- © 2010 American Mineralogist
Interfacial tension between immiscible liquids is an important thermodynamic parameter of silicate melt unmixing and a property that determines the kinetics of phase separation. In this study, we present experimental measurements of interfacial tension between immiscible Fe-rich and silica-rich melts in the system K2O-FeO-Fe2O3-Al2O3-SiO2. We have also measured densities and surface tensions of the individual immiscible liquid phases. The measurements were carried out in air at 1500–1550 °C by the maximum detachment force method employing vertical cylinder geometry and using a gravimetric balance system. We have chosen the most oxidized and contrasting liquid compositions containing 73 and 17 wt% SiO2 and 14 and 80 wt% FeOt, respectively, that have been shown to coexist in air at and above 1465 °C. Interfacial tension between the synthetic immiscible liquids decreases with increasing temperature from 16.4 ± 3.1 mN/m at 1500 °C to 7.8 ± 1.1 mN/m at 1550 °C. Interfacial tension between natural, less compositionally contrasting ferrobasaltic and rhyolitic melts should be even lower by a factor of 2 or 3. Very low interfacial tension implies easy nucleation of immiscible liquid droplets and very slow coarsening of resulting silicate emulsions.
Immiscibility in silicate and other glass-forming liquids has been extensively studied in igneous petrology (Roedder 1978; Philpotts 1982) as one factor to explain the diversity of magmatic rocks, and because of important applications to glass technology, e.g., in manufacturing of glass ceramics (Shelby 2005). Decades of experimental and theoretical research resulted in comprehensive thermodynamic models of silicate liquid immiscibility (see review by Hudon and Baker 2002), and good understanding of physical and chemical driving forces behind unmixing and liquid-liquid element partitioning (Schmidt et al. 2006; Veksler et al. 2006). On the other hand, the kinetics of liquid immiscibility has not received enough attention. To the best of our knowledge, only one study specifically dealt with the kinetics of immiscibility in natural basaltic magma (Martin and Kushiro 1991). Our recent work (Veksler et al. 2008) revealed sluggish nucleation and phase separation kinetics during unmixing of synthetic Fe-bearing aluminosilicate melts. Interfacial energy is a key parameter determining the kinetics of nucleation and growth of immiscible liquid droplets. Theoretical considerations (Hammel 1967) and the morphology of quenched immiscible glasses (Veksler et al. 2008) have implied a very low interfacial tension between immiscible silicate liquids but, as far as we know, interfacial tension has never been measured directly by experimental methods for any pair of immiscible silicate melts.
Here we report results of experimental measurements of interfacial tension between Fe-rich and silica-rich immiscible melts in the system K2O-FeO-Fe2O3-Al2O3-SiO2. We measured interfacial tension in air between the most contrasting, oxidized liquid compositions. Therefore, the values are likely to represent the upper limit of interfacial tension between immiscible Fe-rich and silica-rich aluminosilicate melts. In the discussion, we examine relationships between interfacial tension and surface tensions of the coexisting liquids and touch upon some implications for immiscibility in natural basaltic magmas.
Surface and interfacial tension was measured by the method of maximum detachment force of a vertical cylinder wetted to the interface. The force was measured using a gravimetric balance system. This version of the detachment technique is a classical method that has been broadly used in liquid-gas and liquid-liquid tensiometry (Walker and Mullins 1981; Rusanov and Prokhorov 1996), and its practical and theoretical aspects have been investigated and described in great detail (e.g., Padday et al. 1975). The method and the equipment that we used were successfully tested in our recent study of interfacial tension between immiscible melts in alkaline earth-boron oxide binaries MgO-B2O3, CaO-B2O3, and BaO-B2O3 (Veksler et al. 2010).
The detachment method requires relatively large volumes of liquids, at least a few cubic centimeters in our case. A sufficiently large area of the interface is needed to minimize effects from crucible walls (Rusanov and Prokhorov 1996). To facilitate the formation of homogenous, perfectly separated immiscible liquid layers, pre-synthesized conjugate liquid compositions are loaded separately into a vessel used for the measurements, one composition on top of the other in the order of decreasing density.
The compositions of the two synthetic starting liquids used in this work (Table 1⇓) are based on electron microprobe analyses of the conjugate Fe-rich (Lfe) and silica-rich (Lsi) immiscible liquids in the system K2O-FeO-Fe2O3-Al2O3-SiO2 published by Naslund (1983). Naslund (1976, 1983) investigated the system at oxygen fugacities of 10−12, 10−9, 10−5, and 10−0.7 bar and showed that the miscibility gap broadened with increasing fO2 (Fig. 1⇓). The compositions used in our study (Table 1⇓) represent a pair of the most oxidized and compositionally contrasting liquids equilibrated in air (fO2 = 10−0.7 bar) above the magnetite liquidus at 1465 °C. Obvious advantages of such liquids are that they do not require a protective atmosphere, and should have the maximal interfacial tension due to the greatest compositional contrast. High experimental temperatures may be also viewed as an advantage because of suppressed melt viscosity.
Starting materials were synthesized from weighed and ground mixtures of reagent-grade chemicals SiO2, Al(OH)3, Fe2O3, and K2CO3. The mixtures were loaded in Pt crucibles and fused in an electric resistance furnace at 1500 °C three times for about 5–6 h in total with intermediate quenching, crushing and grinding of the fused products. At 1500 °C, the silica-rich and Fe-rich mixtures Lsi and Lfe were completely molten, and they quenched, respectively, to dark-brown glass and black, brittle ceramic material mostly composed of Fe spinel crystals. Weight control of the charges and containers during syntheses did not reveal significant Fe losses to platinum crucibles. Previous works (e.g., Kilinc et al. 1983) have shown that the formation of Fe-Pt alloys is not a major problem for experiments at oxidizing conditions in air.
Surface tension of the Fe-rich and silica-rich immiscible melts, and the interfacial tension between them were measured at the Ludwig Maximilian University of Munich with a system comprising a GERO vertical-tube electrical-resistance furnace, and a Mettler AE 100 high-precision laboratory balance. This experimental setup is similar to that used in the studies of surface tension of silicate melts by Walker and Mullins (1981) and Padday et al. (1975). The same system has been also used for density measurements via the double-bob Archimedean buoyancy method (Courtial and Dingwell 1999). The furnace is heated by MoSi2 hairpin elements. The inner bore of the alumina muffle tube is 35 mm. Crucibles are bottom-loaded and supported in the hot zone of the furnace by an alumina pedestal (Fig. 2⇓). Hot zone temperature is maintained with an electronic set-point controller and a Pt94Rh6-Pt70Rh30 (Type B) control thermocouple, and monitored with a second Pt-Pt90Rh10 (Type S) thermocouple positioned as closely as possible to the crucible inside the furnace. From control thermocouple readings at different positions in the furnace, we estimate the maximum temperature uncertainty including contributions from thermal gradients and fluctuations at ±2 °C. The balance is positioned above the furnace on a movable pedestal that allows centering of the balance, and vertical displacement within the furnace at a variable speed with minimal steps and the precision of 0.01 mm. By moving the balance vertically, Pt cylinder probes suspended from the balance arm can be submersed into or drawn out of the melt. The electronic balance is connected to a computer, which records measured weights every second and stores the data. An example of a raw data record is presented in Figure 3⇓.
The cylindrical probe used in this study was a Pt rod, 250 mm long and 3.05 mm in diameter, machined to cylindrical shape at the lower end that was in contact with the melts. Special care has been taken to keep the contact face smooth and circular, and to hold it during the measurements in a perfectly horizontal position parallel to the measured liquid surfaces. An attachment-detachment measurement cycle started with the rod inside the furnace right above the crucible. Once the weight and the temperature stabilized, the balance was tared. Then the balance was gradually lowered until contact of the probe with the liquid surface or liquid-liquid interface was made. The contact was indicated by a sudden increase in force on the balance due to the surface tension (Fig. 3a⇑). After the contact, the balance with the probe was raised in 0.1–0.4 mm steps until the point of maximum force was found. The pedestal height was measured and recorded at each step (Fig. 4⇓). High viscosity of the upper silica-rich melt required relaxation times of at least 5 min between the steps to bring the meniscus to equilibrium (Fig. 3b⇑). The upward movement continued further until the probe detached. The detachment resulted in a sudden drop of the apparent weight at the balance (Fig. 3b⇑). The detached weight of the rod was usually a few milligrams higher than its original dry weight due to the presence of adhering melt (Fig. 4⇓). The attachment-detachment cycles were repeated three times for each interface, and showed good reproducibility of the maximal weight (±0.001 g) and pedestal height (±0.02 mm). Experimental static noise at the balance notably increased with decreasing temperature from ±0.0025 g at 1550 °C to ±0.0053 g at 1500 °C, presumably because of the increasing viscosity of the Lsi melt. Further details about the calibration of our gravimetric system, and comparisons of our tensiometry results with published surface tension values can be found in our previous paper (Veksler et al. 2010).
Electron microprobe analyses of run products
After a series of measurements, the crucible with melt(s) was taken out of the furnace and quenched in cold water. Fragments of the quenched Lfe and Lsi layers were analyzed using a Cameca SX-100 electron microprobe (EMP) at the GFZ Potsdam. Analyses were performed in WDS mode at 15 nA beam current and an accelerating voltage of 15 kV. Counting time for all the elements (K, Fe, Al, and Si) was set to 20 s on peak and 10 s on background. The following synthetic and natural standards were used for the calibration: orthoclase (Al and K), wollastonite (Si), and hematite (Fe). Because immiscible Fe-rich liquid quenched to a coarse-grained aggregate of Fe spinel crystals and silicate glass (Fig. 5⇓), it was analyzed with a defocused beam with the diameter up to 50 μm. Dozens of point analyses were performed along vertical profiles across the layers to obtain statistically representative averages and check for compositional gradients.
Calculation of surface or interfacial tension from the maximal pool of a vertical cylinder probe is not a trivial task, especially when contact angles with the meniscus cannot be measured directly. In this study and our previous work on borate melts (Veksler et al. 2010) we used a calculation method developed by Padday et al. (1975), which is briefly explained below.
When a circular face of a vertical cylinder touches an interface between two liquid (or liquid and gas) phases and raises the meniscus above the undisturbed horizontal level (Fig. 6⇓), the vertical force in excess of the dry weight of the cylinder is exactly equal to the weight of the liquid raised above the general horizontal level. This force F, which is measured by the balance, depends on the radius of the cylinder r, density contrast Δρ between the phases above and below the interface, the interfacial tension γ, and the contact angle φ. The relationship is represented by the equation
(Padday et al. 1975), where h is the height of the cylinder above the undisturbed horizontal interface (Fig. 6⇑) and g is acceleration due to Earth’s gravity. The first term represents the pressure on the bottom surface of the cylinder due to the hydrostatic pressure of the liquid below the interface, and the second term the force due to the interfacial tension pool around the perimeter. Equation 1 provides the theoretical framework for calculation of γ from the force F measured by the balance. It has been shown (Padday et al. 1975; Walker and Mullins 1981) that at small r (<0.7 mm for silicate melts) the first term becomes negligible and can be dropped. However, the rod used in the present experiments was too wide for such simplification. The calculation is further complicated by the fact that the contact angle φ at the maximal pool could not be measured in our experiments. Tabulated solutions of Equation 1 proposed by Padday et al. (1975) allow one to circumvent direct measurements of φ, but the calculation method still requires an input of Δρ values in addition to F and r. As noted above, we measured melt densities by the Archimedean method (Courtial and Dingwell 1999). The diameter of our platinum rod r was repeatedly measured using a digital caliper to the precision of ±0.01 mm. The measured r-value was corrected for thermal expansion between room and experimental temperatures using the linear expansion coefficient of pure platinum 10.4 × 10−6 °C−1 (Walker and Mullins 1981). We assumed g = 9.81 m/s2 as a local value for Munich, Germany.
Surface tensions of the Lfe and Lsi melts did not show any significant changes with temperature at 1500–1550 °C with γLfe varying between 342–348 mN/m, and γLsi between about 275–278 mN/m (Table 2⇑). Higher surface tension of the Lfe liquid is in general agreement with known effects of melt composition on surface tension. Melts enriched in di- and trivalent network-modifying cations tend to have a higher surface tension than strongly polymerized, silica-rich liquids (e.g., Weirauch 2005; Kucuk et al. 1999). The calculation method by Kucuk et al. (1999) based on the statistical analysis of experimental data predicts γLfe = 472 and γLsi = 308 mN/m at 1400 °C; values 15–35% higher than our measurements. It should be noted, however, that the statistical model may not work well for Lfe composition because of the extremely high (FeO+Fe2O3) content and low silica. Surface tension of natural silicate melts varies in the range of 350–370 mN/m (Walker and Mullins 1981). This is again higher than our γLsi value for a comparable melt composition, but the difference may be partly due to different calculation methods. Walker and Mullins (1981) calculated γ from the maximal detachment force F using a simplified formula leaving the first term of Equation 1 out, and assuming cos (φ) = 1 (this was justified by a smaller diameter of their rod). If we use the same calculation method, we would get γLsi = 365.2 mN/m, well within the 350–370 mN/m range.
Interfacial tension between Lfe and Lsi is low and decreases with temperature from 16.4 mN/m at 1502 °C to 7.8 mN/m at 1550 °C (Table 2⇑). Such systematic decrease complies with theoretical prediction that interfacial tension between immiscible fluids should decrease with growing temperature, and eventually go to 0 at the critical (consolute) point. The consolute temperature of the Lfe-Lsi binodal at the oxidizing conditions in air is unknown. Rapid decrease of the measured interfacial γ values implies that the consolute temperature is likely to be somewhere between 1580 and 1600 °C.
Electron microprobe study of quenched immiscible melts equilibrated at 1550 °C (Table 1⇑) confirmed chemical homogeneity of liquid layers and perfect separation of the phases by gravity. The meniscus between the liquids is razor sharp (Fig. 5a⇑), and all microscopic heterogeneities revealed optically or in backscattered electron images (BSE) almost certainly formed during quenching. Aggregates of intergrown Fe-spinel crystals and secondary droplet exsolutions of the silica-rich melt are the most prominent quench features of the Lfe layer. A series of BSE images in Figures 5b–5d⇑ illustrates a gradual transition from the fine-grained chilled zone of the Lfe layer without visible silicic secondary droplets right near the crucible walls to progressively coarser quench crystallization and exsolution textures in the inner parts of the crucible where cooling was slower. Apart from the quench crystallization and exsolution, the Lfe layer is remarkably homogenous showing no significant difference between the compositions near the bottom and the top near the interface (Table 1⇑). The upper Lsi layer quenched to dark-brown glass dusted with tiny (less than a few micrometers in size) grains, which are too small for optical or microprobe identification but likely to be quench magnetite crystals. The concentration of dispersed particles is somewhat higher at the bottom of the Lsi layer right above the interface. Microprobe analyses of uncontaminated glass in that region are difficult. This results in a greater compositional scatter of the electron microprobe data (see standard deviations in Table 1⇑), apparently higher Fe2O3 and lower silica of the average. Although a minor compositional gradient in the Lsi liquid cannot be completely ruled out, the difference between the top and the bottom of the glassy Lsi product is probably due to magnetite nucleation and settling during quench. Comparison between compositions of the layers quenched at 1550 °C and the starting mixtures (Table 1⇑) implies a minor increase of mutual solubility between the melts due to the higher equilibration temperature [as mentioned above, the starting mixtures are very close to coexisting melt compositions at 1465 °C published by Naslund (1983)]. The decrease of the K2O/Al2O3 mass ratio in the Lsi layer from unity to about 0.95 may be due to K volatilization. All Fe in the analyses is listed as Fe2O3 but a significant proportion of ferrous iron was certainly present in high-temperature melts as evidenced, for instance, by formation of quench magnetite. According to the empirical regression equation by Kilinc et al. (1983), the ferric-ferrous Fe3+/Fe2+ ratio at 1550 °C in the conjugate Lfe and Lsi melt compositions listed in Table 1⇑ should be around 2.3 and 1.3, respectively. It should be noted, however, that the equation might not work very well for the Lfe composition, which is far outside of the compositional range used for the regression.
Comparison with other types of immiscible liquids
Low γ values at the Lfe-Lsi interface that we report here compare well with the γ value of only 4.6 mN/m calculated by Hammel (1967) for metastable immiscible liquids in the system Na2O-CaO-SiO2, and are very close to γ recently measured at interfaces between immiscible borate melts in the binary systems MgO-B2O3, CaO-B2O3, and BaO-B2O3 (Veksler et al. 2010). Although the direct interfacial tension measurements are scarce, very low liquid-liquid γ values appear to be typical for immiscible, glass-forming oxide liquids. For comparison, water and immiscible organic liquids, such as mineral oil, benzene, or purified vegetable oils have shown somewhat higher γ values of 49, 32.7, and 30–32 mN/m, respectively (Kim and Burgess 2001; Gaonkar 1989). Much greater γ values in the range of 950–1650 mN/m have been measured between molten metals and silicate slags (Utigard and Toguri 1987; Sharan and Cramb 1995).
In theory, γ depends on the balance between cohesive and adhesive forces between the phases on the opposite sides of the interface. Mathematically, this balance is expressed, for example, by the equation proposed by Girifalco and Good (1957)
that relates interfacial tension between immiscible liquids γ12 to surface tensions of the contacting liquids γ1 and γ2. The sum of γ1 and γ2 represents the cohesive forces while the last term, which includes an empirical interaction parameter Φ, represents the adhesive force between the liquids. If all the γ values for interfaces and individual liquid surfaces are known from experimental measurements, as in this study, their substitution to Equation 2 allows calculation of Φ. For the pairs of immiscible borate melts and Lfe and Lsi liquids studied so far (this study; Veksler et al. 2010), the calculated Φ values vary in a narrow range of 0.95–0.99. The closeness of the interaction parameter Φ to unity is an indication of almost equal cohesion and adhesion forces of the phases (Girifalco and Good 1957). This is hardly surprising because covalent and ionic bonding forces of immiscible borate or silicate melts on the opposite sides of the interfaces are virtually the same, and the liquids show a high degree of mutual miscibility. In contrast, experimental values of Φ for interfaces between liquids of unlike types, e.g., metallic and ionic or hydrogen bonding and van der Waals, were shown to significantly deviate from unity. For example, Φ values for water vs. liquid hydrocarbons usually fall in the range of 0.5–0.7 (Girifalco and Good 1957), and many slag-metal liquid-liquid interfaces have Φ values as low as 0.4 (Sharan and Cramb 1995).
Implications for immiscibility in natural silicate magmas
The compositions of high-temperature Lfe and Lsi melts used in this study are extreme and far from immiscible Fe-rich and silica-rich liquids found in natural basaltic and andesitic lavas (Roedder 1978; Philpotts 1982). Nevertheless, we believe that our study has important implications for natural silicate immiscibility. The significance of the γLfe-Lsi values reported here is that they put an upper limit on γ between immiscible Fe-rich silicate melts, and the limit is very low. The interfacial tensions in borate binaries (Veksler et al. 2010) showed a positive, linear correlation of the liquid-liquid γ values with the widths of miscibility gaps expressed in molar units. That simple linear relationship may not hold in complex, multicomponent natural silicate systems where some components preferentially concentrating at the interface (in accordance with the Gibbs adsorption equation) may strongly affect the interfacial tension. Surface active effects of minor components have been reported in other, better studied types of immiscible two-liquid systems. For example, small TiO2 additions were shown to have a dramatic effect on interfacial tension between liquid Fe-Ni alloys and CaO-Al2O3-SiO2 slags (Sharan and Cramb 1995). However, the effects of surface active components, and smaller compositional contrast between natural Fe-rich and silica-rich immiscible liquids can only result in lower liquid-liquid γ values than those that we measured here for the extremely contrasting Lfe and Lsi synthetic compositions. If we assume simple linear proportionality between the compositional width of the miscibility gap and the liquid-liquid interfacial tension, γ values for natural immiscible melts coexisting at temperatures close to 1000 °C (Philpotts 1982) should be lower by a factor of 2 or 3 or roughly at about 5–8 mN/m. This simple estimation does not take into account possible temperature effects on γ that are at the moment poorly known, but the approximation is further supported by the value of 4.6 mN/m that Hammel (1967) calculated for low-temperature liquids in the system Na2O-CaO-SiO2. Notably, for the ternary low-temperature liquids, γ was calculated from homogenous nucleation rates of microscopic immiscible droplets. Therefore, for immiscible silicate melts, there seems to be no major difference between surface properties of macroscopic phases, and those of microscopic droplet nuclei.
In a previous kinetic study of silicate liquid immiscibility (Veksler et al. 2008), we observed the formation of sub-micrometer emulsions, and inferred low interfacial tension between the conjugate melts on the basis of emulsion morphology. Low γ values directly measured in this study confirm those earlier qualitative conclusions. In the context of classical kinetic theories of liquid immiscibility [e.g., see reviews by Filipovich (1984) and James (1975)], low interfacial tension should mean easier nucleation, higher nucleation density but, on the other hand, slow coarsening of the droplets, and protracted stability of fine emulsions. We believe that silicate immiscibility in natural ferrobasaltic, andesitic or rhyolitic magmas is likely to produce very fine, possibly sub-micrometer emulsions that may be stable over considerable time, and have significant effects on magma dynamics. Slow coarsening of the emulsions should hamper gravitational separation of immiscible melts, and may be one of the reasons why traces of immiscibility are usually hard to detect in partly or fully crystallized igneous rocks.
We thank Philippe Courtial, Werner Ertl-Ingrisch, and Kai-Uwe Hess (LMU) for their help in sample preparation and gravimetric measurements. We are grateful to Oona Appelt (GFZ) for her help with electron microprobe analyses. Thoughtful reviews by Pierre Hudon, Bjorn Mysen and Youxue Zhang helped to improve the original version of the paper. This study was supported by the DFG grant FR 557/23-1.
Manuscript handled by Bjorn Mysen
- Manuscript Received November 11, 2009.
- Manuscript Accepted June 16, 2010.