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Volume 31 Issue 3
Jul.  2020
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Zhenjiang Wang, Zhenmin Jin. Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid. Journal of Earth Science, 2020, 31(3): 447-455. doi: 10.1007/s12583-020-1301-2
Citation: Zhenjiang Wang, Zhenmin Jin. Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid. Journal of Earth Science, 2020, 31(3): 447-455. doi: 10.1007/s12583-020-1301-2

Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid

doi: 10.1007/s12583-020-1301-2
More Information
  • Reaction infiltration instability (RII) can cause the formation of melt channels and potentially facilitate the physical transport of sulfide liquid, which contributes to the geochemical evolution of chalcophile elements in the lithospheric mantle. This study conducted some two-layer reaction experiments to explore the feasibility of reaction-driven sulfide migration along high-velocity silicate-melt channels. With increasing duration, the formation of more silicate-melt channels and the transport of more sulfide droplets into a depleted peridotite were observed due to the increase of the local permeability. However, at a longer duration, the presence of some melt-channel relics implies that melt channels are temporary and ultimately closed when the reaction infiltration of silicate melt reached equilibrium in the depleted peridotite. Furthermore, theoretical calculations indicate that the RII of the system is suppressed, which impedes the formation of melt channels. The homogeneous distribution of silicate melt in a sulfide-free experiment implies that the Zener pinning of sulfide probably enhances the RII, thereby facilitating the formation of temporary melt channels. Therefore, this study demonstrates that sufficient silicate melt disequilibrium with solid phases in a liquid source potentially promotes the mechanical extraction of sulfides during reaction infiltration of silicate melt.
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Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid

doi: 10.1007/s12583-020-1301-2

Abstract: Reaction infiltration instability (RII) can cause the formation of melt channels and potentially facilitate the physical transport of sulfide liquid, which contributes to the geochemical evolution of chalcophile elements in the lithospheric mantle. This study conducted some two-layer reaction experiments to explore the feasibility of reaction-driven sulfide migration along high-velocity silicate-melt channels. With increasing duration, the formation of more silicate-melt channels and the transport of more sulfide droplets into a depleted peridotite were observed due to the increase of the local permeability. However, at a longer duration, the presence of some melt-channel relics implies that melt channels are temporary and ultimately closed when the reaction infiltration of silicate melt reached equilibrium in the depleted peridotite. Furthermore, theoretical calculations indicate that the RII of the system is suppressed, which impedes the formation of melt channels. The homogeneous distribution of silicate melt in a sulfide-free experiment implies that the Zener pinning of sulfide probably enhances the RII, thereby facilitating the formation of temporary melt channels. Therefore, this study demonstrates that sufficient silicate melt disequilibrium with solid phases in a liquid source potentially promotes the mechanical extraction of sulfides during reaction infiltration of silicate melt.

Zhenjiang Wang, Zhenmin Jin. Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid. Journal of Earth Science, 2020, 31(3): 447-455. doi: 10.1007/s12583-020-1301-2
Citation: Zhenjiang Wang, Zhenmin Jin. Reaction Infiltration Instabilities in Partially Molten Peridotite and Implications for Driving the Transport of Sulfide Liquid. Journal of Earth Science, 2020, 31(3): 447-455. doi: 10.1007/s12583-020-1301-2
  • The distribution of sulfur in the partially molten mantle plays an important role in many geological processes among Earth's various geochemical reservoirs (Jiang et al., 2019; Nash et al., 2019; Du et al., 2018). During partial melting of the upper mantle, sulfur resides mainly in accessory phases, such as sulfide liquids (e.g., Lorand et al., 2013; Bockrath et al., 2004) that control the distribution of economically important chalcophile elements within the upper mantle as well as the genesis of magmatic sulfide deposits due to very high sulfide-silicate melt partition coefficients of these elements (e.g., Mungall and Brenan, 2014).

    In the hydrostatic partially molten mantle, the distribution of melts evolves toward textural equilibrium to minimize the energy of melt-solid interfaces (von Bargen and Waff, 1986), while maintaining a constant dihedral angle (θ) at solid-solid-melt contact lines. And, the pore geometry of a melt-bearing system is determined by the dihedral angle

    where γs-s and γs-m are respectively the solid-solid and solid-melt interfacial energy per unit area (Bulau et al., 1979). For θ < 60°, a regular interconnected melt network can form along grain edges even at a very low melt fraction (~0.5 vol%, Laumonier et al., 2017), but melts with higher dihedral angles are commonly isolated and trapped at grain corners when melt fraction is lower than percolation thresholds (e.g., for Fe-S or Fe-S-O liquid, ~17.5 vol%, Bagdassarov et al., 2009; 6 vol%-9.5 vol%, Terasaki et al., 2005; ~3 vol%-6 vol%, Yoshino et al., 2003).

    Several lines of evidence (e.g., Holtzman and Kohlstedt, 2007; Kelemen et al., 1995) have suggested that at some stages from melting to eruption, the transport of silicate melts transforms from porous flow along an interconnected grain-scale melt network to the macroscopic high-permeability channelized flow in some regions of the partially molten mantle, which is an efficient pathway for the transport of silicate melt. Stress-driven melt segregation (e.g., Holtzman and Kohlstedt, 2007) is one of the main driving forces for the channelized flow of silicate melt (Soustelle et al., 2014; Holtzman and Kohlstedt, 2007). In addition to the deviatoric stress, the reaction infiltration instability (RII) due to the difference of chemical compositions can also drive the channelized flow of silicate melt, which has been well documented by theoretical analyses (e.g., Aharonov et al., 1995; Chadam et al., 1986) and experimental observations (e.g., Pec et al., 2015; Daines and Kohlstedt, 1994).

    It remains highly controversial for the transport of sulfide liquid with large interfacial energy and complex chemical compositions. Although many studies (e.g., Mungall and Brenan, 2014) suggested that the extraction of sulfide liquid from a mantle peridotite undergoing partial melting needs to be progressively dissolved by the departing silicate melt, the chemical migration of sulfur may be inefficient due to the low solubility of sulfur in silicate melts (about 0.1 wt.%) at the oxygen fugacity of the normal mantle (fO2 ~-1 < ΔFMQ < 1) (Jugo, 2009). Some natural observations and experimental studies (e.g., Wang et al., 2020; Le Vaillant et al., 2017) imply that the physical transport of sulfide liquid is potentially more efficient in the partially molten mantle. Driven by deviatoric stress, sulfide liquid with large dihedral angles (> 60°) can be extracted through liquid-rich sheets and even drained to a very small liquid fraction ~two orders of magnitude lower than the percolation threshold (Groebner and Kohlstedt, 2006; Bruhn et al., 2000). Moreover, under large-strain deformation conditions, the presence of silicate melt can potentially enhance the transport of sulfide liquid by opening the approximately oriented grain boundaries, which further demonstrates the feasibility of the mechanical extraction of sulfide liquid (Wang et al., 2020). During reaction infiltration of silicate melt, the migration velocity of silicate melt in melt channels is relatively high, which can even sustain the advection of large olivine (Ol) phenocrysts (~300 μm) toward channel entrances (Pec et al., 2017). However, it remains unclear whether the RII could also drive the mechanical transport of sulfide liquid along with the channelization flow of silicate melt, and how fast the migration velocity of silicate melt in melt channels could maintain the transport of sulfide liquid in a partially molten rock. Therefore, we conducted some two-layer reaction experiments and theoretical calculations to preliminarily explore the physical migration of sulfide liquid during reaction infiltration of silicate melt.

  • The starting material in the lower part of sample as a liquid source was a mixture of 5 wt.% Ni-Cu sulfides, 10 wt.% basalt and 85 wt.% olivine. For a sulfide-free experiment, the mixture of 90 wt.% olivine and 10 wt.% basalt was used as the starting material of liquid source. And dunite consisting only of olivine crystals was placed in the upper part of sample as a depleted mantle peridotite. Natural olivine crystals were separated from fresh spinel lherzolite xenoliths collected from Damaping (Hannuoba region), North China and were ground to 10-20 μm grain size in an agate mortar. Tholeiitic basalt from the East Pacific Rise (102.704 4ºW, 2.649 61ºS) was ground to < 10 μm grain size. Ni-Cu sulfides were composed of pyrrhotite (59 wt.%), pentlandite (36 wt.%), and chalcopyrite (5 wt.%) separates, similar to the composition of base-metal sulfide aggregates in massif peridotites (Lorand et al., 2010), and were ground to < 10 μm. Compositions of these starting materials are listed in Table 1.

    wt.% Olivine Basalt wt.% Ni-Cu sulfides
    Chalcopyrite (5 wt.%) Pyrrhotite (59 wt.%) Pentlandite (36 wt.%)
    SiO2 41.42(31) 51.73(24) S 35.29(14) 38.63(56) 34.06(41)
    TiO2 0.02(2) 2.30(6) Fe 30.23(27) 59.58(36) 33.04(88)
    Al2O3 0.01(1) 12.85(5) Ni 0.10(13) 0.13(3) 32.18(65)
    Cr2O3 0.01(1) 0b Cu 33.46(15) 0.01(1) 0b
    MgO 48.89(15) 4.62(3) The component of basalt was analyzed by XRF, and the components of olivine and three sulfide minerals were analyzed by EPMA using an accelerating voltage of 15 kV, a beam size of 1.0-2.0 μm, and a beam current of 20 nA, respectively. 1σ error is given in parentheses. a. Total FeO; b. lower the detection limit; c. not analyzed.
    CaO 0.04(2) 8.33(1)
    MnO 0.15(2) 0.23(1)
    FeOa 8.84(28) 14.60(36)
    Na2O 0.01(1) 3.59(4)
    K2O 0.01(1) 0.33(1)
    H2O+ -c 1.19(26)

    Table 1.  The chemical composition of starting materials

  • These two-layer reaction experiments were conducted at the State Key Laboratory of Geological Processes and Mineral Resources (GPMR) of China University of Geosciences using a 150 Ton non-end-loaded type piston-cylinder press. Starting materials were loaded into a 3.75-mm-diameter and 5-6-mm-high cylindrical platinum (Pt) capsule with a graphite inner sleeve (Fig. 1). A low friction assembly consisting of NaCl and Pyrex sleeves, a graphite heater, sintered MgO spacers, and an Al2O3 plug, was used for the piston-cylinder experiments. Pressure calibration was conducted against the quartz/coesite phase transition and is accurate to ±0.1 GPa. The temperature was monitored by a W/Re type C thermocouple located at the bottom of the capsule. These experiments were conducted under a constant pressure of 1.5 GPa and temperatures of 800 to 1 300 ℃ for 12-72 h prior to being quenched to room temperature by shutting off power to the furnace. All capsules were heated before being sealed at 120 ℃ in a vacuum oven for more than 12 h to remove absorbed water vapor in the specimens.

    Figure 1.  Specimen setup. The gray dotted line represents the interface between the upper and lower sample.

  • Polished sections cut parallel to the specimen axis were prepared from the recovered experimental specimens. The microstructure of experimental run products was observed using a Quanta 450 field-emission gun scanning electron microscope (FEG-SEM) at the GPMR with an accelerating voltage of 20 kV, a spot size of 6.0 and a working distance of ~12 mm. Quantitative compositional analyses were performed using an electron probe microanalyzer (EPMA, JXA-8100) at the Key Laboratory of Submarine Geosciences, State Oceanic Administration, China and the X-ray fluorescence spectrometry (XRF) at the ALS Minerals-ALS Chemex (Guangzhou) Co Ltd, China.

    The crystallographic preferred orientations (CPOs) and shape preferred orientations (SPOs) of silicate minerals (olivine, clinopyroxene, and orthopyroxene) were analyzed by indexing of electron backscattered diffraction (EBSD) patterns using a Quanta 450 FE-SEM equipped with an HKL Nordlys EBSD detector at the GPMR. An accelerating voltage of 20 kV, a spot size of 6, a beam current of 6 nA and a working distance of 20-25 mm were used for automatic mapping measurements. And the grain size of silicate minerals can be also measured by the EBSD mapping analyses.

  • Several two-layer reaction experiments (Table 2) were conducted at a pressure (1.5 GPa), different temperatures (800 and 1 250 ℃) and durations (12-96 h) to investigate the mechanical transport of sulfide liquid during reaction infiltration of silicate melt. All back-scattered electron (BSE) images were analyzed using the freeware ImageJ developed by the National Institute of Health (NIH) (http://imagej.nih.gov/ij/, the analysis methodology is described in Wang et al., 2020) to measure area fractions of sulfide and silicate melt and the size of sulfide droplets.

    No. Starting materials Experimental conditions Liquid distribution in the upper part of samples
    Upper part/lower part T (℃), t (h)
    PC350 Olivine/ olivine+basalt+sulfide 800, 10 Not molten
    PC343 1 250, 12 No melt channels
    PC340 1 250, 24 No melt channels
    PC347 1 250, 48 Several melt channels; more sulfide droplets
    PC362 1 250, 72 Apparent melt channels; more sulfide droplets
    PC389 1 250, 96 Some relics of melt channels
    PC401 Olivine/olivine+basalt 1 250, 48 The homogeneous distribution of silicate melt

    Table 2.  Summary of experimental conditions and liquid distributions in the upper part of samples

    In a low temperature (800 ℃) experiment, no silicate melt was produced. Sulfide mineral grains were generally polygonal and homogeneously distributed between olivine and unmolten basalt glass in the lower part of the sample. No sulfide was observed in the upper part of the sample.

    Under a higher temperature (1 250 ℃) condition, based on the calculation of mass balance, the basalt in the lower part of samples was molten to produce ~6.70 wt.%-8.96 wt.% silicate melt, which was consistent with these results (about 6%-8%) by analyzing BSE images. Silicate melt was mainly observed in melt junctions/pockets and melt channels between olivine-grain edges, forming locally interconnected melt networks (Figs. 2a-2c, 3a-3d). Sulfide liquid formed isolated and roundish droplets that were surrounded by silicate melt in silicate-melt-filled pockets and melt channels (Figs. 2a-2c, 3a-3d). A few large sulfide droplets were directly contacted with silicate minerals and squeezed into a wormlike shape, especially in these experiments with a long duration (Fig. 3d). With increasing duration, both the area fraction and average size of sulfide liquid in the lower part of samples were approximately constant within the error of measurement based on analyses of BSE images (~2.64%±0.20% and ~3.24±2.56 μm at the duration of 12 h; ~2.69%±0.11% and ~5.79±5.06 μm at the duration of 96 h). The average size of olivine grains was constant in the lower part of samples (~25.1±12.6 μm at 48 h, ~27.0±13.8 μm at 72 h) based on EBSD mapping analyses.

    Figure 2.  Microstructure of the distribution of sulfide and silicate melts in the lower part (a)-(c) and the upper part (d)-(i) of two-layer experiments under different duration (12-48 h) conditions (backscattered scanning electron microscopy). Red lines and red dotted lines are the interface between the upper and lower sample and melt channels in the upper part of sample, respectively. Mineral abbreviations: Ol. olivine; Opx. orthopyroxene.

    Figure 3.  Microstructure of the distribution of sulfide and silicate melts in the lower part (a)-(d) and the upper part (e)-(i) of two-layer experiments at the duration of 72 h (backscattered scanning electron microscopy). Symbols and mineral abbreviations are the same as Fig. 2.

    In the upper part of samples, with increasing duration, more dendritic melt channels were formed, and more and larger sulfide droplets can be observed in melt junctions/pockets and channels (Figs. 2d-2i, 3e-3i, and 4). The area fraction and average size of sulfide droplets respectively increased from ~0.034% and 2.1±0.8 μm at the duration of 12 h to ~0.232% and 5.2±2.1 μm at the duration of 72 h (Fig. 4). The average size of olivine grains was approximately constant in upper samples with increasing duration from 48 (~30.7±18.4 μm) to 72 h (~35.3±22.5 μm) based on EBSD mapping analyses, which were both larger than those in the lower samples. Especially, when the duration increased to 72 h (experiment PC362), in the upper part of the sample, much more dendritic melt channels and larger sulfide droplets can be observed (Figs. 3e-3i and 4) and the area fraction of silicate melt is about 3.2%-6.1% based on BSE image analyses. About 21 melt channels can be distinguished in the upper part of experiment PC362 (Fig. 3i). The direction of these melt channels was approximately perpendicular to the interface between the upper and lower sample in 2-D sections, and their average length was ~221±101 μm (the longest one ~420 μm) with a space interval of about ~582±67 μm. However, at the duration of 96 h, there were only some relics of closed melt channels observed in the upper sample (red dotted lines in Fig. 5), and the area fraction and average size of sulfide droplets almost remain constant with those in the experiment with the duration of 72 h (Fig. 4). These both imply that the content of silicate melt in the liquid source was not enough to maintain the open of melt channels at a longer duration (96 h). In addition, the biggest size of sulfide droplets in BSE images of upper samples increased from about 3.7 μm at the duration of 12 h to about 10.7 μm at the duration of 96 h (Fig. 4).

    Figure 4.  The area fraction, biggest and average size of sulfide droplets in the upper part of samples with increasing duration. The statistical area for each sample is the same (~185 μm×1 000 μm in the upper part of samples).

    Figure 5.  Overview (backscattered scanning electron microscopy) of the distribution of two immiscible liquids in experiment PC389 at the duration of 96 h. The red line is the interface between the upper and lower sample, and red dotted lines represent the relics of melt channels.

    To explore the effect of sulfide droplets as secondary phase particles on the migration of silicate melt, a sulfide-free experiment (PC401) with a duration of 48 h has been conducted under the same temperature (1 250 ℃) and pressure (1.5 GPa) condition. The area fraction of silicate melt in the upper part of sample was approximately the same as the sulfide-bearing experiment with the same duration (PC347, 48 h), but the distribution of silicate melt was more homogeneous in the sulfide-free experiment, and no apparent melt channel was observed (Fig. 6a). The size of olivine grains was almost the same in the upper part (~24.3±14.7 μm) and the lower (~26.4±17.3 μm) part of the sample, which were both similar with that (~25.1±12.6 μm) of the lower sample of experiment PC347 within error.

    Figure 6.  Microstructure (backscattered scanning electron microscopy) of the distribution of silicate melt in the upper part of sulfide-free experiment PC401. Silicate melt was observed in triple junctions or melt pockets.

    Notably, no planar reaction layer was present between the upper and lower part of samples in all experiments.

  • The Mg# (=100×Mg/(Mg+Fe) in molar unit) of olivine in the starting material was ~90.9±0.2. When duration was shorter than 48 h, the olivine Mg# in the upper part of samples was approximately constant within errors (~90.6±0.2 at 12 h, ~90.5±0.2 at 24 h and ~90.6±0.4 at 48 h) and both higher than those in the lower part of samples (~89.7±0.4 at 12 h, ~89.7±0.2 at 24 h and ~89.8±0.3 at 48 h) (Fig. 7a). In contrast, under the long duration condition (72 h), the Mg# of olivine (~90.1±0.2) in the upper sample was almost the same as that (90.0±0.3) in the lower sample. With increasing duration to 96 h, the olivine Mg# in the upper part and lower part of the sample increased to 90.9±0.2 and 91.0±0.3, respectively, which were both the same as that of the starting material (Fig. 7a). With increasing duration, Ni contents of olivine in the upper part and lower part of samples were both almost constant, and the olivine Ni contents in the lower part were lower than those in the starting material and the upper part of samples (Fig. 7b). Silicate melt in the liquid source was disequilibrium with olivine grains, thus the melt-rock reaction can occur: melt1+Mg2SiO4 (Ol)←→Mg2Si2O6 (Opx)+melt2 (reaction 1), leading to the presence of small orthopyroxene (Opx) grains in the lower and upper part of samples (Figs. 2a-2c, 3a-3d). However, with increasing duration, silicate melt was gradually evolving toward the composition of melt2 saturating with Opx in the liquid source, then more melt2 can be migrated into the upper part of samples causing the occurrence of the left-hand of the reaction 1. Thus, at the duration of > 72 h, the content of Opx in the upper part of samples was decreasing, and only several Opx grains were observed in the 96 h experiment. The Mg# of Opx in the upper part of samples were higher than those in the lower part of samples (Fig. 7c). With increasing the duration from 12 to 96 h, the Mg# of Opx in the lower part of samples increased from 89.9±0.3 to 91.4±0.2, whereas those in the upper part of samples were approximately constant within errors (Fig. 7c). Additionally, no significant change in the Ni/S ratio of sulfide liquid was observed in the upper and lower part of samples within errors, and these values in the upper part of samples were commonly higher than those in the lower part of samples (Fig. 7d).

    Figure 7.  Plots of Mg#, Ni content and Ni/S ratio in olivine, orthopyroxene, and sulfide as a function of the duration. The red dot in (a) and (b) represents the Mg# and Ni content of olivine in the starting material.

  • During the reaction-driven melt segregation, a reaction fluid percolates through a dissolvable matrix, fluid flow can be channelized as a result of a positive feedback between flow and reaction, that is, reaction infiltration instabilities (RII) (Chadam et al., 1986). This process can cause the formation of finger-like or dendritic melt channels with a high migration velocity as demonstrated experimentally (e.g., Pec et al., 2017, 2015; Osselin et al., 2016; Daines and Kohlstedt, 1994) and theoretically (e.g., Jones and Katz, 2018; Szymczak and Ladd, 2014, 2013; Spiegelman et al., 2001; Aharonov et al., 1995). Due to the low-efficient chemical transport of sulfide liquid, Wang et al. (2020) have proposed that the mechanical extraction of sulfide liquid can more directly re-fertilize the previously depleted lithospheric mantle, which may be an important complement for the chemical migration. Recently, some experiment studies (Pec et al., 2017, 2015) about RII show that during reaction infiltration of silicate melt, even some large olivine phenocrysts (the largest size ~300 μm) can be entrained physically toward channel entrances or into melt channels along with the high-velocity (~0.5 μm/s) migration of silicate melt in finger-like melt channels.

    For an ideal porous rock, a simple power-law relationship has been derived between permeability (k) and porosity (Φ) (von Bargen and Waff, 1986)

    where dOl is the grain size (the size of olivine in the upper part of the 72 h experiment ~35 μm), Φ is represented by melt fraction (~3.2%-6.1%), n and C are parameters that depend on the topology of melt phase (e.g., Wark and Watson, 1998; Faul, 1997). Equation (2) can estimate the permeability of silicate melt flowing along grain edges in non-channel regions of the upper part of samples. Based on a numerical model of McKenzie (1989), for a Darcy-type flow with the constant porosity and without compaction, the migration velocity of silicate melt with respect to a stationary matrix is estimated by

    where Δρm ~600 kg/m3 is the density contrast between solid mantle and silicate melt, g is the acceleration due to gravity (~10 m/s2), μm ~5 Pa·s is the melt viscosity (Bockrath et al., 2004). Recently, using a three-dimensional melt analysis technology, Miller et al.(2016, 2014) obtained exact estimations on the parameter n=2.4-2.8 (mean value ~2.6) and C=36-94 (mean value ~58) for the permeability of olivine-basalt and olivine-orthopyroxene-basalt aggregates. Thus, n=2.4 and C=36 are chosen to estimate an initial migration velocity of silicate melt (w0 ~3.3×10-4-8.1×10-4 μm/s) in olivine aggregates of the 72 h experiment. Moreover, during reaction infiltration of silicate melt, both the porosity (Φ) and the grain size of olivine (dOl) are evolving properties of the system and increase as the duration increases and more solid phases (Opx) are dissolved, thus k and w0 both increase with the progressing reaction between silicate melt and solid phases, which further enhances the positive feedback between melt flow and melt-rock reaction.

    The consistent distribution between sulfide droplets and melt channels are clearly observed in Figs. 2d-2f, 3e-3i, indicating that these sulfide droplets in the upper part of samples are entrained by the migration of silicate melt along these melt channels. The biggest size of observed sulfide droplets in the upper part of samples is about ~10.7 μm. Thus, based on Stokes Law (Stokes, 1851), the settling velocity of the biggest sulfide droplet can restrict the minimum melt velocity in these melt channels

    where ρsulfide and ρfluid is the density of sulfide (~4 300 kg/m3, Kress et al., 2008) and silicate melt (~2 600 kg/m3), respectively, and r is the size of sulfide droplets. To entrain the largest sulfide droplet (r ~10.7 μm) into the channels, the lower bound for silicate-melt flow velocity (wc) through melt channels is approximately ~0.09 μm/s, which is almost two orders of magnitude faster than w0 but still lower than the lower bound (~0.1 μm/s) of the formation of melt-rich channels based on the estimation of Pec et al. (2017).

    Based on the theoretical background about RII (Spiegelman et al., 2001; Aharonov et al., 1995), we calculated some parameters to describe evolving physical properties of a system during reaction infiltration of silicate melt. First, we cast two main controlling parameters for the relationship between reaction or diffusion rate and transport rate-Damköhler number (Da) and Péclet number (Pe). The two dimensionless parameters can determine whether the reaction front propagates in a stable manner or instabilities. The Da describes the reaction extent that takes place in the time it takes fluid to move one characteristic length scale and is defined as

    where L is a characteristic length scale of interest, such as sample length, w0 is initial melt velocity at initial melt fraction Φ0. A large Da value implies that the reaction rate is higher than the transport rate. In Eq. (5), Reff is the effective reaction rate constant defined as

    where R is the linear dissolution rate (~1.11×10-8 m/s, Edwards and Russell, 1996), ρsolid is the density of solid (~3 300 kg/m3), and SSA is the specific surface area available for reaction calculated as

    where Фc is the content of grains in contact with reactive melt (assuming ~0.25) (Pec et al., 2017), which represents the ratio of solid-liquid surface area to the total surface area because only wetted grains can be dissolved in melt. Based on Eqs. (5)-(7), the Da value is very large (~2.44×104-1.15×105 > 103) calculated with the sample length (~2.00 mm).

    The equilibration length

    quantifies the distance over which fluid will travel before equilibrating with its surroundings. The value of Leq (~1.75×10-8- 8.21×10-8 m) implies that the convection length of melt is very short before equilibrating with surrounding materials.

    The second governing quantity is the Péclet (Pe) number, which quantities the advection rate with respect to the diffusion rate as

    where D is the diffusion or dispersion constant (~10-12 m2/s, Morgan and Liang, 2003) of the fluid and L is the sample length. A large Pe value implies relative to transport rate, diffusion or dispersion is negligible. The estimated Pe value is relatively small (~0.66-1.63, < 10). Combining with the low convection length of silicate melt (the low Leq value), the larger reaction and diffusion rate (the large Da and low Pe values) than the transport rate of silicate melt indicate that silicate melt has been in equilibrium with solid phases before the formation of melt channels. Furthermore, the Mg# of olivine in the upper and lower part of the 96 h experiment is both the same as the starting material (Fig. 7a), and there are few Opx grains dissolved by silicate melt in the upper part of the sample. Therefore, these theoretical calculations and compositional evolutions both indicate that when the duration is longer than 72 h, the RII in this study is potentially suppressed by the insufficient supply of reactive silicate melt in disequilibrium with olivine and cannot sustain the open of these melt channels permanently. Apparently, more melt channels can be formed due to a positive feedback between the increase of permeability due to the melt-rock reaction and the associated increase of melt flux in reaction regions (Spiegelman et al., 2001; Chadam et al., 1986). Thus, we would anticipate that if there is enough melt in disequilibrium with olivine in a liquid source, more and larger sulfide droplets could be extracted along with the channelization flow of silicate melt into the upper part of samples. In comparison with the sulfide-free experiment (PC401), the homogeneous distribution of silicate melt in the upper part of the sample (Fig. 6) implies that the Zener pinning of sulfide droplets as secondary phase particles can inhibit the grain growth of local olivine grains and lead to more heterogeneous permeability, thereby contributing potentially to the instability of the system and the formation of temporary melt channels (Hsiang et al., 2015).

    Therefore, we suggest that the combination of the melt-rock reaction consuming Opx grains in the upper part sample and the Zener pinning effect of sulfide droplets can potentially facilitate the formation of transient silicate-melt channels by enhancing the RII and ultimately lead to the mechanical extraction of sulfide liquid along with these melt channels. And, the insufficient supply of reactive silicate melt is probably the main reason that melt channels are finally closed with increasing the duration to 96 h.

  • This study proposes an alternative feasible process by which sulfide liquid (droplets size < 10.7 μm) can be partially removed mechanically through silicate-melt channels with a high migration velocity (> 0.09 μm/s) of silicate melt during the reaction infiltration of silicate melt. Laboratory experiments and theoretical calculations indicate that both sufficient silicate-melt to react with olivine and the heterogeneous porous flow of silicate melt causing by the Zener pinning of sulfide droplets potentially enhance the RII and are the prerequisites for the formation of these transient melt channels.

  • We are grateful to two anonymous reviewers and Prof. Yao Wu for their useful suggestions and comments. We thank Prof. Jihao Zhu for technical support during EPMA analysis and Dr. Wenlong Liu for help with EBSD analysis. This research was supported by the National Natural Science Foundation of China (No. 40172068). The final publication is available at Springer via https://doi.org/10.1007/s12583-020-1301-2.

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