Molten salt electrometallurgy

C. Osarinmwian

School of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester

M13 9PL, United Kingdom

Abstract

Molten salt is a wonder liquid with many superlatives to its name. It possesses low volatility,

good heat transfer capacity, high electrical and thermal conductivity, radiation insensitivity, and

low viscosity up to 1773 K. It is a universal electrolyte, chemical reaction medium, and energy

storage medium while opening new opportunities for ecologically-safe, economically favourable

methods for materials processing. Predominant Coulomb interaction between particles in molten

salt makes it the best medium for physical and computer simulation of liquid structure and

properties. Here we investigate molten salt electrometallurgy and related processes, and attempt

to identify future mathematical modelling directions in which the field is likely to develop.

1. Introduction

Metals and alloys are predominantly produced at an industrial scale using pyrometallurgical

techniques such as carbothermic and metallothermic reduction. However, electrometallurgy is

the art of extracting metals out of ores and refining them to a purity required for everyday use

[1]. Modern technologies not only strongly rely on the unique properties of metals, but urgently

call for even better metals with higher strength without sacrificing other properties critical for

their competitiveness [2]. Further to traditional electrometallurgical processes [3], applied molten

salt research in electrometallurgy over the past century [46] has culminated in new molten salt

electrometallurgical and electrolytic processes [713] that offer an exciting opportunity for

addressing the grand challenges facing modern society. For instance, developments in different

metallurgical families may benefit from each other by tuning strength/toughness ratios. Also, the

electrometallurgical treatment of spent nuclear fuel in pyrochemical technology offers inherent

simplicity, small footprint, low capital cost, and the generation of a small volume of high-level

waste compared to other treatment technologies [1418]. In this work, we lay no claim to

comprehensiveness but single out topics that appear to us to merit further attention and to offer

the prospect of a deeper insight into the applications of molten salt in electrometallurgy and

chemical engineering.

2. Hall-Héroult process

The evolution of molten salt electrometallurgy in the early nineteenth century with Humphry

Davy in 1808 is a story of a novel technology emerging from the electrolysis of alkali metals

from their molten salts using multiple Volta cells connected in series. Since then most existing

molten salt technologies have undergone incremental improvements in current and energy

efficiencies including the Hall-Héroult process discovered in 1886. This process is now at the

heart of primary Al production involving Al ore (bauxite) mining and Al2O3 production in the

Bayer process [19]. The current efficiency of the Hall-Héroult process (> 95 %) underlies the

affordability of Al, and remains the hallmark of primary metal extraction by electrolysis [20].

Electric current enters a Hall-Héroult cell, containing either monolithic self-baked (Soderberg) or

prebaked carbon-based anodes, and reduces Al2O3 dissolved in molten cryolite (Na3AlF6)

electrolyte leading to molten Al deposition at the cell base. The dissolution can be promoted by

the installation of sloped 0.570.61 cm high drainable, TiB2-coated carbon cathodes for Al

wettability [21] opposite shaped anode undersides [22]. The resulting electrolyte chemistry is a

major determinant of cell temperature (typically 12231233 K) in which self-heating due to

engineering of irreversibility (i.e. Joule effect due to Ohmic potential drop) stabilises the

temperature [20].

In a novel Hall-Héroult cell, anodic gas bubble release through the upper end of an annulus

anode enclosing a cathode rod facilitated molten salt circulation through the lower end; the effect

of bubble layer resistance on current density was minimised by minimising anode immersion

depth [23]. The resulting uniformity in current distribution can be optimised by lowering anode

wall thickness while tapering the cathode cross-sectional area from top to bottom [24]. This

uniformity may be complimented by horizontal carbon blocks inlaid with steel and current

distributor bars into the cell base lining [25]. Despite a previous Alcoa process plant shut down,

advanced bipolar electrodes and their connections allow electrical energy to be introduced into a

cell by increasing voltage rather than current while generating highly uniform current

distributions [26,27]. However, the intrinsic loss of current efficiency caused by bypass current

would need to be quantified [28] and minimised by increasing current and bipolar cell height,

bounding bipolar electrode edges with upwardly extending rims, and electrically insulating the

internal cell wall [29]. Also, controlling operating variables becomes more critical at decreasing

temperature even though such a change may have a minor effect on theoretical energy

requirements [30].

3. FFC Cambridge process

The production of Ti sponge, using the Kroll process, is of strategic importance owing to its

usage in manufacturing Ti alloys for aerospace, automotive, and military applications. However,

the Ti industry has a long history of seeking low cost Ti production processes in combination

with low cost direct consolidation or powder metallurgy production routes. The latter is a mature

commercial metal-forming technology with the intrinsic advantage of near-net-shape capability;

the drive for near-net Ti manufacture is associated with the traditionally high buy-to-fly ratio of

Ti components. In contrast to current incumbent technologies for Ti production, the FFC

Cambridge process is a simple, inexpensive, and environmentally friendly process capable of

directly producing Ti from the electro-deoxidation of titania ore (Fig. 1c; Fig. 2; [3140]). The

current efficiency ξe for Ti extraction using this process is low (< 2000 ppm oxygen, ξe = 32.3 %)

but relatively high for Cr extraction (< 2000 ppm oxygen, ξe > 70 %) [41]. Although oxygen-

evolving inert anodes could improve ξe, the several 100 patents describing such anodes in Hall-

Héroult cells are not totally satisfactory [6]. Thus, utilising liquid metal anodes [42] may lead to

less polluting and more energy efficient electro-deoxidation relative to using carbon-based

anodes.

Scalable electro-deoxidation is challenging due to the requirement for molten salt flow, low

labour intensity, and high Ti production per unit volume. Fig. 3a shows that perforated and

sloped anodes generate the most uniform primary current distributions (which only consider

electric field effects) where improvements in uniformity could involve replacing the top and

bottom cathode with a near-net-shape finger cathode [43]. The electro-deoxidation of a random-

loose packing of low-aspect ratio, near-net-shape raschig cathode rings (Fig. 3c) in a modular

bipolar electro-deoxidation cell (Fig. 3b) eliminates the complexity and minimises the cost

compared with attaching porous cathode pellets to current collectors. The packing arrangement

minimises cathode settling, ordering, and alignment, which would otherwise hinder molten salt

and current flow through the packing thereby increasing pumping pressure requirements [44]. To

this end, improvements in molten salt pumping (Fig. 4b, c) in a new long-lifetime, fully ceramic

pumping system [45] could lead to integration within a semi-continuous recirculation loop of a

bipolar electro-deoxidation cell [46]. The electro-deoxidation of a random TiO2 particle (62.5

µmto4 mm diameter) packing at a void fraction > 43 % per bipolar electrode (Fig. 3b) in the

absence of substantial particle sintering and alloying [47] is best achieved at low particle size and

packing depth [48].

4. Electrode engineering

In order to establish a diffusion-controlled electro-deoxidation model for simulating three-phase

interline (3PI) movement in a porous cathode, it is important to understand the limitations of the

selected moving mesh technique. A first attempt at this involved the experimental validation of

an electron-transfer-controlled electro-deoxidation model in which an arbitrary Lagrangian-

Eulerian method described 3PI movement (Fig. 1a, [49]). However, the dependence of electro-

deoxidation rate on electric field effects and electron transfer kinetics led to element point(s)

velocity ve in the finite element mesh coinciding with material point(s) velocity vm along the 3PI;

this induced a Lagrangian description. The subsequent lack of control over mesh movement

resulted in a distorted mesh with large changes in element dimensions causing slow convergence

and premature termination of the simulation [49]. In the latter, two element edges may intersect

at a point which is not a vertex, vertex ordering may fail to satisfy a right-handed rule (i.e.

vertices disordered in a counter-clockwise manner) and/or vertex ordering may induce negative

element volume. The resulting inverted elements can be detected by a negative Jacobian matrix

determinant. Hence, applying the velocity-based arbitrary Lagrangian-Eulerian boundary

condition will ensure ve ≠ vm and positive element volume during diffusion-controlled 3PI

movement. Future development of a diffusion-controlled electro-deoxidation model will provide

an opportunity for validation against experiment (Fig. 3d).

Gas generated on a carbon-based anode during electro-deoxidation is strongly related to

efficiency [50], anode corrosion (Fig. 1b), anodic 3PIs [51] and bubble dynamics [22]. In the

latter, the anodic CO gas flowrate is greater than that for CO2 gas at temperature T = 1223 K

(Fig. 5d) in which the near steady-state flowrate is consistent with the numerically predicted near

steady-state volume fraction Vf of CO gas bubbles in a given volume of molten CaCl2 (Fig. 5d).

The bubbly-flow model for CO gas is a simplification of the two-fluid Euler-Euler model and

relies on the following assumptions: gas density is negligible compared to molten CaCl2 density,

gas bubble motion relative to molten CaCl2 is a balance between viscous drag and pressure

forces, and the gas and molten CaCl2 share the same pressure field. Hence, Vf is derived from

solving a momentum equation for molten CaCl2 velocity, a continuity equation, and a transport

equation for the gas volume fraction. Assuming low gas concentrations, the mass conservation

equation is ∇∙u = 0 and the gas transport is

𝜕𝜌𝑔𝛽𝑔

𝜕𝑡+ ∇ ∙ (𝛽𝑔𝜌𝑔𝐮𝑔) = −𝑚 1

where ug = u + uslip is the gravity vector where uslip is the relative velocity between CO gas and

molten CaCl2, m is the mass transfer rate from CO gas to molten CaCl2 (assumed negligible), βg

is the volume fraction of CO gas and ρg = (P + Pref)Mg/RT is the density of CO gas where R is the

universal gas constant, Pref = 105 Pa is reference pressure and P is pressure, and Mg = 28 g mol1

is the molar mass of CO gas. Pressure forces approximately balance viscous drag forces on a gas

bubble for upward buoyancy-driven bubble motion according to (3ρgCd/4dg)|uslip|·uslip = ∇P

where db = 4 mm is the bubble diameter and Cd = 0.622[(σ/gρgdb2) + 0.253]1 is the drag

coefficient where σ = 0.07 kg s1 is the assumed surface tension coefficient [22]. The generation

of these gas bubbles originate from the anode reaction kinetics (Fig. 5b):

In 𝑗𝑎 = 𝑏𝜂𝑎 + In 𝑗0 2

where ja is the anodic current density, b = αanF/RT = 10.66 is the Tafel slope, In j0 = 5.86 is the

intercept, n is the electron stoichiometry and ηa is the anodic overpotential. Assuming CO2 + 4e

→ C + 2O2 is the dominant reaction, the exchange current density j0 = 352 A m2 and anodic

transfer coefficient αa = 0.28 could contribute to anode design for electro-deoxidation. The

strong dependence of the Tafel slope on overpotential and temperature (Fig. 5b) leads to

deviations from linear Tafel behaviour according to Marcus-Hush theories.

Although cathodic protection is well-known for preventing oxidation and corrosion in aqueous

solutions, it has rarely been applied at temperatures above the boiling point of water. Matson et

al. [52] found that vessels experience severe corrosive attack in contact with a molten fluoride.

Similarly, Andriiko et al. [53] tested a number of sacrificial anodes to cathodically protect

graphite crucibles used in Ge electrodeposition from a molten fluoride. Obtaining the required

cathodic current density with a graphite crucible anode was difficult, and the degradation of

cathode material was oxidised near the anode resulting in product contamination. They also

found that the corrosion resistance of Cu and Ni was significantly better than Fe. Kolosov et al.

[54] found that imposing an impressed current density provided sufficient corrosion protection of

process vessels containing a molten chloride. However, Ives and Goodman [55] ruled out the use

of cathodic protection as it failed to provide corrosion protection of a molten carbonate storage

vessel in vapour regions; they recommended lower operating temperature. More recently,

Schwandt and Fray [56] demonstrated the feasibility of cathodic protection of both solid and

liquid Ti and its alloys at elevated temperature by means of an electrolytic cell containing a

molten fluoride and an appropriate anode.

5. Molten electrolyte

Previous barriers to developing diffusion-controlled electro-deoxidation models may have been

related to historic arguments regarding the concept of ion association in molten salt. The

simultaneous movement of neighbouring ions of opposite charge into paired vacancy sites and

differences in cross-correlation functions of ionic velocities in molten salt lead to deviations

from Nernst-Einstein behaviour. Thus, mass, charge and momentum transport in molten salt

tends to involve correlated ionic collisions and caging motions [57]. In the absence of complex

formation [58,59], the Stokes-Einstein equation is a better fit for Ca2+ ions than Cl ions in

molten CaCl2; the Cl ion diffusion coefficient increases more rapidly [60]. By monitoring

temperature in-situ during electro-deoxiadtion, the self-diffusion of Ca2+ and Cl ions can be

approximated using Aexp(ED/RT) [58] where A is the pre-exponential factor for self-diffusion

and ED is the energy of activation for diffusion. Differences in ion size and activation entropy

associated with site-to-site ionic transport between Ca2+ and O2 ions may explain large

discrepancy between theoretical and experimental O2 ion diffusion coefficients. Furthermore,

temperature control at T < 1273 K (Fig. 5e) lowers vapour pressure in equilibrium with molten

CaCl2, minimises current inefficiency, and avoids excess pressurisation of the electro-

deoxidation cell.

Current waves during potential ramping at t < 1 h (Fig. 5a) are associated with different Ca-

incorporation reactions in the porous cathode (Fig. 6 and Fig. 7). Oscillations in electronic

background current (see Fig. 5c) arise from the existence of a distribution of ion-ion separations

and local compositions. The polarizability derivative of an ion in molten CaCl2 tends to be

modulated by anti-phase motions of oppositely-charged neighbouring ions [61]. The CaO

decomposition during electro-deoxidation at 2.6 V contributes to electron trapping, by an

electron pair exchange equilibrium (Ca2)2+ ↔ 2Ca2+ + e at low Ca concentration, which leads to

an electron pair dissociation at equilibrium e2 ↔ 2e at increasing Ca concentration [62]. Electron

trapping probably occurs in an F-centre-like state where electron hopping occurs from one

localized site to another via ACa(I) + BCa(II) ↔ ACa(II) + BCa(I) [63]. This is reasonable since

localized electrons tend to be temporarily delocalized or become mobile in metal-molten salts

thereby contributing to transport by thermally activated diffusional hopping [64,65]. This is

important since electronic conduction in an electrolyte is one of the main causes of decreasing

current efficiency during molten salt electrolysis [66].

6. Fluid mechanics

The main difficulty in Li extraction arises from the low density of Li and Cl relative to the

molten salt electrolyte leading to large inter-electrode spacing and an Ohmic potential drop

greater than the decomposition potential. One way to address this, without increasing the Li and

Cl back reaction, is to apply a centrifugal force to encourage phase separation. In this case, Cl

gas passes to the centre of an extraction cell where it escapes while Li is restrained by surface

properties to a stainless steel cathode until the rotational force and density difference overcomes

the surface forces; Li is radially projected and rises in the electrolyte at a different position to

that of Cl [67]. In contrast to a Cochran-type extraction cell, Fig. 8c, d demonstrates that the

limitation of outer boundaries and finite size of a solid disk in a practical extraction cell

overcomes the suction effect when displaced molten salt reaches the outer boundaries and then

changes direction. In other words, the radial flow is directly responsible for axial velocity uz

leading to two rotational flow vortices with no suction effect. Alongside the boundary conditions

required for this simulation (Fig. 1d), attempts need to be made to develop electrochemical cells

with greater mass transfer capabilities [68,69].

Based on disk rotation [7074], the rotation rate 10 rev s1 ≤ ω/2π ≤ 99 rev s1 in Fig. 8c, d is

assumed low enough to avoid turbulence and sufficiently high so that forced convection

dominates over free convection. Given that the theoretical dimensionless axial velocity H∞ =

0.88446 at a dimensionless axial distance ξ = z(ρω/μ)0.5 ˃ 1, the hydrodynamic boundary layer

thickness δh = 3.6(μ/ρω)0.5 (or ξ = 3.6) corresponds to uz(δh) = 0.8u0 where u0 = 0.88(μω/ρ)0.5 is

the limit jet velocity. The low uz adjacent to the rod section of the rotating disk, flattens the

dimensionless axial velocity H = uz(μω/ρ)0.5 profile at 16 mm ≤ r ≤ 19 mm while the radial

velocity ur moves molten salt away from the top of the disk section. As ω increases the rotational

velocity uθ becomes strongly affected by boundary-layer skewing near the disk section which is

indicative of a flow structure transition by inviscid (irrotational) crossflow instability. The

restrictions associated with Levich theory explain the discrepancy between H approximations at

ξ ˃ 0 (Fig. 8a, b). In particular, the Ariel approximation to H [72] suggests that the empirical

correction to the Levich equation imposes a threshold ω above which the Levich equation

becomes invalid [73].

The scale-up of molten salt electrometallurgy with Ti powder-molten CaCl2 suspensions

introduces a number of challenges including continuous operation, agitation and pumping, and

maintaining salt in the molten state [75,76]. Assuming incompressibility and negligible

anisotropy, the suspension dynamics can be described by a momentum transport equation for the

suspension, a continuity equation, and a transport equation for particle volume fraction [77].

Based on the density ρ = 2009 kg m3 and viscosity μ = 0.157 Pa s of molten CaCl2 at 1223 K

[78], the suspension density ρs = (1 φt)ρ + φtρt, where φt is the particle volume fraction, ρt is the

density of Ti particles, and the suspension viscosity μs follows a Krieger-type expression. Fig. 4a

shows that Ti particles migrate from high-to-low shear-rate regions in which φt decreases with

increases in radial distance r at 600 rpm because these particles experience both a higher shear

rate and shear-rate gradient than those further away. Peak 1 φt near the stationary outer

cylinder at 600 rpm occurs due to the influence of geometrically hindered packing. This localised

behaviour is smoothed by φt gradients leading to φt becoming strictly increasing with r at 1000

rpm.

7. Outlook

An understanding of electro-deoxidation through the use of mathematical tools allows a deeper

description and analysis of the complex phenomena involved. Complex microscopic behaviour

of 3PIs [7986] in a cathodic TiO2 particle underlies its macroscopic motion during electro-

deoxidation. The averaging out of microscopic fluctuations at larger scales gives averaged

quantities that satisfy classical continuum equations [87] within the multiphysics framework

[88]. Furthermore, the macroscopic recovery of deoxidized Ti particles from a recirculation loop

[46] can be achieved using a circular secondary clarifier within the recirculation process. This is

visualised by simulating Ti powder-molten CaCl2 suspension velocity, pressure, and Ti

concentration based on a multiphase flow model using a momentum balance and mass

conservation of each phase (Fig. 9). In addition, a decrease in the tap density/apparent density

ratio (or Hausner ratio Hr) for recovered Ti powder probably occurs with increasing particle size

d50 at a flow property: 1 < Hr < 1.25 [89]. This fair-to-excellent flow, with a 2540° angle of

repose [90] that agrees with the angle of repose for Ti powders [91], may lead to a greater

increase in Hall flow for irregular-shaped Ti particles [89] and a gradual decrease in the angle of

repose due to a cohesive-to-free flow transition.

Existing electro-deoxidation models suffer limitations such as the inability to simulate electro-

deoxidation around cathode corners. Instead of boldly dismissing existing electro-deoxidation

models [92], the future development of diffusion-controlled electro-deoxidation models need

experimental validation while the application of the Scharifker-Hill model [43,93] may be

complimented by the Isaev-Baraboshkin model [94,95]. In terms of scale-up, predictive

visualisation models [17,96] could help retrofit multiple bipolar electro-deoxidation cells into an

existing industrial site thereby offering distributed manufacturing ‘just-in-time’ options and

factory-of-the-future for thousands of tonnes per annum of high-value metal powders for the

fourth industrial revolution. This is timely since the additive manufacturing of metals (or metal

3D printing) is now considered to be a potentially transformative manufacturing process for

many industrial sectors [97]. For instance, the buy-to-fly ratio of near-net-shape components and

low-cost Ti powders in aerospace applications needs to be lowered from 10:1 to 5:1 [98] given

the more than 28,000 new large commercial aircraft on the global market for the period

20122031 [99]. Also, the FFC Cambridge process could help lower the cradle-to-gate

environmental impacts for Ti production by 3035% relative to the Kroll process [100].

Acknowledgements

C.O. thanks The University of Manchester and Metalysis Ltd for use of their experimental

facilities. C.O. is grateful to Josephine Osarinmwian, Agatha Adesode Erhumwunse (Papal

Medallist) and Margaret Dutton for useful discussions.

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Fig. 1| (a) 2D electro-deoxidation cell. (b) Arrangement of alumina crucible and graphite annulus anode in the cell.

(c) Electro-deoxidation of a rutile TiO2 porous cathode (cathode thickness = 2.6 mm) generate oxygen vacancies that

introduce occupied defect levels in the bulk band gap leading to a dark grey colour. Computed X-ray tomography

images of the cathode interior where Beer’s law describes the passage of X-rays through each volume element;

tomographic image reconstructions were computed using a Feldkamp-Davis-Kress algorithm. A stainless steel clip

held the cathode in position during imaging. Scale bar: 5 mm. (d) Boundary conditions for the extraction cell are

sliding rod and disk surfaces in a tangential direction (Sliding wall u∙n = 0), free molten CaCl2 surface for flow in

axial and rotational directions (Symmetry), and outer boundary surfaces are stationary (No-slip u = 0). Symmetry

boundary allows flow in the axial and rotational directions while the zero pressure condition Pref = zero (bottom

right corner) accounts for a non-outflow boundary.

No-slip

Symmetry

Sliding wall

z

0 r zth

Molten CaCl2

Current collector

cathode

Annulus

Anode

Porous cathode

a

d

b c

Fig. 2| Ex-situ SEM analysis: Band offset at TiO/TiO2 interface at the microscopic length scale at 0.5 h indicates

localization of the valence band and conduction band minima at TiO and TiO2, respectively; TiO channels inside

TiO act as electron donors for oxygen ionisation. Subsequent diffusion-controlled growth of Ti2O3/CaTiO3 floret

patches at 2 h is probably due to electrochemical nucleation and growth as oppose to Ostwald ripening. Scale bar

from left to right: (a) TiO2: 1 mm, 100 µm, 50 µm; (b) 0.5 h: 1 mm(× 2), 50 µm(× 3); (c) 1 h: 1 mm, 100 µm, 10

µm, 50 µm, 10 µm; (d) 2 h: 1 mm, 100 µm, 50 µm, 10 µm, 50 µm, 10 µm, 100 µm; (e) 4 h: 1 mm, 50 µm, 1 mm; (f)

7 h: 1 mm; (g) 15 h: 1 mm(× 2), 50 µm, 1 mm, 10 µm, 50 µm(× 2), 10 µm; (h) 22 h: 1 mm, 200 µm; (i) 24 h: 1 mm,

50 µm, 500 µm; (j) 22 h (3.3 mm): 1 mm, 1 mm; (k) 22 h (5.3 mm): 2 mm(× 2), 500 µm.

a b

c

d

e f

g

h i

j k

Fig. 3| (a) Standard deviation in current distribution along the current collector/porous cathode interface (js.d.) in

electro-deoxidation cells containing shaped anode undersides and porous TiO2 cathode stacks (Cathode 1 and 5:

bottom and top cathode, respectively) (Boundary conditions: interface φ = 3.2 V and anode boundary φ = zero). (b)

Bipolar electro-deoxidation cell [46]. (c) Porous TiO2 Raschig rings within a stainless steel cathode mesh basket

opposite horizontal anode. (d) Ex-situ SEM images of electro-deoxidation. Scale bar: 1 mm (Inner), 50 µm (Core: 1,

2, 11 and 24 h), 1 mm (Core: 22 h) and 1 mm (Outer). Inner: adjacent to stainless steel current collector.

Packable TiO2 preforms

Cathodic bipolar side

Anodic bipolar side

CaCl2 melt

Terminal

anode

Terminal

cathode

Bipolar

electrode

Housing

Sloped Anode Undulated Anode Perforated Anode Flat Anode

TiO2

stack

Sloped

Undulated

Perforated

Flat

50 150 250 350 1.6 1.8 2.0 2.2

js.d. (A m2) js.d. (105 A m2)

Cathode 2 3 4 1 5

a b

Stainless steel

current collector

Graphite

anode

Porous TiO2

raschig rings

c d

1

h

2 h

1

1 h

22

h

24 h

Fig. 4| Rotational flow mechanics: (a) Spherical Ti particles (280 µm diameter) in molten CaCl2 migrate until the

region of lowest shear rate in the wide-gap Couette contains nearly the maximum volume fraction of a random

packing for spheres. Local suspension viscosity μs = μ(1 φt/φm)2.5φm, where φm is the limit of maximum particle

packing, is dependent on local φt. To account for surrounding particles, the Stokes settling velocity of a particle is

multiplied by the hindered settling function fh = μ(1 φave)/μs where the average volume fraction φave is the initial

volume fraction for closed Couette flow. The sedimented initial condition is 1 φave = 0.59 while the suspension

velocity satisfies No-slip (u = 0) boundary conditions at each cylinder. The pump impeller in (b) and (c) rotate

clockwise at 1750 rpm for 20 s. (b) Two eddies form as the impeller blades of the pump pass inlet and outlet

sections thereby lowering the pump efficiency. In addition, the velocity streamlines show that a large part of molten

CaCl2 rotates around the blade without leaving the pump. (c) Reducing the cross-sectional recirculation area inside

the pump improves the velocity field. In comparison with (b), the net flow through the pump is increased without

increasing the rotational speed of the pump.

0 0.5 1.0 1.5 2.0

0.5 1.0 1.5 2.0

0.9

0.8

0.7

0.6

1

φt

r (cm)

0.5

0.4

0.3

0.2

0.1

0 φ

t

0 0.64

φs

Ti powder

r CaCl2

melt

1000 rpm

800 rpm

600 rpm

1000 rpm

800 rpm

600 rpm

1000 rpm

1000 rpm

m s

1

0.45

0

0.45

0

m s

1

b c

a

Fig. 5| In-situ analysis: (a) Slow voltage ramping eliminates excessive currents thereby improving ξe and

reproducibility of electro-deoxidation. (b) Tafel plot derived from current-potential data at T = 1173 K from a three-

electrode electrochemical cell (stainless steel working electrode, graphite counter electrode, Ni reference electrode,

and molten CaCl2 electrolyte) (correlation coefficient > 93 %). (c) Breakdown in Scharifker-Hill Ti nucleation (Red:

progressive and Blue: instantaneous) in a 5.3 mm thick cathode. In relation to the background current, in contrast to

the law of mass action, e2 ↔ 2e indicates a probable increase in the van’t Hoff factor between 1 and 2, and positive

relative partial molar entropy of Ca [62]. This involves lowering the contribution of repulsive Coulomb interaction

between like ions [60]. (d) Gas release from an annulus anode during electro-deoxidation in which the anode gas

flowrate Vg is derived from online process mass spectrometry [22]. Inset: volume fraction of CO gas in molten

CaCl2 reaches near steady state after 20 s. The bubbly flow model tracks the average gas concentration in a bubble

column with dimensions: 0.2 m diameter and 2.1 m height with a 0.1 m cylindrical wall diameter. (e) Temperature

control chart for the electro-deoxidation of TiO2 in molten CaCl2.

0 1.0 2.0 3.0 4.0 5.0 0.5 1 2 4 7 11 15 22 24

t (h)

T (

K)

0.8

0.6

0.4

0.2

0

1223.6

1223.3

1222.9

a

b

3.2

2.5

2.0

Voltag

e (V)

ηa (V)

In j

10.8

8.8

6.8

4.8

2.8

9.0

8.0

7.0

6.0

5.0

1.0

0.9

0.8

0.7

0.6

In j = 10.66η + 5.86

d

e

0 0.05 0.10 0.15 0.20

t (h)

J (A

)

0 0.1 0.2 0.3

t/tm

(J/J

m)2

CO

CO2

1.3

1.0

0.7

0.4

Vf (

10

3 m

3/m

3)

0 5 10 15

0 2.0 4.0 6.0 8.0 10.0 t (h)

Vg (

L h

1)

Upper Control Limit

Mean

Lower Control Limit

t (s)

c

Fig. 6| Elemental analysis of porous cathode cross-section after 2 h: Element line-scan and spot-analysis (X-

EDS) across a polished cathode cross-section: Ti, Ca, O and Cl profiles. Detection of silicon originates from its

relatively high impurity concentration (i.e. 5000 ppm) in as-received TiO2 powder (average particle size d50 = 0.61

μm and average BET = 6.54 m2 g1) (Tronox, 99.5 % rutile TRHP2). The thermodynamic complexity of multivalent

Ti in the porous cathode can be addressed using TiCaOCl predominance diagrams [33,37] since they indicate

thermodynamic effectiveness (i.e. high pO2 > 6 and < 500 ppm oxygen in Ti at Ca activity aCa > 103) or severe

diminishment (i.e. low pO2 < 3 and < 500 ppm oxygen in Ti at aCa < 106). Based on percolation threshold porosity

for tessellations in a Bethe lattice, the minimum porosity ε required for a connected diffusion path is ~ 0.16 ≤ ε ≤

0.25 [17]; ε is calculated from ρb = ρab(1 ε) where ρb and ρab is the experimental bulk and absolute cathode density

respectively. Also, the modified, corrected tortuosity factor τm of the diffusion path is τm1 = τc

1f = 1.46 where τc is

the corrected tortuosity factor and f is an empirical correction factor [17]; this is in good agreement with the

Carniglia tortuosity factor τ = 2 [17]. Scale bar: 100 µm.

0 1.0 2.0 0.8 2.4 4.0 5.6

Cathode thickness (mm)

400

200

50

25

200

100

160

80

0

Inte

nsi

ty (

a.u.)

Inten

sity (a.u

.) In

tensity

(a.u.)

Inten

sity (a.u

.)

Energy (keV)

Ti

Ti

Ti

Ca

Ca

Ca

Si

Si

Si

O

O

O

Ti

O

Ca

Cl

Fig. 7| Elemental analysis of porous cathode cross-section after 4 h: Element line-scan and spot-analysis (X-

EDS), and electron map (viewed in BSEI) across a polished cathode cross-section: Ti, Ca, O and Cl profiles in

which Ca and O atoms function as interruption atoms during preferential Ti growth on active sites at the 3PI.

Accumulation of CaTiO3 in the core and near the 3PI contributes to slow O2 ion diffusion out of the cathode.

Detection of Si originates from its relatively high impurity concentration (i.e. 5000 ppm) in as-received TiO2 powder

(Tronox, 99.5 % rutile TRHP2). The difference between incoming and outgoing vacancy fluxes Jv (i.e. divergence

of vacancy flux) and the vacancies generated at grain boundaries and dislocations (i.e. vacancy sources) within a

control volume U in the porous Ti layer may be estimated by ∂Nv/∂t = (∇∙Jv + ğ)U where Nv is the number of

vacancies in U, and ğ is the vacancy generation rate per unit volume. Vacancies are created at positive sources (ğ >

0) near the 3PI and annihilated at negative sources (ğ < 0) near the cathode surface. Scale bar: 1 mm.

150

75

0

65

33

0

27

14

0

0 1.0 2.0 0.8 2.4 4.0 5.6

Thickness (mm)

Inte

nsi

ty (

a.u.)

Energy (keV)

Ti

Ca

O

Ti

Ti

Ti

Ca

Ca

Ca

O

O

Si

Si

Inten

sity (a.u

.) In

tensity

(a.u.)

Inten

sity (a.u

.) In

tensi

ty (

a.u.)

In

tensi

ty (

a.u.)

Fig. 8| Steady-state velocity distribution: (a) Effect of r on numerical H for ω = 20π (Re = ρωrc2/µ = 158) where rc

= 0.014 m is the disk radius and Re is the Reynolds number. (b) Comparing numerical H profiles with theoretical

Padé [74], Ariel [72], Cochran [70], and Newman [71] H profiles. (c) Velocity field in molten CaCl2 at ω = 20π. The

centrifugal force radially ejects molten CaCl2 outward accompanied by axial inflow towards the disk to satisfy

continuity and two contra-rotational flow vortices. (d) Velocity field in molten CaCl2 at ω = 198π (Re = 1560).

1.0

0

1.0

2.0

3.0

4.0

50

10

50

10

50

10

0

0 10 20 30 40 0 0.25 0.50 0.75 1 ξ

H (

10

5)

0.6

0.4

0.2

0

0.2

0.4

50

10

50

10

50

10

0

H

ξ

0 14 33 0 14 33

1.2

2.8

1.6

0.7

0.3

0

uz

ur

uθ

10

3 m s

1

10

3 m s

1

m s

1

1.2

2.6

1.4

0.7

0.03

0

uz

ur

uθ

10

6 m s

1

10

6 m s

1

m s

1

r (mm) r (mm)

z (m

m)

z (m

m)

z (m

m)

z (m

m)

z (m

m)

z (m

m)

r = 3 mm

r = 19 mm

Padé

Ariel

Cochran

Newman

r = 19 mm

r = 16 mm

r = 14 mm

r = 8 mm

r = 3 mm

a b

c d

Fig. 9| Ti recovery from molten CaCl2: Initially, velocity as well as Ti volume fraction is assumed zero in the

entire circular secondary clarifier. Incoming suspension, a mixture of molten CaCl2 and spherical mono-sized Ti

particles (140 µm diameter) enters through the inlet in the middle of the clarifier at a fixed 1.25 m s1 suspension

velocity. The central outlet at the bottom of the clarifier (fixed 0.05 m s1 suspension velocity) removes Ti sediment

while the peripheral outlet removes purified molten CaCl2. In the multiphase flow model, the slip velocity is

described by the Hadamard-Rybczynski drag law for solid particles while the k-ε turbulence model calculates the

turbulent viscosity. The particle dispersion coefficient is determined on the basis of a 0.35 turbulent Schmidt

number. Steady-state velocity streamlines and Ti concentration after 24 h is shown in which turbulent flow tends to

mix Ti particles and molten CaCl2 at 1223 K (a) 0.02 vol.% of Ti particles in incoming suspension and (b) 0.2 vol.%

of Ti particles in incoming suspension. This has a negative effect on phase separation and Ti recovery at relatively

high Ti volume fractions. Boundary conditions: constant pressure at peripheral outlet, symmetry conditions at the

molten CaCl2 surface and symmetry axis, and logarithmic wall functions with insulation of all solid walls.

1.217

0.470

9.820

2.296

kg m

3 T

i conc.

kg m

3 T

i conc.

a

b

Inlet Peripheral Outlet

Suspension Outlet