of each component of a mixture. Density variables are those thermodynamic variables which are not equal in coexisting phases in equilibrium. Examples of density variables are mass density, entropy per unit volume, and mole fraction of each chemical component. In a two-phase system, a measure of two-phase dissimilarity may be formed by subtracting the value of any density variable in one phase from the value of the same variable in the other phase. Of course, any linear combination of density variables can also be used. Such a measure of dissimilarity is called an “order parameter”. As a two-phase system moves toward its critical point, the phases become more identical in all respects; hence, any choice of the order parameter approaches zero. C



Article

Extended Scaling Theory. The evident interest is to verify consistency of the experimental binodal curve with the recently developed so-called complete scaling theory.12−14 For a binary liquid mixture with demixing, this theory predicts the shape of the coexistence curve via two parameters, the so-called width and diameter. According to the theory, the width, which is a difference of the order parameter between different branches of the coexistence curve in the proximity of the critical point, is proportional to the reduced temperature t = |Tc − T|/Tc in the power of the universal critical exponent β. The dimensionless critical exponent, β, is predicted15 to be 0.326. Usually, in binary mixtures, one of the concentrations is taken as the order parameter, so the width of the coexistence curve near the critical point is defined as Δc =

c″ − c′ = B0 t β 2

Figure 5. Width of the coexistence curve in the range of asymptotic behavior as a function of reduced temperature t = |Tc − T|/Tc when β = 0.3255; (dots) experimental points; (dashed curve) prediction according to simple scaling, eq 1; (solid curve) prediction according to extended scaling, eq 2.

(1)

with only parameter B0 varying for different mixtures and concentration choices. c″ and c′ are the mass fractions of FC72 on the opposite branches of the coexistence curve. To predict the behavior of the coexistence curve far from the critical point, the extended scaling (Wegner’s expansion) is needed for the width Δc =

c″ − c′ = B0 t β + B1t β+Δ + ... 2

Determination of the coexistence curve diameter is less explicit. Usually, in the conventional scaling formulation, only the term with the amplitude D2 is considered. However, even in complete scaling, all of the exponents in eq 3 are of a similar order, and it is sometimes argued that the term with the amplitude D3 cannot be resolved, as it is easily absorbed by the term with D2. To elucidate this problem, we have performed the analysis of the diameter data with a different number of terms in eq 3. The results of different trials are summarized in Figure 6 and Table 2.

(2)

where Δ = 0.50 is another universal exponent and B1 is another material-dependent parameter. For the diameter, which is a locus of the middle points of the coexistence curve, the complete scaling theory predicts the following expansion cd =

c″ + c′ = cc + D1t 2β + D2t 1 − α + D3t 2

(3)

where cc is the critical concentration, α = 0.110 is another universal critical exponent, and Di are material-dependent coefficients. A direct comparison of raw data with predictions by the scaling is hampered by the fact that the cloud-point measurements do not allow simultaneous assessment of the symmetric points on different branches of the curve, which is necessary for calculating its width and diameter. To solve this problem, we apply an interpolation. After several tested options, it has been found that the cubic spline method is the best. The points found by the interpolation are also listed in Table 1 in parentheses. The interpolation allows obtaining values for the width and diameter of the coexistence curve as a function of temperature. Then, using eqs 1 and 3, the critical temperature and concentration, first, are estimated by interpolation of the dependencies of Δc1/β vs T and then cd vs t2β in the vicinity of the critical point. This procedure provided the following location of the critical point: Tc = 315.22 K and cc = 0.686 mass fraction. Figure 5 compares the experimental data for the coexistence curve with the considered-above scalings. In the vicinity of the critical point (t < 2.5 × 10−2), the width of the coexistence curve well follows the critical behavior outlined by eq 1, but later it begins to deviate. In accordance with expectation, the extended scaling, eq 2, offers a much better description of all of the experimental points, and the determined amplitudes are B0 = 0.9356 and B1 = −0.3609.

Figure 6. Diameter of the coexistence curve in the range of asymptotic behavior as a function of reduced temperature; experimental points (dots) and estimates with a different number of expansion terms in eq 3 (dashed and solid curves).

For a one-term fit, we have tested two options: the single first term with the lowest power D1t2β and the single second term D2t1−α, with the latter option corresponding to the conventional scaling theory. Figure 6 shows that in these two cases the fit of the data can be considered only at the nearcritical region when t < 2.5 × 10−2. Further, the deviation is too large. Table 2 indicates that at the near-critical region both cases have comparable accuracy in terms of an average absolute deviation (AAD), although the fit with the exponent 1−α starts D



Article

the number of experimental points used to estimate the coefficients; a smaller number of points will provide a higher uncertainty in predicting the coefficients. The coefficients given in Table 3 have been obtained by minimization of the experimental data deviations from the

Table 2. Parameters for Fitting the Diameter to eq 3 with a Different Number of Terms Di, Expressed in Mass Fractiona case no.

D1

D2

D3

AAD (%)

(i) (ii) (iii) (iv)

−0.596 − −0.797 0.256

− −1.593 0.501 −6.770

− − − 7.059

0.24b 0.25b 0.35 0.12

Table 3. Numerical Values of the Coefficients of eqs 5−7, Describing the Coexistence Curve and Obtained by Fitting of the Full Set of Experimental Data

a

Dash indicates that the term with corresponding coefficient did not participate in the fit at a particular case. AAD stands for average absolute deviation. bData fit and AAD estimate are made for t < 2.5 × 10−2.

deviating from experimental points earlier. Hereafter, the value of AAD is calculated as AAD =

1 N

N

∑

yi ,exp − yi ,calc

i=1

yi ,exp

where N is the number of experimental data points and yi,exp and yi,calc are the experimental and calculated values of an evaluated parameter, respectively. Next, we will check the hypothesis about the possibility to distinguish inputs of the terms with the amplitudes D2 and D3. To do so, we examine how well the full data set is described by a two- and three-term fit. Figure 6 shows that the two-term fit provides a satisfactory agreement with all of the data points but winds around them a little bit. The best fit was obtained using all the three terms, which means that it is possible to distinguish contributions from the second and third terms in eq 3 even considering a relatively limited set of data. This conclusion is effectively confirmed by the comparison of AAD values for these two fits presented in Table 2. With accurate correlations for the width and diameter of the coexistence curve, its shape can be readily reconstructed by (4)

Independent Analysis of the Branches of the Coexistence Curve. We have also tested an alternative approach which suggests an independent description of the experimental data for both wings of the coexistence curve. Originally, this approach was developed for nonassociated substances16 and then extended to refrigerant/oil solutions and a wide class of binary mixtures. The authors suggest operating with the logarithmic form of these equations17−19 ln

c′ = B1c τ βF1(τ) , cc

ln

c″ = B2c τ βF2(τ) cc

(5)

0.4 F( 1 τ ) = 1 − 1.113τ /ln τ

(6)

F2(τ ) = 1 + 4.861τ 0.6/ln τ

(7)

B2c

Tc (K)

cc, mass frac.

−1.8661

315.25

0.7212

calculated values simultaneously for both wings of the coexistence curve. The critical temperature Tc = 315.25 is in a very good agreement with that determined in the previous section, but the critical concentration cc = 0.7212 is 5% larger. Partly, this difference can be attributed to the flat shape of the coexistence curve near the critical point (see Figure 4); the temperature remains almost constant in a large interval of compositions. Density and Viscosity Data. Experimental Data. Our investigations have been complemented by simultaneous measurements of density and viscosity for various concentrations of FC-72 + silicone oil (1 cSt). Measurements have been done every 1 degree on the cooling starting from 318.15 K down to the two-phase region, 5−7 degrees below the coexistence curve. For the mixtures in which liquid−liquid transition occurred in the investigated temperature range, we have observed a change in the slope in the temperature dependence of density and viscosity at Tdv. It is worth noting that Tdv is very close to Tcp estimated by the cloud-point detection method. Examples of density and viscosity measurements for concentrations are shown in Figure 7. It can be seen that at a certain temperature the separation of the components in the mixture starts and the measured values of density and viscosity significantly deviate from the general trend. The last temperature at which the separation has not yet been observed is taken as the liquid−liquid transition temperature and marked as Tdv. Figure 4 demonstrates a very good agreement between viscosity-density measurements Tdv and the results of the cloud-point method. The results of the measurements are summarized in Table 4 for the concentrations left to the critical point and in Table 5 for the concentrations right to the critical point. The graphical summary of the experimental results is given in Figure 8. Significant potential interest for applications presents the concentration dependencies of density and viscosity. Usually, for simplicity, these dependencies are supposed to be linear. Figure 7 shows the temperature dependencies of the density and viscosity of the FC-72 + silicone oil (1 cSt) binary mixture at 298.15 K. It can be easily seen that the dependencies are nonmonotonic and treating them as linear, when developing a concentration dependence for viscosity, can lead to large errors, up to 40%. In the following sections, we will analyze and correlate all of the data measured over the one-phase region of the (c, T) plane with use of different approaches. Polynomial Analysis of the Density Data. Investigation of the critical divergence of the properties is not the goal of the current study, and our measurements do not approach close to the critical point. Thus, we may correlate the experimental

× 100%

c′ , ″ = cd ± Δc

B1c 0.7337

where τ = |ln(Tc/T)| is the logarithm of dimensionless temperature, F1(τ) and F2(τ) are the universal functions,16,18 and β is the critical exponent as before. The strong points of this approach are the following: dimensionless coefficients B1c and B2c as well as cc and Tc in eqs 5−7 do not depend on the interval of variables T or c, while they are estimated from experimental data; coefficients B1c, B2c, cc, and Tc can be estimated from a limited number of experimental data even from two points because the temperature dependencies of physical properties in logarithmic coordinates are linear. Of course, the error bars depend on E



Article

Figure 7. Simultaneous measurements of density (left) and viscosity (right) when c = 0.9299 kg kg−1, Tdv ≈ 298.15 ± 1.0 K, and Tcp ≈ 298.95 K. The measurements were started at 303.15 K. Then, with a step of 1 K, the sample was heated up to 318.15 K. After that, it was cooled down and measured from 303.15 to 287.15 K with the same step.

Table 4. Experimental Data on Density and Dynamic Viscosity for FC-72 + 1 cSt Silicone Oil Mixtures for the Compositions Left to the Critical Point c = 0.0

c = 0.0997

c = 0.1999

c = 0.2801

c = 0.3455

T

ρ (g/cm )

μ (mPa s)

ρ (g/cm )

μ (mPa s)

ρ (g/cm )

μ (mPa s)

ρ (g/cm )

μ (mPa s)

ρ (g/cm3)

μ (mPa s)

280.15 281.15 282.15 283.15 284.15 285.15 286.15 287.15 288.15 289.15 290.15 291.15 292.15 293.15 294.15 295.15 296.15 297.15 298.15 299.15 300.15 301.15 302.15 303.15 304.15 305.15 306.15 307.15 308.15 309.15 310.15 311.15 312.15 313.15 314.15 315.15 316.15 317.15 318.15

0.83295 0.83194 0.83092 0.82991 0.82889 0.82789 0.82687 0.82586 0.82484 0.82382 0.82281 0.82179 0.82077 0.81976 0.81874 0.81772 0.81670 0.81568 0.81467 0.81365 0.81262 0.81160 0.81058 0.80956 0.80853 0.80751 0.80649 0.80546 0.80444 0.80341 0.80238 0.80135 0.80033 0.79930 0.79827 0.79724 0.79621 0.79518 0.79417

1.106 1.091 1.076 1.061 1.047 1.033 1.020 1.006 0.993 0.980 0.967 0.954 0.941 0.929 0.916 0.904 0.892 0.880 0.868 0.856 0.845 0.833 0.823 0.812 0.802 0.791 0.781 0.771 0.760 0.750 0.741 0.731 0.721 0.713 0.703 0.694 0.686 0.677 0.669

0.87195 0.87086 0.86977 0.86868 0.86759 0.86650 0.86541 0.86431 0.86322 0.86212 0.86103 0.85994 0.85884 0.85773 0.85668 0.85559 0.85449 0.85339 0.85229 0.85119 0.85009 0.84899 0.84789 0.84679 0.84568 0.84458 0.84348 0.84237 0.84126 0.84016 0.83905 0.83794 0.83683 0.83572 0.83460 0.83350 0.83238 0.83127 0.83014

1.029 1.014 1.000 0.985 0.971 0.956 0.942 0.928 0.914 0.901 0.888 0.876 0.864 0.852 0.840 0.828 0.817 0.806 0.795 0.784 0.774 0.763 0.753 0.743 0.734 0.724 0.715 0.706 0.697 0.688 0.680 0.671 0.662 0.656 0.647 0.639 0.633 0.625 0.618

0.90750 0.90630 0.90511 0.90392 0.90272 0.90153 0.90033 0.89914 0.89794 0.89674 0.89554 0.89438 0.89318 0.89198 0.89078 0.88958 0.88837 0.88717 0.88597 0.88476 0.88355 0.88234 0.88114 0.87992 0.87872 0.87750 0.87629 0.87507 0.87386 0.87263 0.87143

0.870 0.858 0.846 0.834 0.822 0.811 0.800 0.789 0.779 0.769 0.758 0.748 0.739 0.729 0.719 0.710 0.701 0.692 0.683 0.675 0.666 0.658 0.649 0.641 0.633 0.626 0.618 0.611 0.603 0.597 0.589

0.93427 0.93297 0.93167 0.93037 0.92887 0.92765 0.92635 0.92504 0.92373 0.92242 0.92111 0.91980 0.91849 0.91717 0.91586 0.91454 0.91323 0.91191 0.91059 0.90927

0.727 0.720 0.711 0.703 0.690 0.685 0.675 0.667 0.659 0.650 0.642 0.634 0.626 0.618 0.611 0.603 0.597 0.589 0.583 0.575

0.96199 0.96058 0.95916 0.95774 0.95633 0.95491 0.95349 0.95207 0.95066 0.94931 0.94784 0.94642 0.94500

0.652 0.644 0.637 0.627 0.619 0.613 0.604 0.597 0.590 0.583 0.575 0.570 0.562

3

3

3

F

3



Article

Table 5. Experimental Data on Density and Dynamic Viscosity for FC-72 + 1 cSt Silicone Oil Mixtures for the Compositions Right to the Critical Point c = 0.8972 T (K) 280.15 281.15 282.15 283.15 284.15 285.15 286.15 287.15 288.15 289.15 290.15 291.15 292.15 293.15 294.15 295.15 296.15 297.15 298.15 299.15 300.15 301.15 302.15 303.15 304.15 305.15 306.15 307.15 308.15 309.15 310.15 311.15 312.15 313.15 314.15 315.15 316.15 317.15 318.15

ρ (g/cm3)

1.47339 1.47048 1.46763 1.46478 1.46193 1.45910 1.45628 1.45347 1.45067 1.44788 1.44511 1.44234 1.43934

c = 0.9299

μ (mPa s)

0.584 0.576 0.568 0.560 0.553 0.545 0.537 0.531 0.524 0.518 0.511 0.504 0.497

ρ (g/cm3)

c = 0.9720

μ (mPa s)

1.54835 1.54558 1.54282 1.54004 1.53731 1.53426 1.53156 1.52876 1.52596 1.52316 1.52035 1.51753 1.51470 1.51186 1.50902 1.50617 1.50331 1.50044 1.49757 1.49469

0.649 0.638 0.630 0.620 0.609 0.604 0.595 0.586 0.578 0.570 0.562 0.555 0.548 0.540 0.533 0.526 0.518 0.512 0.507 0.500

ρ (g/cm3)

1.67163 1.66880 1.66598 1.66280 1.65994 1.65693 1.65420 1.65137 1.64856 1.64574 1.64290 1.64007 1.63723 1.63437 1.63151 1.62864 1.62577 1.62289 1.62000 1.61710 1.61419 1.61127 1.60835 1.60541 1.60248 1.59952 1.59656 1.59359 1.59061 1.58762 1.58462 1.58161 1.57861 1.57558 1.57255 1.56951

c = 1.0

μ (mPa s)

ρ (g/cm3)

μ (mPa s)

0.841 0.826 0.813 0.798 0.787 0.771 0.760 0.750 0.738 0.729 0.717 0.707 0.697 0.687 0.677 0.667 0.657 0.648 0.639 0.631 0.621 0.613 0.604 0.596 0.588 0.579 0.571 0.564 0.556 0.548 0.542 0.535 0.528 0.521 0.514 0.507

1.74193 1.73907 1.73621 1.73334 1.73048 1.72760 1.72472 1.72182 1.71892 1.71602 1.71311 1.71019 1.70727 1.70432 1.70138 1.69843 1.69547 1.69250 1.68949 1.68742 1.68442 1.68142 1.67841 1.67539 1.67237 1.66932 1.66629 1.66323 1.66016 1.65708 1.65398 1.65088 1.64778 1.64466 1.64154 1.63841 1.63526 1.63208 1.62885

0.915 0.899 0.885 0.871 0.858 0.845 0.832 0.819 0.807 0.795 0.782 0.770 0.758 0.746 0.735 0.724 0.713 0.702 0.691 0.683 0.674 0.664 0.656 0.646 0.637 0.628 0.620 0.611 0.602 0.594 0.586 0.578 0.570 0.564 0.556 0.549 0.542 0.534 0.527

Figure 8. Summary of the experimental data on density (left) and dynamic viscosity (right) as a function of temperature and FC-72 mass fraction.

The temperature dependence of the specific density of pure components can be approximated by the second-order polynomial

density data with approaches used for liquid mixtures far from criticality. G



Article

ρi (T ) = ρi0 + d1(T − T0) + d 2(T − T0)2

ρ0i

(8)

th

where is the density of the i component at the reference temperature T0 = 298.15 K. The obtained polynomial coefficients which indicate linear or weakly quadratic behavior of the function ρi(T) are presented in Table 6. Quadratic term Table 6. Coefficients of the Polynomial Expression for the Temperature Dependence of the Specific Density of Pure Components (eq 8) FC-72 1 cSt

ρ0 (g cm−3)

d1/10−3 (g cm−3 K−1)

d2/10−6 (g cm−3 K−2)

1.68996 0.81466

−2.95 −1.02

−4.46 −0.25

coefficients d2 are very small for both components, ∼10−6. Furthermore, for the silicone oil, it is almost vanishing and may be neglected without violating accuracy. It can be seen from Figure 8 that for all of the mixtures of interest the density exhibits a weak dependence on temperature and can be described by the same eq 8 as for a pure component. Indeed, our estimations show that the coefficient d2 is also small for the mixtures. The first-order coefficient d1, which is proportional to the volumetric thermal expansion coefficient, gradually rises with the increase of FC-72 concentration, becoming finally 3 times larger in comparison with pure silicone oil. In order to analyze the concentration dependence of the density, we apply an efficient approach to treat the deviation of the property on mixing, instead of the property itself. The same approach has been successfully applied for the mixtures with demixing in the earlier work.20 The approach is based on the decomposition of the property into a linear mixing term and a deviation term ρ(c) = ρ lin + Δρ = cρ1 + (1 − c)ρ2 + Δρ

Figure 9. Change in specific density as a function of the mixture composition. The points include data for all of the measured temperatures and indicate that Δρ does not depend on temperature.

concentration. The values of the coefficients Ai are listed in Table 7. Table 7. Coefficients of eq 10 Describing TemperatureIndependent Behavior of the Change in Density of the Mixtures FC-72 + 1 cSt Silicone Oil, Ai (g/cm3) A2

−0.71648

0.36558

−0.21729

ρ(c , T ) = c1ρ1(T ) + (1 − c1)ρ2 (T ) 2

(9)

+ c1(1 − c1) ∑ A n(1 − 2c1)n

(11)

n=0

It is worth noting that temperature enters into the correlation in the linear term only, while concentration dependence is strongly affected by the deviation term. The experimental data for density are very well reproduced by eq 11, resulting in an average absolute deviation (AAD) of 0.1% and maximum absolute deviation of 0.45% over all of the measured points. Correlations for the Viscosity Data. Similar to density, we start an analysis of the viscosity data from pure liquids. The temperature dependence of viscosity is nonlinear, but for liquids, this nonlinearity can be effectively eliminated by relating the natural logarithm of dynamic viscosity to the reciprocal absolute temperature as B ln μi = A + (12) T 22 which is usually referred to as the Andrade equation. The coefficients determined by fitting of the measured viscosity data for pure liquids to eq 12 are given in Table 8. Table 8. Coefficients of eq 12 for the Logarithm of Dynamic Viscosity of Pure Components, ln μi

N n=0

A1

Such temperature-independent behavior of density deviation allows an elegant correlation of the density over the full range of c and T:

where c is the mass fraction of FC-72, the mass fraction of silicone oil is (1 − c), and ρi are defined by eq 8. The next target is to find the expression which will describe the dependence of density simultaneously on the temperature and concentration. We have to note here that the typical way of presenting a concentration dependency of the volumetric property is in providing a value of excess volume (molar or specific). However, on the way of analyzing the excess specific volume alone with the values of the change in density Δρ = ρexp − ρlin for all of the assessed temperatures in the range 280.15−318.15 K, we have made an important observation: the density deviation does not depend on temperature in the studied range, while the excess specific volume does. This temperature independence can be seen in Figure 9, where all measurements done at different temperatures form a single curve. Thus, the change in specific density has been chosen as a parameter which is more convenient for the density parametrization. The concentration dependence of the change in specific density can be fitted by the Redlich−Kister type polynomials:21 Δρ = c(1 − c) ∑ A n(1 − 2c)n

A0

(10)

The best fit to the experimental data was achieved with three terms in eq 10 (N = 2), and consequently, the deviation in density is a power-series polynomial of the fourth order on

FC-72 1 cSt H

A

B (K)

−4.6966 −4.1183

1291.0 1184.4 DOI: 10.1021/acs.jced.8b00278 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Figure 10. Concentration dependence of pseudocritical temperature (upper panel) and density (middle panel) for the FC-72 + 1 cSt silicone oil binary mixture. The bottom panel shows the coefficient B1ρ defined by eq 17. The points indicated by the black circles were obtained by the leastsquares minimization procedure using eq 14 for each concentration. The red curves correspond to eqs 15−17.

Using eqs 15−17, the density of the FC-72 + silicone oil (1 cSt) mixture can be calculated in the whole range of concentrations and temperatures where the mixture exists in a single liquid phase. The deviations (AAD) of the experimental density data from those calculated by eqs 14−17 do not exceed 1%. The experimental dynamic viscosity data for each concentration of the mixture, μ, were fitted using the following equation18

Following the analogy with density, the analysis of the concentration dependence of viscosity can be advanced by representing its logarithm as a combination of the linear mixing rule with an excess term (Grunberg−Nissan approach22,23) ln μ = x1 ln μ1 + x 2 ln μ2 + x1x 2G12

(13)

where xi is the mole fraction of the ith component, μi is defined by eq 12, and G12 is an interaction parameter. In this approach, it is necessary to use the mole fraction instead of the mass fraction, because otherwise the concentration dependence ln μ loses its symmetry and needs a more extended excess term. By fitting the experimental data to eq 13, we have found that the deviation term Δ ln μ = x1x2G12 for the logarithm of viscosity is independent of temperature (within the experimental error), similarly as it was found for the density. This fact allowed us to fit all of the measured viscosity data to eq 13 with a single value of the interaction parameter, G12 = −0.7305, which covers the entire considered range of temperatures and concentrations. The suggested method describes the experimental data on viscosity with AAD of 1.1% and a maximum absolute deviation not exceeding 3.0%. Alternative Prediction of Density and Viscosity Data. Here we will discuss prediction of density and viscosity data using the ideas developed in section Independent Analysis of the Branches of the Coexistence Curve. The obtained density data of the mixtures in a single phase were fitted using predictive equations similar to eqs 5 and 6. The scaling equation for density takes the form ρ = B1ρτccβF1(τcc) ln ρcc (14)

μ = μ0 ·θ (α(θ) +Δ′)

where θ = 1 − T/Tcc is the reduced temperature based on the pseudocritical temperature of the mixture; Tcc is the pseudocritical temperature of the mixture estimated from the experimental density data described by eq 15; α(θ) is the universal function of this reduced temperature α (θ ) =

(15)

ρcc (c) = 0.225 + 0.2254c − 0.133c 2 + 0.367c 3

(16)

B1ρ(c) = 1.9811 − 0.4113c

(17)

0.61538 + 16.155θ − 33.098θ 2 1 + 10.591θ − 33.506θ 2 + 24.077θ 3

where μ0, mPa s, and dimensionless Δ′ are the coefficients dependent on the concentration of FC-72. These coefficients were estimated by fitting the experimental dynamic viscosity data to eq 18 and approximated by the following equations: Δ′(c) = 0.47296 − 2.44496e−3.40790c

(19)

ln μ0 (c) = −4.82618 − 3.28705e−1.99975c

(20)

Using eqs 18−20, the dynamic viscosity of the FC-72 + silicone oil (1 cSt) mixture can be calculated in the whole range of concentrations and temperatures where the mixture exists in a single liquid phase. The deviations (AAD) of the experimental data of dynamic viscosity from those calculated by eqs 18−20 do not exceed 8%. This method was developed and successfully tested on refrigerant/oil solutions.18

where B1ρ is the dimensionless coefficient, ρ is the density of the binary mixture, and ρcc and Tcc are the pseudocritical density and temperature defined as the end point of the vapor pressure coexistence curve for each concentration c; correspondingly, τcc = ln(Tcc/T). In logarithmic coordinates, the dependence expressed by eq 14 is linear and the quantities B1ρ, ρcc, and Tcc entering into the equation were estimated for each mixture by the least-squares minimization procedure. The concentration dependencies of estimated coefficients are shown in Figure 10 and approximated by polynomials: Tcc(c) = 595.00 − 212.03c + 58.03c 2

(18)

■

CONCLUSIONS We have measured the liquid−liquid phase diagram for the binary mixture FC-72 + 1 cSt silicone oil from 286.21 K to the upper critical solution temperature using the cloud-point detection method. This procedure provided the following location of the critical point: Tc = 315.22 K and cc = 0.686 mass fraction. We have reported experimental liquid density and dynamic viscosity data for pure substances (FC-72 and 1 cSt silicone oil) and their mixtures. We have observed a change of slope in the temperature dependence of density and viscosity on cooling at about the same temperature estimated by the cloud-point detection method. Taking into account the scaling principle and the correlations for prediction of density and dynamic viscosity on the saturation line (coexistence

Here the temperature is in K and density in g/cm3. I



Article

Mixtures by Refractometry Method). J. Chem. Eng. Data 2006, 51, 1316−1320. (11) Gaponenko, Y.; Torregrosa, M.; Yasnou, V.; Mialdun, A.; Shevtsova, V. Interfacial pattern selection in miscible liquids under vibration. Soft Matter 2015, 11, 8221−8224. (12) Cerdeiriña, C. A.; Anisimov, M. A.; Sengers, J. V. The nature of singular coexistence-curve diameters of liquid-liquid phase equilibria. Chem. Phys. Lett. 2006, 424, 414−419. (13) Wang, J.; Cerdeiriña, C. A.; Anisimov, M. A.; Sengers, J. V. Principle of isomorphism and complete scaling for binary-fluid criticality. Phys. Rev. E 2008, 77, 031127. (14) Pérez-Sánchez, G.; Losada-Pérez, P.; Cerdeiriña, C. A.; Sengers, J. V.; Anisimov, M. A. Asymmetric criticality in weakly compressible liquid mixtures. J. Chem. Phys. 2010, 132, 154502. (15) Sengers, J. V.; Sengers, J. M. H. L. Thermodynamic Behavior of Fluids Near the Critical Point. Annu. Rev. Phys. Chem. 1986, 37, 189− 222. (16) Zhelezny, V. P. The methods of prediction of the properties for substances on the coexistence curve including vicinity of the critical point. Proceedings of the NATO Advanced Research Workshop on Nonlinear Dielectric Phenomena in Complex Liquids. 2003; pp 163− 175. (17) Zhelezny, P. V.; Zhelezny, V. P.; Procenko, D. A.; Ancherbak, S. N. An experimental investigation and modelling of the thermodynamic properties of isobutane compressor oil solutions: Some aspects of experimental methodology. Int. J. Refrig. 2007, 30, 433−445. (18) Zhelezny, V. P.; Sechenyh, V.; Semenyuk, Y. V.; Grebenkov, A. J.; Beliayeva, O. V. An experimental investigation and modelling of the viscosity refrigerant/oil solutions. Int. J. Refrig. 2009, 32, 1389−1395. (19) Zhelezny, V.; Sechenyh, V.; Nikulina, A. A New Scaling Principles-Quantitative Structure Property Relationship Model (SPQSPR) for Predicting the Physicochemical Properties of Substances at the Saturation Line. J. Chem. Eng. Data 2014, 59, 485−493. (20) Lapeira, E.; Gebhardt, M.; Triller, T.; Mialdun, A.; Köhler, W.; Shevtsova, V.; Bou-Ali, M. M. Transport properties of the binary mixtures of the three organic liquids toluene, methanol, and cyclohexane. J. Chem. Phys. 2017, 146, 094507. (21) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (22) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The properties of gases and liquids, 5th ed.; McGraw-Hill Education: 2000; p 768. (23) Grunberg, L.; Nissan, A. H. Mixture Law for Viscosity. Nature 1949, 164, 799−800.

curve) and liquid−liquid coexistence curve itself, a good data fitting was achieved with limited empirical information and a minimum number of free parameters. Moreover, these correlations can be used to predict the density and dynamic viscosity of the binary mixture FC-72 + silicone oil (1 cSt) in the whole range of temperatures and concentrations where the mixture exists in a single liquid phase. In order to characterize the shape of the coexistence curve, the extended scaling theory was used with the concentration in mass fraction as the order parameter. The simple asymptotic scaling describes well the experimental data for the binary mixture FC-72 + silicone oil (1 cSt) in the region t ≤ 2.5 × 10−2, while the extended theory was tested and found to be consistent up to t ≤ 0.1.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Valentina Shevtsova: 0000-0001-6109-5048 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is supported by the Belgian Federal Science Policy Office (PRODEX program of ESA).

■

REFERENCES

(1) Guevara-Carrion, G.; Gaponenko, Y.; Janzen, T.; Vrabec, J.; Shevtsova, V. Diffusion in Multicomponent Liquids: From Microscopic to Macroscopic Scales. J. Phys. Chem. B 2016, 120, 12193− 12210. (2) Janzen, T.; Zhang, S.; Mialdun, A.; Guevara-Carrion, G.; Vrabec, J.; He, M.; Shevtsova, V. Mutual diffusion governed by kinetics and thermodynamics in the partially miscible mixture methanol + cyclohexane. Phys. Chem. Chem. Phys. 2017, 19, 31856−31873. (3) Park, C. Y.; Jang, Y.; Kim, B.; Kim, Y. Flow boiling heat transfer coefficients and pressure drop of FC-72 in microchannels. Int. J. Multiphase Flow 2012, 39, 45−54. (4) Das, A.; Niven, R. Use of perfluorocarbon (fluorinert) to enhance reporter gene expression following intratracheal instillation into the lungs of Balb/c mice: Implications for nebulized delivery of plasmids. J. Pharm. Sci. 2001, 90, 1336−1344. (5) Yano, T.; Maruyama, K.; Matsunaga, T.; Nishino, K. Effect of ambient gas flow on the instability of Marangoni convection in liquid bridges of various volume ratios. Int. J. Heat Mass Transfer 2016, 99, 182−191. (6) Ferrera, C.; Montanero, J. M.; Mialdun, A.; Shevtsova, V.; Cabezas, M. G. A new experimental technique for measuring the dynamical free surface deformation in liquid bridges due to thermal convection. Meas. Sci. Technol. 2008, 19, 015410. (7) Matsuda, H.; Ochi, K.; Kojima, K. Determination and Correlation of LLE and SLE Data for the Methanol + Cyclohexane, Aniline + Heptane, and Phenol + Hexane System. J. Chem. Eng. Data 2003, 48, 184−189. (8) Vale, V. R.; Rathke, B.; Will, S.; Schröer, W. Liquid-Liquid Phase Behavior of Solutions of 1-Hexyl-3-methylimidazolium Bis((trifluoromethyl)sulfonyl)amide (C6mimNTf2) in n-Alkyl Alcohols. J. Chem. Eng. Data 2011, 56, 1330−1340. (9) Bendova, M.; Wagner, Z. Liquid-Liquid Equilibrium in Binary System [bmim][PF6] + 1-Butanol. J. Chem. Eng. Data 2006, 51, 2126−2131. (10) Mohsen-Nia, M.; Rasa, H.; Modarress, H. Cloud-Point Measurements for (Water + Poly(ethylene glycol) + Salt) Ternary J


Coexistence Curve, Density, and Viscosity for the Binary System of

Recommend Documents