Interfacial tensions and viscosities in multiphase systems by surface light scattering (SLS)

Accepted Manuscript Interfacial Tensions and Viscosities in Multiphase Systems by Surface Light Scattering (SLS) Thomas M. Koller, Tobias Prucker, Junwei Cui, Tobias Klein, Andreas P. Fröba PII: DOI: Reference:

S0021-9797(18)31416-4 https://doi.org/10.1016/j.jcis.2018.11.095 YJCIS 24360

To appear in:

Journal of Colloid and Interface Science

Received Date: Revised Date: Accepted Date:

5 October 2018 23 November 2018 24 November 2018

Please cite this article as: T.M. Koller, T. Prucker, J. Cui, T. Klein, A.P. Fröba, Interfacial Tensions and Viscosities in Multiphase Systems by Surface Light Scattering (SLS), Journal of Colloid and Interface Science (2018), doi: https://doi.org/10.1016/j.jcis.2018.11.095

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Interfacial Tensions and Viscosities in Multiphase Systems by Surface Light Scattering (SLS) Thomas M. Koller,*,a Tobias Prucker,a Junwei Cui,a,b Tobias Klein,a and Andreas P. Fröbaa

a

Institute of Advanced Optical Technologies ‒ Thermophysical Properties (AOT-TP),

Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 6, 91052 Erlangen, Germany b

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

__________________________ *

Author to whom correspondence should be addressed. Tel. +49-9131-85-23279, fax +49-9131-85-

25878, E-mail [email protected], ORCID number 0000-003-4917-3079. 1

Abstract Hypothesis Multiphase systems are relevant in many fields of process engineering. For process and product design in connection with multiphase systems, knowledge on the thermophysical properties of the individual phases such as viscosity and on the interfacial tension between these is required but often lacking in literature. Experiments In the present study, the applicability of surface light scattering (SLS) for the simultaneous measurement of interfacial tensions and viscosities in multiphase systems in macroscopic thermodynamic equilibrium is demonstrated. For two model systems consisting of n-decane and methanol as well as n-dodecane and methanol forming a vapor-liquid-liquid equilibrium at atmospheric pressure, surface fluctuations which show an oscillatory behavior at the vapor-liquid and liquid-liquid interface could be associated with hydrodynamic modes. Findings From an exact theoretical description of the dynamics of the surface fluctuations, absolute data for the dynamic viscosities of the two liquid phases as well as the vapor-liquid and liquid-liquid interfacial tensions could be determined at temperatures between (333 and 358) K with total measurement uncertainties (k = 2) down to about 2%. For both systems studied at temperatures close to the upper critical solution temperature, the viscosities of the two liquid phases approach each other and the liquid-liquid interfacial tension tends to zero.

2

Keywords: interfaces interfacial tension liquid-liquid systems multiphase systems surface light scattering upper critical solution temperature vapor-liquid systems viscosity

3

Nomenclature Symbols a

experimental constant

b

experimental constant

g(2)()

normalized intensity correlation function

kI

modulus of wave vector of refracted light, m-1

kS

modulus of wave vector of scattered light, m-1

M

dimensionless parameter

n

refractive index

q

modulus of scattering vector, m-1

R

dimensionless parameter

S

reduced frequency

T

absolute temperature, K

Ur

relative uncertainty

x

mole fraction



complex frequency, rad·s-1



damping constant of surface waves, s-1



dynamic viscosity, Pa·s

E

external angle of incidence, rad

L1

incident angle in the intermediate liquid phase, rad

S

scattering angle, rad

V

incident angle in the vapor phase, rad



wavelength of surface waves, m

C

critical wavelength of surface waves, m

0

laser wavelength in vacuo, m



kinematic viscosity, m2·s-1







density, kg·m-3 4



surface or interfacial tension, N·m-1



delay time, s

C

correlation time of surface waves, s

0

characteristic viscous time, s



phase term, rad

q

frequency of surface waves, rad·s-1

Abbreviations CH3OH

methanol

LL

liquid-liquid

L1

intermediate liquid phase

L2

lower liquid phase

MeOH

methanol

n-C10H22

n-decane

n-C12H26

n-dodecane

Nd:YVO4

neodymium-doped yttrium orthovanadate

SLS

surface light scattering

UCST

upper critical solution temperature

UNIFAC-VISCO

Universal Quasichemical Functional Group Activity Coefficients-Viscosity

V

vapor phase

VL

vapor-liquid

VLL

vapor-liquid-liquid

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1. Introduction Multiphase systems are of interest in many processes of energy engineering such as enhanced oil recovery for the mobilization of residual oil from porous rock structures [1,2], the production of polyurethane foams [3,4], and the development of high-performance insulating materials [5,6]. For process and product design in connection with multiphase systems, knowledge on the thermophysical properties of the individual phases and on the interfacial tension between these is necessary. This work focuses on the simultaneous determination of interfacial tensions of the individual phase boundaries and viscosities of the individual phases in multiphase systems. The viscosity is of importance for the characterization of heat, mass, and momentum transfer [7]. The interfacial tension is not only relevant for the physics of interfaces, but also important for technical processes and questions, e.g., in connection with wetting of machinery and porous materials [8], mass transfer between contacting phases [9] as well as formation and stability of emulsions [8]. Until now, no rigorous theory allows for the modeling of the viscosities and the interfacial tensions in multiphase systems. The viscosity and interfacial tension are very sensitive to the underlying molecular interactions and structural effects which cannot fully be represented in theoretical methods [10] including computer simulations [11] or empirical methods [12]. Furthermore, the lack of appropriate modeling approaches for multiphase systems might be related to the lack of reliable experimental data. An overview about the experimental techniques for the determination of surface or interfacial tension and viscosity can be found in Refs. [13,14] and [7]. For the measurement of the interfacial tension, it can be differentiated between static and dynamic techniques. While in dynamic methods the size of the interface changes during the measurement time, static methods are characterized by the presence of a static non-changing interface. In connection with the measurement of the interfacial tension of liquid-liquid systems, the dynamic drop volume [15] and maximum bubble pressure [16] tensiometers and the static techniques given by the pendant [17,18] or spinning [19,20] drop, DuNoüy ring [21], and Wilhelmy plate [21,22] methods are commonly employed. These conventional methods for the measurement of interfacial 6

tensions make often use of working equations whose boundary conditions can hardly be fulfilled by the experimental realization [13,23]. The metrological challenges in the accurate determination of interfacial tensions for liquid-liquid systems are often larger for low or even vanishing interfacial tension values. Although the spinning-drop technique has been shown to be a reliable method for the measurement of small interfacial tensions, see, e.g., Refs. [19] and [20], the necessity of realizing measurements at or very close to equilibrium conditions is often in contradiction to the measuring principle of conventional interfacial tensiometry. For this measurement category, during the sample preparation or the measurement procedure itself, the interface is changed as a result of an applied external force. For the measurement of the transport property viscosity by conventional techniques such as rotational [24], capillary [25], falling-body [26], oscillating cup [27], or vibrating-wire [28] technique, a shear gradient is applied related to the desired property. In principle, the macroscopic gradient subjected to the sample has to be large enough to get rise to a measurable effect, but small enough to avoid disturbances of the thermodynamic equilibrium. In connection with the determination of the viscosities of the individual phases of multiphase systems, investigations lack in literature so far. An alternative to conventional techniques is the surface light scattering (SLS) method which studies the dynamics of thermal fluctuations on the surface of a liquid or, in a more general formulation, at phase boundaries in a contactless way. The technique can be used as a quasi-primary method for the determination of viscosity of liquids in the medium viscosity range [29]. Besides its use within thermophysical property research of simple fluids, which is also of interest in the current study, the SLS method has been applied for the characterization of surfaces and interfaces of complex fluids such as polymer solutions [30,31], surfactant monolayers [32-34], liquid crystals [35]. The technique is based on rigorous working equations according to the linearized hydrodynamic description of surface fluctuations [36], and can be used by taking certain precautions against line broadening effects, which will be discussed later, without any need for a calibration procedure. Surface fluctuations at the phase boundary of two contacting fluids showing 7

relatively low viscosities and/or large interfacial tensions, which are of interest in this study, decay in form of a damped oscillation. For the surface fluctuations studied in the SLS experiment, amplitudes in the nm range and wavelengths between (0.1 and 1000) µm are characteristic values [37]. Light interacting with such an oscillating surface structure is scattered. Surface fluctuations with a defined wave vector result in a temporal modulation of the scattered light intensity containing the information on their characteristic dynamics, i.e. their damping and frequency. For a two-phase system, in addition to the measured frequency, damping, and wave vector, only information on the densities of both phases and the viscosity of either phase are needed to simultaneously determine the viscosity of the other phase and the interfacial tension in an absolute way in macroscopic thermodynamic equilibrium [23,37,38]. Starting from the late 1960s until the end of the 1990s, SLS had not been adequately explored for thermophysical property research and was restricted to investigations of systems especially suited to the method. Despite the experimental efforts demonstrating the feasibility of the technique, a relatively poor accuracy was still reported for the determination of viscosity and surface or interfacial tension by light scattering by surface waves [39-45]. During the past two decades, research activities at the Department of Chemical and Biological Engineering (CBI) and at the Erlangen Graduate School in Advanced Optical Technologies (SAOT) of the Friedrich-AlexanderUniversity Erlangen-Nürnberg (FAU) were devoted to develop a proper execution of the SLS method for an accurate measurement of surface or interfacial tension and liquid viscosity for working fluids at vapor-liquid equilibrium. For diverse systems such as the references fluids including toluene [46], diisodecyl phthalate [47], carbon dioxide [23], and n-pentane [48], refrigerants [49-51], hydrofluoroethers [52], ionic liquids [53-56], and hydrocarbons [57,58], viscosity and surface or interfacial tension data could be determined with typical total measurement uncertainties (k = 2) below 2% over wide range of states. In conclusion, all these investigations demonstrate that the SLS technique is a valuable tool for thermophysical property research.

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In connection with the investigation of the thermophysical properties of liquid-liquid systems by SLS, only four studies could be found in literature. The measurements of Katyl and Ingard [59] on the biphasic liquid system consisting of n-hexane and water at temperatures between (298 and 308) K were based on the spectral analysis of the frequency-shifted Brillouin lines giving access to damping and frequency of the surface fluctuations. For observing the Brillouin lines in the work of Katyl and Ingard [59], very small moduli of the scattering vector below 105 m-1 were applied. Especially at conditions near the critical damping where the temporal behavior of the surface fluctuations is changing from an overdamped to an oscillatory behavior, the dynamics of surface fluctuations, however, cannot longer be described by a first-order approximation (see in Refs. [23,46]) as used in the study of Katyl and Ingard [59]. Such an approach used in literature, see, e.g. Refs. [39,40,60], does not allow the determination of interfacial tension and viscosity with low uncertainty. Furthermore, in the work of Katyl and Ingard [59], line broadening effects caused by the detection of scattered light originating from a spread of wave vectors around the adjusted wave vector might have been present and affecting the final results. Another investigation of a liquidliquid system by SLS is given by Löfgren et al. [61] who studied the liquid-liquid interfacial tension for various binary systems with a water-rich lower phase and an upper hydrophobic phase based on, e.g., n-hexane and benzene at ambient conditions. For a reliable execution of SLS, the authors applied not only a heterodyne detection scheme where the light scattered from the surface fluctuations is superimposed with coherent reference light of much higher intensity, but also used a complete theoretical description of the dynamics of surface fluctuations [62] to evaluate the viscosity of the hydrophobic phase and the liquid-liquid interfacial tension. Nevertheless, they observed capillary effects in the measurement cell resulting in an unwanted curvature of the scattering plane, and, thus, line broadening effects may have affected their results. Furthermore, in the work of Löfgren et al. [61], lacking information on density and viscosity used for the evaluation of the SLS experiment make reported uncertainties of 1.5% for  and  questionable. Two further SLS studies on liquid-liquid systems consisting of binary mixtures of water and different 9

hydrocarbons at 298.15 K and atmospheric pressure were performed by Sauer et al. [32,63]. By using an optical grating, very small moduli of the scattering vector in the range between (2.6 and 5.2) × 104 m-1 were analyzed. This approach required a calibration of the optical setup for eliminating line broadening effects [32]. Based on this calibration, the liquid-liquid interfacial tension and viscosity of the intermediate hydrocarbon-rich phase were obtained [63]. In the works of Sauer et al. [32,63], no information about the data evaluation procedure and experimental uncertainties can be found. The present contribution represents a comprehensive study critically evaluating the feasibility of SLS experiments for the simultaneous determination of interfacial tensions and viscosities in multiphase systems with high accuracy. For this purpose, an exact description of the dynamics of surface fluctuations by the hydrodynamic theory as well as a proper experimental design, where instrumental line broadening effects are eliminated and the detection scheme for the analysis of the scattered light is clearly defined to be heterodyne, are necessary requirements which are fulfilled in our SLS experiments. To prove the capabilities of the SLS method in studying multiphase systems, two vapor-liquid-liquid (VLL) model systems consisting of n-decane and methanol as well as ndodecane and methanol were studied at saturation conditions in the vicinity to their upper critical solution temperatures for temperatures between (333 and 358) K. Furthermore, a strategy is presented for the determination of interfacial tensions and viscosities of the individual liquid phases within a multiphase system. After an introduction to the SLS technique, the materials and sample preparation as well as the experimental setup are described. Thereafter, a measurement example and the data evaluation procedure are presented. In connection with the main objectives of the present work, the hydrodynamic theory for describing the dynamics of surface fluctuations at vapor-liquid and liquid-liquid phase boundaries as well as reversely for determining liquid viscosities and interfacial tensions will be validated. Besides a critical analysis of the experimental uncertainties of the measurement results, the latter are also discussed in terms of structure-property relationships.

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2. Surface light scattering (SLS) – Interfacial tension and liquid viscosity In the following, only brief information on the principles of the SLS technique is given. For more details, the reader is referred to the literature, see, e.g., Refs. [23,36-38]. In our present investigations, the studied binary multiphase systems containing an n-alkane and methanol at saturation conditions consist of three phases with an upper vapor phase (V), an intermediate nalkane-rich liquid phase (L1), and a lower methanol-rich liquid phase (L2). For the study of surface fluctuations at the two phase boundaries between two contacting fluid phases, i.e. the vapor-liquid (VL) and liquid-liquid (LL) interface, the scattering geometry is schematically shown in Fig. 1a. Fig. 1b illustrates the sample inside the measurement cell providing the three different phases for the multiphase system consisting of n-C10H22 and methanol. Optical access is provided via the top and bottom window of the measurement cell. The main feature of the optical arrangement is based on the analysis of scattered light at variable and relatively high moduli of the wave vectors of the studied capillary waves of an order between (5 and 8) × 105 m-1, whereby line broadening effects are negligible. Furthermore, light scattered by surface fluctuations is observed in the forward direction near refraction and detected perpendicular to the two phase boundaries. By choice of the external angle of incidence outside the measurement cell, E, which is defined by the direction of the incident light and the detection    direction, a specific scattering angle S and, thus, a specific scattering vector q  k I  kS is    determined. Here, k I and k S denote the projections of the wave vectors of the refracted ( k I ) and  scattered ( k S ) light into the corresponding plane of the phase boundary. Furthermore, elastic scattering (i.e. k I  kS ) can be assumed. In the following, first, the interaction of light with the upper VL interface in Fig. 1a is considered, which represents the typical situation for the study of vapor-liquid systems [37,38,46,47]. Based on the external angle of incidence E as well as the refractive indices of air nair = 1 and of the vapor phase nV ≈ 1, a specific incident angle in the vapor phase V is given. The latter quantity in combination with the refractive indices of the vapor phase nV and of the upper liquid phase nL1 define the scattering angle S,VL as well as the wave vectors kI,VL and kS,VL . The 11

modulus of the scattering vector related to the VL interface, qVL, can be deduced from Snell’s refraction law and simple trigonometric identities resulting in   kS,VL  qVL  kI,VL 

2

0

sin(E ) ,

(1)

where 0 is the laser wavelength in vacuo. Here, the advantage of detecting the scattered light perpendicular to the phase boundary is that no information on the refractive index of the individual phases is required to obtain q. Each scattering vector chosen solely from the adjusted external angle of incidence corresponds to a specific wavelength (VL = 2/qVL) of surface vibration mode as it is shown in Fig. 1a.

liquid phase L1

Fig. 1. (a) Schematics of the scattering geometry at the two phase boundaries between the contacting vapor-liquid and liquid-liquid interface used for SLS. (b) Experimental situation inside the measurement cell containing the VLL system consisting of n-C10H22 and methanol at saturation conditions and a temperature of 333.15 K. For an adjusted external angle of incidence E = 3°, the refraction of the transmitted light at the upper VL interface and at the lower LL interface can be observed.

As for the VL phase boundary, similar considerations are carried out for the interaction of light with the lower LL interface in Fig. 1a. It should be mentioned that the consecutive analysis of the scattered light from both the VL and LL interfaces within the same experimental setup

12

represents a new development. For the study of the surface fluctuations at the LL interfaces in the experiment, the incident light having the same external angle of incidence E as in the previous situation is shifted to the left in Fig. 1a in order to move the scattering volume from the VL interface to the LL interface. Due to the fact that nL2 < nL1 for the studied systems, the moduli of the wave vectors kI,LL and kS,LL are smaller than those of the wave vectors kI,VL and kS,VL , while the scattering angle S,LL is larger than S,VL. Based on the characteristic incident angle L1 which is equal to S,VL for the adjusted detection scheme, it can be derived from Snell’s refraction law that the modulus of the scattering vector related to the LL interface, qLL, is the same as it is given for the VL interface, qVL, according to   kS,LL  qLL  kI,LL 

2

0

sin(E )  qVL .

(2)

For the experimental situation with 0 = 532 nm and a typical value of E = 3°, it can be calculated from Eq. (2) that the corresponding wavelength  of the studied vibration modes at the VL and LL interfaces are 10.2 µm. The relaxation behavior of a selected surface wave with a defined wave vector q depends on the thermophysical properties of the fluid. For large viscosities and/or small interfacial tension, the surface waves show an overdamped behavior and do not propagate. In the case of small viscosities and/or large interfacial tension, the surface waves show an oscillatory behavior and propagate. The latter case has always been observed in the current study and is solely considered in the following. The scattered light is analyzed by a post-detection filtering scheme using photon correlation spectroscopy. For heterodyne conditions and in the case that line broadening effects are suppressed, the normalized intensity correlation function for the analysis of surface fluctuations with an oscillatory behavior as a function of the delay time  takes the form [36] g(2) ( )  a  b cos(q    )exp(    C ) .

(3)

Thus, the measurement data related to a signal from surface fluctuations with a defined scattering vector can be represented by the correlation function Eq. 3 containing five fitting parameters. Here, the experimental constants a and b are essentially determined by the total number of counts 13

registered, the ratio of the intensity of the scattered light to reference light, and the coherence properties of the optical system. While the phase term  mainly accounts for the deviations of the spectrum from the Lorentzian form, the correlation time C and the frequency q are identical with the mean lifetime or the inverse of the damping constant (C = ‒1) of the surface waves and their frequency of propagation [37]. While the dynamics of the surface fluctuations at the VL interface is given by C,VL and q,VL, those for the LL interface are given by C,LL and q,LL. For an accurate determination of kinematic viscosity  or dynamic viscosity  ( =  with the density ) and surface or interfacial tension  by SLS, the dispersion relation for hydrodynamic surface fluctuations at the interface between two contacting fluid phases must be considered in its complete form [36,62]. For details to the dispersion relation for hydrodynamic surface fluctuations, the reader is referred to Refs. [36,38,62,64]. For thermal waves at the interface between two simple fluids neglecting viscoelastic effects, the dispersion equation can be transformed into its reduced form [36]

D( S )  Y 

  2    2  2 R    ( M   1)   ( M   1) S  ( M   1)   ( M   1) (     ) 2    ( M  2  1)   M   1  M ( M   1)   (     ) ( M   1)  ( M   1)   ( M   1) 

   ( M  2  1)   M   1  M ( M   1) 2 S (     ) ( M   1)  ( M   1)   ( M   1) 

(4)

,

where the lower and upper phases are indicated with ' and ''. In Eq. 4, the dimensionless properties R, M', and M'' are given by

R

         , (    ) (     )

M   1 2

     S,       R  14

(5)

(6)

and

M   1  2

     S.       R 

(7)

The reduced frequency S is related to the complex frequency  ( = q + i) and to the characteristic viscous time 0. Furthermore, the real part of the complex frequency  represents the frequency q and the imaginary part the damping  of the observed surface vibration mode with the corresponding wave number q. The relation Eq. 4 can be expressed as a function of the parameters measured in the SLS experiment and the thermophysical properties by D(V, L1, V, L1, VL,

C,VL, q,VL, q) in the case of the VL interface and D(L1, L2, L1, L2, LL, C,LL, q,LL, q) in the case of the LL interface. For the analysis of the VL interface, the input quantities given by the measured data for the frequency q,VL and decay time C,VL at a defined wave number q as well as the reference data for the dynamic viscosity of the vapor phase V and density data for both phases,

V and L1, are used to obtain the liquid viscosity L1 and interfacial tension VL1 by solving the dispersion relation D(S) = 0. The corresponding procedure can also applied for the evaluation of the LL interface, where the value for the dynamic viscosity of the intermediate liquid phase L1 accessed in the previous step can be combined with the measured data for q,LL and C,LL to determine the liquid viscosity L2 and interfacial tension LL. Due to the finite size of illumination and detection optics and the spatial proximity of the two interfaces, the scattered light originating from one fluctuating surface cannot be observed without any superposition of scattering contributions from the other interface and from the bulk of the fluid, i.e., the vapor and/or the two liquid phases. Scattered light from the bulk of the vapor phase and the two liquid phases can originate from Rayleigh and Brillouin scattering processes. Brillouin signals from both the vapor and the liquid phases related to periodic pressure fluctuations show typically very small characteristic lifetimes [65] and cannot be detected without using a frequency-shifted local oscillator [34,45,66]. In this study, Rayleigh contributions from the vapor phase can be 15

neglected because of the low vapor densities. Further Rayleigh signals from the liquid phases originating from microscopic fluctuations in temperature and concentration are generally much weaker and show distinctly larger decay times in comparison with SLS signals [67]. In the present study, the focus was solely on the detection of light scattering signals from surface waves. During the study of one of the VL or LL interfaces, a simultaneous detection of light scattered from the other interface is likely because of the adjusted relatively small external angles of incidence between E = (2.5 and 4)° and the close distance between the two interfaces of approximately 1 cm. Nevertheless, this distance is sufficiently large to exclude any mutual interaction between the surface waves at the VL and LL interface affecting their dynamics. Whether and, if present, to which extent two SLS signals appear in the correlation function depends on the thermophysical properties of the fluid and the relative signal strength. The latter is mainly determined by the extension and position of the scattering volume, the wave number of the studied fluctuations, and the thermodynamic state of the fluid. For all investigations reported here, the measured correlation functions contained always contributions from both interfaces.

3. Experimental section 3.1. Materials and sample preparation The linear alkanes n-decane (n-C10H22, molar mass M = 142.29 g∙mol-1) and n-dodecane (n-C12H26, M = 170.33 g∙mol-1) were provided by Alfa Aesar GmbH & Co. KG and Merck GmbH. The nominal mass fraction purities given by the suppliers are larger than 0.997 for n-C10H22 and 0.9945 for n-C12H26. Methanol (CH3OH or MeOH, M = 32.04 g∙mol-1) was purchased from Merck GmbH with a mass fraction of 0.999. Helium which was used as an inert gas for the handling of the samples during filling was supplied by the Linde AG with a respective volume fraction purity of 0.99999. First, n-C10H22 or n-C12H26 was filled in the cell through the upper window. Then, an appropriate amount of the heavier MeOH sample was added until the VLL system with two phase 16

boundaries could be observed from the side window of the measurement cell as it is shown in Fig. 1b. During the filling procedure, the vapor phase of the cell was flushed with helium simultaneously to avoid any contamination of the sample with air or other gases. Afterwards, the cell was closed and a sufficient time for equilibration of the three-phase systems consisting of an upper vapor phase, an intermediate n-alkane-rich liquid phase, and a lower MeOH-rich liquid phase was ensured. Once a constant temperature was reached, light scattering experiments were performed. The pressure was not registered during the measurements in order to keep the system volume and the disturbances from the thermodynamic equilibrium small, but could be estimated to be smaller than 0.2 MPa in all cases. Because of the very small amount of He dissolved in the samples [68], all present measurements are considered to be carried out at saturation conditions.

3.2. Experimental setup and procedure The experimental setup used for the investigation of the multiphase systems is the same as used in our former studies [38,57,58,67] of vapor-liquid systems and thus only briefly described here. A frequency-doubled continuous-wave Nd:YVO4-laser (Coherent, Verdi-V2) operated in a single mode with a wavelength of 0 = 532 nm serves as a light source. The laser power irradiating the transparent fluids was about 150 mW. For the analysis of fluctuations at the VL and LL interface, scattered light is analyzed in transmission direction at relatively high moduli of the scattering vector q, and, thus, instrumental broadening effects are negligible [38]. To realize heterodyne conditions, additional stronger reference light was superimposed to the scattered light. The time-dependent intensity of the scattered light is detected by two photomultiplier tubes operated in cross-correlation. The signals are amplified, discriminated, and fed to a digital linear-tau correlator with 256 equally spaced channels for calculating the normalized intensity correlation function g (2)(). To adjust the modulus of the scattering vector q via the external angle of incidence E, the latter was measured with a high precision rotation table with an expanded uncertainty of 0.005° based on a confidence level of more than 95% (coverage factor k = 2). 17

A sample cell made of stainless steel with four optical accesses and a total inner volume of about 105 mL was used, see Ref. [58]. The cell provides an effective interface length of 7 cm which is sufficiently large enough to avoid disturbing capillary effects present at the inner cell wall. For a complete suppression of line broadening effects, the verification of a flat interface is important, which could be ensured with our used sample cell. The temperature of the sample cell was controlled by resistance heating and measured by a calibrated Pt-100 Ω resistance probe close to the fluid interfaces with an absolute expanded uncertainty of 0.015 K (k = 2). For the systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH, temperatures of T = (333.15 and 358.15) K as well as T = (343.15 and 358.15) K were investigated. These temperatures are in vicinity to the upper critical solution temperature (UCST) TC which is 363.9 K for n-C10H22/MeOH [69] and about 380 K for n-C12H26/MeOH. For each system, investigations were performed at first at the lower temperatures. After temperature increase, waiting times of about 12 h were sufficient to obtain steady-state conditions. For each temperature, up to six individual measurements at different external angles of incidence E between (2.5 and 4.0)° were performed for the consecutive study of surface fluctuations at the VL and LL interface. Here, the laser was irradiated from either side with respect to the axis of observation to check for a possible misalignment. Typical measurement times for a single run were in the order of fifteen minutes.

4. Data evaluation 4.1. Measurement example for a correlation function The upper part of Fig. 2 shows an example for a normalized correlation function obtained from the simultaneous scattering at the VL interface between the upper vapor phase and the intermediate nC10H22-rich liquid phase as well as at the LL interface between the intermediate n-C10H22-rich liquid phase and the lower MeOH-rich liquid phase at saturation conditions at a temperature of T = 333.15 K and an external angle of incidence of E = 3°. For the present measurement example, the

18

scattering volume was aligned in a way that the signals from both interfaces are resolved simultaneously with a similar strength. The measured correlator data represented by the black squares can only be well represented by two contributions originating from signals from the VL interface (dashed blue line) and the LL interface (dotted red line) which appear at different time scales. In Fig. 2, for legibility purposes, the two signals represented by damped oscillations according to Eq. (3) are shifted downwards. The signal with a larger frequency is related to the VL interface because of its larger interfacial tension compared to the LL interface. The signal with the lower frequency is clearly associated with the LL interface. To ensure heterodyne conditions, the amplitude of each signal should be smaller than 1.5%, which is valid for the measurement example and all further measurement signals of the present study.

Fig. 2. Measurement example of a normalized correlation function (upper part) and the residuals (lower part) for the multiphase system consisting of n-C10H22 and MeOH at saturation conditions at a temperature of 333.15 K using an external angle of incidence of E = 3°. The two signal contributions to the global fit (solid green line) are related to the VL interface between the upper vapor phase V and the intermediate n-C10H22-rich liquid phase L1 (dashed blue line) as

19

well as the LL interface between the intermediate n-C10H22-rich liquid phase L1 and the lower MeOH-rich liquid phase L2 (dotted red line).

The measured correlation function was fitted by a sum of two damped oscillations according to Eq. (3) which is visualized by the solid green line in Fig. 2. All fitting procedures were performed by nonlinear regression based on a Levenberg-Marquardt algorithm in which the squared sum of residuals is minimized. Within the entire fit range, no systematic deviations between the measured data and the fit can be observed, as it can be seen from the lower part of Fig. 2. For the decay time and frequency, values of C,VL = (2.46 ± 0.11) µs and q,VL = (2.37 ± 0.02) × 106 rad·s-1 and of C,LL = (5.75 ± 0.31) µs and q,LL = (0.297 ± 0.012) × 106 rad·s-1 were obtained for the VL and LL interface. Here, the uncertainties for the four characteristic properties are given on a 95% confidence level (k = 2) and are approximately a factor two larger than in corresponding consecutive measurements. In the latter case, the position of the scattering volume was optimized to primarily focus on only the VL or LL signal. Nevertheless, the absolute values for C and q obtained for the simultaneous detection of signals from both interfaces agree well within combined uncertainties with the results from the consecutive investigations optimized solely for the resolution of either the VL or the LL interface.

4.2. Proof of hydrodynamic theory In the following, a strategy is suggested for the determination of the VL and LL interfacial tensions as well as the viscosities of the two liquid phases in the studied multiphase VLL systems by SLS. For an accurate analysis of the individual surface fluctuations present at the different phase boundaries, separate consecutive light scattering measurements focusing either on the VL or the LL interface were performed. First, measurements were carried out at the upper VL interface to access the dynamics of the surface fluctuations i.e., q,VL and C,VL, which is connected with the interfacial tension VL and the liquid dynamic viscosity L1. Then, the scattering volume was shifted to the lower LL interface to obtain information on the dynamics of the surface fluctuations present there. 20

By using the values for the dynamics of the LL interface, i.e., q,LL and C,LL, in combination with the value for the dynamic viscosity of the intermediate liquid phase L1 accessed via the analysis of the VL interface, the LL interfacial tension LL and the liquid dynamic viscosity L2 are determined. The suggested approach of consecutively analyzing the upper and lower interface within the same experimental setup is utilized to prove the hydrodynamic theory for the description of the dynamics of surface fluctuations present at phase boundaries [62]. For this, a comparison between our experimental data and theoretically calculated values for C and q is performed. In detail, surface fluctuations at both the VL and LL interface are considered, where the modulus of the scattering vector was varied between (5.15 and 8.24) × 105 m-1. While this approach was often applied for the proof of the hydrodynamic theory in connection with the VL interface of two-phase systems [23,46,67], it was never carried out in connection with a LL interface alone as well as a LL interface in combination with a VL interface forming a multiphase system. For the VLL system consisting of n-C10H22 and MeOH at saturation conditions, the results for the characteristic dynamic properties related to the signal from the VL interface, i.e., C,VL and

q,VL, as well as from the LL interface, C,LL, and q,LL, obtained from consecutive SLS measurements are shown in Fig. 3 as a function of the modulus of the scattering vector q at the two studied temperatures of T = 333.15 K (green color) and T = 358.15 K (red color). In Fig. 3a, the measured values for the damping VL (= C,VL‒1) and the frequency q,VL of the surface fluctuations at the VL interface are shown by the open symbols and are given for three different values for q corresponding to three different external angles of incidence of (3.0, 3.1, and 3.2)°. For the dynamics of surface fluctuations at the LL interface, i.e. for LL and q,LL, a broader q range corresponding to eight incident angles between (3.0° to 4.0)° and four incident angles between (2.5 and 3.0)° was studied for 333.15 K and 358.15 K as it is shown in Fig. 3b by the filled symbols. For each interface, the measured results for C and q are compared to the theoretical values calculated by two different approaches based on an exact solution of the dispersion relation for the dynamics of surface fluctuations [36,62]. Here, the densities and viscosities of the two contacting 21

phases as well as the corresponding interfacial tension at saturation conditions are required as input data to solve the dispersion relation for the respective interface as it was described in section 2. For the input quantities V, L1, L2 and V, data and correlations are adopted from literature and are discussed in the Supplementary material. Therein, also the modeling of the composition of the two liquid phases and the vapor phase is detailed for both studied multiphase systems.

Fig. 3. Dispersion relations for the dynamics of surface fluctuations at the vapor-liquid (a) and liquid-liquid (b) interface for the multiphase system consisting of n-C10H22 and MeOH at temperatures of 333.15 K (green color) and 358.15 K (red color). Damping (upper part) and frequency (lower part) of surface fluctuations as a function of the modulus of the scattering vector q. Open green squares (T = 333.15 K) and filled red squares (T = 358.15 K), SLS measurement, this work; solid green lines (T = 333.15 K) and dashed red lines (T = 358.15 K), theoretical calculation based on exact solution of dispersion relation [36,62] using the measured average results for L1 and VL in (a) as well as for L1,L2, and LL in (b); dotted green lines (T = 333.15 K) and chain red lines (T = 358.15 K) in (b), theoretical prediction based on exact solution of dispersion equation [36,62] using data for L1 andL2 estimated according to the UNIFAC-VISCO model [70,71] as well as data for LL estimated from the absolute difference of the vapor-liquid surface tensions of n-

22

C10H22 [72] and of MeOH [72]. For all theoretical calculations, further input for V, L1, L2 and V were used from literature as discussed in the Supplementary material.

The difference between the two approaches is given by the input values for the viscosities of the two liquid phases, L1 and L2, as well as the interfacial tensions for the VL and LL interface,

VL and LL. While L1 and VL are required for the analysis of surface fluctuations at the VL interface, L1, L2, and LL are input quantities for the analysis of surface fluctuations at the LL interface. For these data, the measured mean values averaged over all individual measurements at different q values were used to solve the dispersion equation [36,62]. The corresponding theoretical calculations for the damping VL and LL as well as the frequency q,VL and q,LL based on the knowledge of the measured thermophysical properties of interest are given by the solid green lines for 333.15 K as well as dashed red lines for 358.15 K in Fig. 3. In connection with the LL systems, it was also of our special interest to test whether prediction schemes for the interfacial tension LL as well as the viscosities L1 and L2 can be used as input data for the exact solution of the dispersion relation [36,62] to describe the behavior of LL and q,LL as a function of q. One method to represent the viscosity of liquid mixtures is given by the UNIFAC-VISCO model [70,71] which is commonly employed for the study of mixtures with components strongly differing in size [73,74]. The model requires information on the molar composition and density of the liquid mixture as well as the dynamic viscosities and densities of the corresponding pure saturated liquids. While the values for the pure liquid viscosities were adapted from Huber et al. for n-C10H22 [75] and Xiang et al. [76] for MeOH, data for the liquid densities of the pure substances and of the mixtures as well as for the molar composition were employed or calculated as it is detailed in the Supplementary material. Furthermore, the selected viscosity model includes a combinatorial term accounting for the shape of and structural differences between the involved molecules as well as a residual part accounting for molecular interactions. The parameters required for the calculations of both terms were obtained from Ref. [77]. For the multiphase system 23

consisting of n-C10H22 and MeOH, the predictions based on the UNIFAC-VISCO model [70,71] can represent our experimental data for L1 within ±5% and for L2 within ±17%. For the estimation of LL interfacial tensions, several modeling schemes [10,12,78,79] have been developed in literature. Most of these schemes are restricted to specific systems, require many parameters, and/or cannot be used as reliable prediction schemes. For example, the model of Bahramian and Danesh [10] overpredicts our measured LL data by about one order of magnitude. For a direct estimation of the LL interfacial tension, the difference between the surface tensions of pure n-C10H22 and pure MeOH was utilized in this study. The corresponding VL data were employed from the work of Mulero et al. [72]. The suggested simple approach can predict our measured LL data satisfactorily within ±(14 and 320)%, taking into account the relatively small absolute values for LL between about (0.2 and 1.1) mN∙m-1. As a result of the theoretical predictions, the final results for LL and

q,LL are shown as dotted lines for 333.15 K and as chain lines for 358.15 K in Fig. 3b. For the characteristic dynamic quantities VL and q,VL related to the VL interface of the studied multiphase system consisting of n-C10H22 and MeOH, agreement can be found between the measured values and the theoretical values obtained from the exact solution of the dispersion relation [36,62] for all investigated wave vectors at the two studied temperatures; see Fig. 3a. Thus, the oscillatory signals originating from the fluctuations at the vapor-liquid interface are well described by classical hydrodynamic theory [36,62]. For the first time, we can demonstrate that the hydrodynamic theory [36,62] is also valid for the fluctuations at LL interfaces. This can be seen in Fig. 3b from the agreement of the measured and theoretical values for LL and q,LL at both studied temperatures over the broad range of wave vectors investigated. It is worth mentioning that the frequency of the capillary waves at 358.15 K first increases with increasing q, before it reaches zero at a q value of about 0.85  106 m-1 corresponding to a critical wavelength of the surface fluctuations of C = 7.4 µm. Here, a transition from an oscillatory to an overdamped behavior of surface fluctuations is found for comparably low 24

wave numbers. This behavior is mainly attributable to the relatively low LL interfacial tension in vicinity of the UCST of the multiphase system consisting of n-C10H22 and MeOH at TC = 363.9 K. Using the estimations for the viscosities of both liquid phases and the LL interfacial tension as input quantities in the dispersion equation [36,62], the prediction results for LL and q,LL can also be considered in Fig. 3b. For the damping, qualitative agreement between the measured and predicted data is given, which is caused by the sound description of the liquid viscosities by the UNIFAC-VISCO model [70,71]. The datasets for the frequency, however, show significant deviations, especially at 358.15 K. Here, the predictions cannot describe the characteristic behavior of the measured q,LL data close to the critical damping where q,LL converges to 0. The main reason for the inaccurate description of the frequency of the capillary waves at the LL phase boundary is caused by the poor representation of the LL interfacial tensions by the simple correlation based on the surface tensions of the pure compounds. The agreement between the measured and theoretical values for the damping and frequency of the surface fluctuations at the VL and LL interface for the multiphase system consisting of n-C10H22 and MeOH was also found in connection with the multiphase system consisting of n-C12H26 and MeOH which is not shown here. Furthermore, first-order approximations of the dispersion relation [23,46] which are often adopted in the literature [39,40,60,80] cannot be used for the description of the dynamics of the hydrodynamic fluctuations at the VL and LL interface, and, thus, cannot be applied for the accurate determination of viscosities and interfacial tensions.

5. Results and discussion 5.1. Summary of experimental data and uncertainty analysis For the absolute determination of the two liquid viscosities and the two interfacial tensions of the studied multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions, the following procedure has been applied. At first, an exact numerical solution of the dispersion relation [36,62] was carried out for the analysis of surface waves at the 25

VL interface based on the measured data for C,VL and q,VL as well as literature data for L1, V, and V. This gives access to the liquid dynamic viscosity L1 of the intermediate n-alkane-rich liquid phase and the interfacial tension VL between the upper vapor phase and the intermediate liquid phase. Then, an exact solution of the dispersion relation [36,62] was performed for the analysis of surface waves at the LL interface. Here, in addition to literature data for L1 and L2, the measurement results for C,LL and q,LL as well as the data obtained for L1 from the previous study of the VL interface were used. By this, the liquid dynamic viscosity L2 of the lower MeOH-rich liquid phase and the interfacial tension LL between the two liquid phases were determined. For all individual measurements performed in this study, the expanded uncertainties (k = 2) for the four properties of interest, L1, L2, VL, and LL, were analyzed by an error propagation calculation scheme as suggested in Refs. [38,58]. This scheme takes into consideration the uncertainties of the measured quantities as well as of the literature data adopted for data evaluation. Considering the estimated uncertainties of the data for the pure substances and the used correlation methods adopted from literature and described in the Supplementary material, expanded relative uncertainties (k = 2) for the density of the upper vapor phase Ur(V), the density of the intermediate liquid phase Ur(L1), the density of the lower liquid phase Ur(L2), and the dynamic viscosity of the upper vapor phase Ur(V) of 10%, 1.5%, 1.5%, and 10%, respectively, can be specified for both systems studied. For the mole fractions x of the liquid phases, estimated expanded absolute uncertainties U(x) of 0.01 are considered to calculate the uncertainties in the liquid densities. The results for the liquid dynamic viscosities L1 and L2 as well as the interfacial tensions

VL1 and L1L2 of the two multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions between (333.15 and 358.15) K obtained from SLS are summarized in Tables 1 and 2. Most of the listed data are average values of at least six independent measurements with different external angles of incidence E. Only two measurements were performed for the system n-C12H26 and MeOH at 333.15 K. In addition to the calculated mole 26

fractions of MeOH, xMeOH, in both liquid phases, the overall expanded uncertainties (k = 2) of the SLS results are given in Tables 1 and 2. Table 1 Dynamic viscosities  of the intermediate liquid phase L1 (L1) and the lower liquid phase L2 (L2) for the multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions obtained by surface light scattering at temperatures T and corresponding MeOH mole fractions xMeOH in the liquid phases.a phase intermediate liquid phase L1 lower liquid phase L2 phase intermediate liquid phase L1 lower liquid phase L2 a

Multiphase system consisting of n-C10H22 and MeOH T/K xMeOH / (mPa∙s) 333.15 0.227 0.5010 358.15 0.525 0.3779 333.15 0.950 0.3871 358.15 0.885 0.3738 Multiphase system consisting of n-C12H26 and MeOH T/K xMeOH / (mPa∙s) 343.15 0.173 0.6404 358.15 0.228 0.4807 343.15 0.959 0.2870 358.15 0.938 0.3474

100∙Ur() 2.3 2.2 6.1 5.6 100∙Ur() 2.4 3.0 6.6 7.4

The expanded uncertainties U are U(T) = 0.015 K and U(xMeOH) = 0.01, while the relative expanded uncertainties Ur()

are given in the table (level of confidence = 0.95).

Table 2 Interfacial tensions  between the vapor phase V and the intermediate liquid phase L1 ( VL) as well as between the intermediate liquid phase L1 and the lower liquid phase L2 (LL) for the multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions obtained by surface light scattering at temperatures T.a Multiphase system consisting of n-C10H22 and MeOH interface T/K / (mN∙m-1) 333.15 18.88 upper vapor phase V – intermediate liquid phase L1 (VL) 358.15 16.04 333.15 1.085 intermediate liquid phase L1 – lower liquid phase L2 (LL) 358.15 0.211 Multiphase system consisting of n-C12H26 and MeOH interface T/K / (mN∙m-1) 343.15 18.71 upper vapor phase V – intermediate liquid phase L1 (VL) 358.15 17.08 343.15 1.461 intermediate liquid phase L1 – lower liquid phase L2 (LL) 358.15 0.911 a

100∙Ur() 1.6 2.2 4.8 4.6 100∙Ur() 1.5 1.8 5.2 6.0

The expanded uncertainties U are U(T) = 0.015 K, while the relative expanded uncertainties Ur() are given in the table

(level of confidence = 0.95).

For the dynamic viscosities of the intermediate liquid phase L1 and the VL interfacial tensions determined from the analysis of surface fluctuations at the VL interface, average measurement uncertainties (k = 2) of Ur(L1) = 2.5% and Ur(VL) = 1.8% could be obtained. These 27

values are similar to those determined in our recent SLS studies [57,58,67] of systems consisting of one vapor phase and one liquid phase. While the uncertainties of the reference data for the vapor phase have comparatively small influence on the final results for L1 and VL obtained in this study, the main factors determining the overall uncertainties are given by the standard deviations of the individual measurements and the uncertainties in the liquid density Ur(L1). From the analysis of surface fluctuations at the LL interface, average measurement uncertainties (k = 2) for the liquid dynamic viscosities of the lower liquid phase L2 of Ur(L2) = 6.4% and for the LL interfacial tensions of Ur(LL) = 5.2% were achieved. These uncertainties are per se larger than those related to L1 and VL. On the one hand, the liquid properties L1 and L1 used as input data in the error propagation calculation scheme for the LL interface have a much stronger impact on the output quantities than the vapor properties V and V used as input data in the error propagation calculation scheme for the VL interface. On the other hand, also the percentage standard deviations of the independent measurements for L2 and LL were about a factor of three larger than those for L1 and VL. This is caused by the challenging analysis of the LL signals showing fewer oscillations than the VL signals; see Fig. 2. The experimental results for the liquid dynamic viscosities and the interfacial tensions of the two studied multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions are shown as a function of temperature in Figs. 4 and 5. Here, open and filled symbols refer to the values obtained from the consecutive analysis of the dynamics of surface fluctuations at the VL and LL interface. Different symbols indicate the results for the two MeOHbased systems containing the hydrophobic n-alkanes n-C10H22 or n-C12H26. For comparison, also the experimentally-based correlations for the liquid dynamic viscosities [58,75,76] and the surface tensions [58,72] of the three pure substances n-C10H22, n-C12H26, and MeOH under saturation conditions are given as lines in Figs. 4 and 5.

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Fig. 4. Dynamic viscosities  of the intermediate liquid phase L1 (L1, open symbols) and the lower liquid phase L2 (L2, filled symbols) for the multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions from surface light scattering in comparison with literature data for the corresponding pure substances at saturation conditions as a function of temperature: solid line, MeOH, Xiang et al. [76]; dashed line, nC10H22, Huber et al. [75]; chain line, n-C12H26, Koller et al. [58].

Fig. 5. Interfacial tensions  between the upper vapor phase V and the intermediate liquid phase L1 (VL, open symbols) as well as between the intermediate liquid phase L1 and the lower liquid phase L2 (LL, closed symbols) for the multiphase systems consisting of n-C10H22 and MeOH as well as n-C12H26 and MeOH at saturation conditions from surface light scattering in comparison with surface tension data from literature for the corresponding pure substances at saturation conditions as a function of temperature: solid line, MeOH, Mulero et al. [72]; dashed line n-C10H22, Mulero et al. [72]; chain line, n-C12H26, Koller et al. [58].

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5.2. Discussion of viscosity and interfacial tension First, the liquid viscosities for the two studied multiphase liquid systems are discussed. For each temperature, the experimental L1 data for the intermediate n-alkane-rich liquid phases are larger than the L2 data for the corresponding lower MeOH-rich phases. This goes along with the larger viscosities for the n-alkanes than for MeOH as it can be seen from the correlations for the pure substances in Fig 4. The trend with respect to the viscosities of the pure substances holds also when comparing the L1 data for the n-C10H22-rich liquid phase with those for the n-C12H26-rich liquid phase. At the lower temperature studied for each system, the viscosities for the lower MeOH-rich liquid phases are closer to the viscosity of pure MeOH than those for the intermediate n-alkane-rich liquid phases relative to the viscosity of the corresponding n-alkane. This behavior can be assigned to the much smaller mole fraction of n-alkanes in MeOH than vice versa; see Table 1. For both systems, a temperature increase from 333.15 K to 358.15 K for the multiphase system consisting of n-C10H22 and MeOH as well as from 343.15 K to 358.15 K for the multiphase system consisting of n-C12H26 and MeOH results in a convergence of the viscosity data of the two coexisting liquid phases. This trend is related to the enhanced mutual solubilities in each liquid phase with increasing temperature. For the viscosities of the MeOH-rich phase in the multiphase system consisting of nC12H26 and MeOH, even an increase of L1 with increasing T is identified. While the L1 and L2 data at 358.15 K match within combined uncertainties for the multiphase system consisting of nC10H22 and MeOH, they still deviate by about 38% for the n-C12H26/MeOH system. These observations can be expected due to the lower TC value of 363.9 K [69] for the multiphase system consisting of n-C10H22 and MeOH compared to about 380 K for the multiphase system consisting of n-C12H26 and MeOH. The measured LL interfacial tensions LL for the studied multiphase systems consisting of nC10H22 and MeOH as well as n-C12H26 and MeOH are at least an order of magnitude smaller than the corresponding VL interfacial tensions VL. The trend of decreasing VL and LL interfacial tensions with increasing temperature is also in agreement with the behavior of fluid systems. It is 30

worth mentioning that the VL interfacial tensions VL for both multiphase systems are close to or even below the values of pure MeOH although the mole fraction of MeOH is generally much smaller than that of the n-alkanes in the intermediate liquid phase of both systems; see Tab. 1. This indicates that MeOH showing a lower surface tension than the two n-alkanes is mainly present at the VL phase boundary and acts a surface active substance which lowers the interfacial tension. Similar effects were also observed for the VL interfacial tensions for mixtures of an ionic liquid and ethanol where the latter compound is enriched at the VL interface starting from a critical concentration [81]. For a given temperature, the measured interfacial tensions between the two coexisting liquid phases are larger for the n-C12H26-based system compared to the n-C10H20-based system. This can be related to the larger surface energy of n-C12H26 than n-C10H22, which is reflected by the corresponding surface tension values, and to the larger difference between the measurement temperatures and the UCST for the multiphase system consisting of n-C12H26 and MeOH system. According to the theory for near-critical phenomena [82], the interfacial tension between the two liquid phases gradually vanishes as the UCST is closely approached. This behavior is in agreement with our measurement results. For the multiphase system consisting of n-C10H22 and MeOH, the low LL value of 0.21 mN∙m-1 at 358.15 K can be attributed to the vicinity of the studied temperature to the UCST of the system. To the best of our knowledge, no experimental data for the viscosities and interfacial tensions related to the studied multiphase systems at saturation conditions are available in literature. The measurement results for the kinematic viscosity of the n-C10H22/MeOH system at temperatures between (298.15 and 313.15) K reported by Totchasov et al. [83] were performed in the regions of low n-C10H22 concentration. Here, complete miscibility of the two substances is given resulting in only one single liquid phase.

31

6. Conclusions The present contribution has proved that SLS is a suitable method for the reliable determination of interfacial tensions and viscosities in multiphase systems at macroscopic thermodynamic equilibrium. This represents a further development of the method which has already been established in the past two decades as reliable and routine tool for the determination of liquid viscosity and surface tension in vapor-liquid systems [23,37]. The multiphase systems investigated in this work are the two partially miscible binary model systems consisting of n-decane and methanol as well as n-dodecane and methanol at saturation conditions. They form an upper vapor phase, an intermediate n-alkane-rich liquid phase, and a lower methanol-rich liquid phase. Former studies [59,61] investigating the dynamics of capillary waves at liquid-liquid phase boundaries by SLS suffer from the application of a first-order approximation for data evaluation and an improper experimental realization. In this study, we have taken care of the conditioning of the three-phasic samples in a measurement cell which provides flat phase boundaries and which allows for the analysis of the scattered light without the presence of any line broadening effects. By irradiating the laser beam onto the vapor-liquid and liquid-liquid phase boundaries, two oscillatory signals originating from surface fluctuations at both interfaces could be detected simultaneously within one single experiment. Based on an exact treatment of the capillary wave problem for the vapor-liquid and liquid-liquid interface [36,62], we could demonstrate that the measured dynamics of capillary waves, i.e. their frequency and damping, is in agreement with theory. With the information from the experiment and further data from literature, i.e. the densities of the three coexisting phases and the vapor viscosity, absolute data for the viscosities of the two liquid phases as well as the vapor-liquid and liquid-liquid interfacial tensions could be determined for the two model systems at saturation conditions at temperatures between (333 and 358) K with total measurement uncertainties (k = 2) ranging from (2.2 to 7.4)% as well as from (1.5 to 6.0)%. The SLS results representing the first experimental data for the investigated multiphase systems show the expected trends of approaching liquid viscosities and vanishing liquid-liquid interfacial tensions in the vicinity to the upper critical 32

solution temperatures of the systems. The advantages of the SLS method and of the suggested approach can be found in the determination of multiple properties in a single experimental setup probing the very same sample at well-defined conditions without any calibration procedure. The present study may stimulate further investigations of multiphase systems with ultralow interfacial tensions smaller than 10 -1 mN∙m-1. For the reliable determination of interfacial tensions and viscosities of such systems, also a further improvement in connection with signal analysis and separation needs to be carried out. By this, measurement uncertainties of the accessible thermophysical properties in the percentage level are intended to be achieved.

Author information Corresponding Author *

E-mail: [email protected]. Tel.: +49-9131-85-23279.

Acknowledgements This work was financially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative.

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at the corresponding link.

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Graphical abstract

Interfacial Tensions and Viscosities in Multiphase Systems by Surface Light Scattering (SLS) Thomas M. Koller,*,a Tobias Prucker,a Junwei Cui,a,b Tobias Klein,a and Andreas P. Fröbaa

a

Institute of Advanced Optical Technologies ‒ Thermophysical Properties (AOT-TP),

Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 6, 91052 Erlangen, Germany b

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

*

Author to whom correspondence should be addressed. Tel. +49-9131-85-23279, fax +49-9131-85-

25878, E-mail [email protected], ORCID number 0000-003-4917-3079.

Graphical abstract

36