Evaluating Field-Effect Separation on Rare Earth and Critical Metals

Abstract

The unique electromagnetic properties of rare earth elements (REEs) have led to rapid technological advances, creating a sharp increase in demand for these materials. The inherent challenges of separating REEs and the significant drawbacks of existing processes have driven the development of a new method known as field-effect separation (FES). This technology leverages electrical and magnetic fields to achieve separation by exploiting the differences in magnetic moments or effective charges of REEs in solution. Experiments on REEs were conducted using a microchannel based separation device, which confines fluid flow to facilitate separation within a field, with metal cations in solution being transported based on their respective electrostatic or magnetic properties. The results demonstrate that separation based on effective charge or paramagnetic properties is achievable. The confinement of fluid flow to microchannels allowed advective and osmotic forces to be suppressed sufficiently such that a reasonable separation of ions was achieved, though the impact of these forces were not completely removed. This innovative approach promises to improve the efficiency and effectiveness of REE separation, addressing both the growing demand and the limitations of current methods.

1. Introduction

Recently, fast advances in the fields of electronics and energy storage have led to high demand for rare earth elements (REEs). The high demand for these critical materials, combined with their scarcity and the difficulty of producing them in large quantities, has led many governments globally to classify these elements as critical strategic resources for the future of technology. REEs are seen as key elements in a global renewable energy transition, and the use of heavier REEs in defense applications makes securing stable REE reserves a priority for a nation’s economic viability, energy independence, and defense posture [1,2]. REEs are considered crucial for the renewable energy transition in the near future. Neodymium and other light to medium REEs, essential for strong permanent magnets, significantly contribute to the demand, primarily through their use in electric car motors and wind turbine generators [3,4]. As a result, new and more efficient methods of extracting and separating REEs for commercial use will be critical in the coming future.

REEs possess unique properties that result from their 4f valence orbital shells. However, the relatively similar physical properties of these elements as a result of each element having a similar ionic radius and their propensity to form +3 ions almost exclusively means that they all exhibit remarkably similar chemical properties that prove difficult to exploit in separation [2,5]. Generally, the REEs can be divided by atomic mass into light (La-Sm) and heavy (Eu-Lu), with some making a further distinction into a middle, medium REE class (Sm, Eu, Gd) [3,4,6]. A primary driver of recent demand for REEs has been the heavy REEs (HREEs), which have incredibly unique photo, electrical, and magnetic properties that make them the most useful of the lanthanides for advanced technologies, particularly crucial for advanced sensors used in the defense industry [6]. Currently, most industrial production of REEs uses liquid–liquid extraction, otherwise known as solvent extraction, which utilizes the small differences in chemical affinities of the REEs for a particular extractant to separate them [7].

Solvent extraction for REE separations has some significant disadvantages, including high consumption of the chemicals needed to achieve required purity, which make the process expensive and inefficient [2,8]. The process also has markedly worse performance in separating HREEs, and incomplete stripping of the solvent can lead to heavy losses of critical elements during processing [6]. Additionally, the organic solvents necessary for this process are flammable, toxic, carcinogenic, and environmentally damaging, making them a large source of problematic waste which can be challenging to safely store and dispose of [7]. Solvent extraction for rare earth production using monazite/bastnasite ore has a relatively high global warming impact per kg of produced REE due to release of greenhouse gases as well as generation of compounds that have some toxicity [9]. While actual energy consumption within a process is dependent on a number of factors that relate to the feed material such as the type and grade, the solvent extraction step can consume more than 50% of the required energy to produce one ton of rare earth metal [10]. However, until further research into alternative methods of separating these metals can be done, solvent extraction remains the most feasible process for separating bulk quantities of REEs [11]. As a result, a significant step forward in making REE extraction more economically feasible, and, more importantly, less environmentally damaging and safer for humans, will be any progress that can be made towards improving or replacing the tradition solvent extraction process. The demand for critical metals extends beyond REEs to other transition and alkali metals such as cobalt, nickel, copper, and lithium [12]. These metals are critical for a nation’s energy future, and securing more environmentally friendly ways of recovering these metals is important. Additionally, as demand for these metals increase, and the quality of the supply decreases, the environmental impact of extracting these metals increases significantly [13].

The unique chemical challenge these elements present in their separation has inspired the present research on field-based separation. While the REEs may exist in identical ionic forms with similar chemical affinities, they have different electron configurations resulting in differing magnetic moment strengths. In this context, any ion with unpaired electrons in its valence orbital will have a magnetic moment [14]. It is this property which allows the 4f and 3d metals tested to respond to the magnetic fields, as well as allowing for the mobilities of these ions in the solution to be quite different depending on the number of unpaired electrons each ion has. Additionally, the REEs have been shown to exhibit differing affinities for complexing with certain organic molecules at different pH levels, which modifies their effective charge to be different enough from one another that they can be separated on the basis of charge [15,16]. This is largely due to the small differences in atomic radius of the lanthanides, as well as the difference in coordination number from the heavy to light REEs [5,17]. The aim of this research is to exploit these differences in physical properties to drive separation without the use of traditional solvent extractants. The process proposed is envisioned to either replace or supplement traditional solvent extraction; therefore, the system in question is a solution of relatively concentrated mixed REE–chloride salts with some additional valuable critical metals and contaminants. Work was carried out to understand how ions of differing magnetic moments can be separated in solution as well as how ions of differing charge can be separated electrostatically using methods similar to magnetic separation. The fundamental underlying idea behind the studied separation mechanism is that, given a fixed residence time for a dilute solution of mixed REE ions, these ions will diffuse different distances in response to a force field. The difference in this mobility can be exploited to drive separation on the basis of this generated concentration gradient if external, inhibiting forces can be sufficiently mitigated. This has already to be proven feasible; however, both the timescale and scalability of previous set-ups need to be improved to work on an industrial scale [18,19,20].

1.1. Theory

The concentration profile for a solution of susceptible ions subject to a force field is given by:

$${\displaystyle \frac{\partial C}{\partial t}}+\nabla ·\left[{\displaystyle \frac{D}{RT}}\left(-\nabla C+C{F}_f\right)+Cv\right]+r=0$$

(1)

The partial differential on the left is changing concentration over time, the second and third terms represent diffusion under a field and convection respectively, and the last term describes volumetric generation from a chemical reaction [21]. D is the diffusion coefficient of the species, R is the universal gas constant, T is the thermodynamic temperature, C is concentration, F_f is the external force field applied, v is the fluid velocity, and r is the volumetric generation term. Assuming no chemical reaction takes place and steady state conditions are reached, the concentration profile of the ions in solution becomes:

$$0=-\nabla ·\left[{\displaystyle \frac{D}{RT}}\left(-\nabla C+C{F}_f\right)+Cv\right]$$

(2)

This equation describes three sources of changing concentration which will be of significant concern to performing separations on an ionic scale. These sources of ion flux will be: (1) Migration due to external applied force, (2) diffusion due to an induced concentration gradient, and (3) convection due to fluid flow. As a result, each of these must be individually addressed to optimize ion separation.

1.1.1. Magnetic Separation

The separation of paramagnetic ions in an inhomogeneous magnetic field is done based on the significant variability in the magnetic moments of 3d transition metals and 4f lanthanides. The strength of the magnetic moments of each of the ions can be predicted from their electron structures using their orbital quantum numbers S, L, and J. The effective magnetic moment of an ion can be calculated as:

$${\mu }_{eff}={{\mu }_{b}g}_j\sqrt{J\left(J+1\right)}$$

(3)

where μ_b is the Bohr magneton ( ${\mathit{\mu }}_{\mathit{b}}\mathit{=}\frac{\mathit{e}\mathit{\hslash }}{2{\mathit{m}}_{\mathit{e}}}\mathit{)}$ and g_j is the Landé g-factor [18]:

$$g_j=1+{\displaystyle \frac{J\left(J+1\right)+S\left(S+1\right)-L\left(L+1\right)}{2J\left(J+1\right)}}$$

(4)

The values of μ_eff are calculated for the various lanthanides and a few select 3d transition metals in

Table 1. Quantum numbers and magnetic properties of a few selected metals.

Ion	Configuration	S	L	J	gj	µeff/µB	Type
Ce3+	4f1	0.50	3.00	2.50	0.86	2.54	LREE
Pr3+	4f2	1.00	5.00	4.00	0.80	3.58	LREE
Gd3+	4f7	3.50	0.00	3.50	2.00	7.94	MREE
Dy3+	4f9	2.50	5.00	7.50	1.33	10.63	HREE
Er3+	4f11	1.50	6.00	7.50	1.20	7.57	HREE
Li+	1s2	0.00	0.00	0.00	0.00	0.00	Alkali
Fe3+	3d5	2.50	0.00	2.50	2.00	5.90 *	TM
Co2+	3d7	1.50	3.00	4.50	1.33	6.63 *	TM

* Experimental moments of 3d metals are complex and lower than the theoretical values by a significant amount due to orbital quenching [14].

. When placed inside of an inhomogeneous magnetic field of strength B, the solution of paramagnetic ions will have a volumetric potential energy (E) given by:

$$E={\displaystyle \frac{{\chi }_{sol}}{2{\mu }_0}}{B}^2$$

(5)

where χ_sol is the magnetic susceptibility of the solution, which is the weighted average of the individual susceptibilities of the components of the solution, and μ₀ is the permeability of free space [18,19]. The molar magnetic susceptibility of a material is related to the strength of its magnetic moment described in Equation (3). Molar Susceptibility (${\chi }_m$) can be calculated using Curie’s law, which states:

$${\chi }_m={\displaystyle \frac{C_m}{T}}={\displaystyle \frac{{\mu }_0{N}_a{{\mu }_{eff}}^2}{3K_{B}T}}$$

(6)

where N_a is Avogadro’s number and K_B is the Boltzmann constant [19]. The volumetric force exerted on the solution by the magnet (F_m) is therefore:

$$F_m=\nabla E_m={\displaystyle \frac{{\chi }_{sol}}{2{\mu }_0}}{\nabla B}^2$$

(7)

The following volumetric force term can then be used in Equation (2) to describe the concentration gradient generated by a given magnetic field. Equation (7) shows the clear dependence of the magnetic separation on both the individual susceptibility of the ions in solution as well as the strength of the magnetic field gradient, showing that this kind of separation would not be possible in a homogenous magnetic field (∇B = 0).

1.1.2. Electrostatic Separation

Separation based on electrostatic (ES) attraction is relatively simple compared to magnetic separation, and the main factor impacting separation will be ionic charge of the species in solution. The force term (F_e), which is to be substituted into Equation (2), is simply Coulomb’s equation for electrostatic attraction:

$$F_e={\displaystyle \frac{K_c{q}_1{q}_2}{r^2}}$$

(8)

where K_c is Coulomb’s constant, q₁ and q₂ are the charges of the high voltage source and the ion respectively, and r is the distance between the two charges. Using the definition for electrostatic potential, $V=K_c{\displaystyle \frac{q}{r}}$, Equation (8) can be rewritten as:

$$F_e={\displaystyle \frac{V{q}_{ion}}{r}}$$

(9)

This form of the force term shows the electrostatic separation to be determined primarily by the voltage of the source used for separation, the charge of the ionic species in solution, and the separation distance. The first two factors are, for the present purposes, unchanging and therefore effective ionic charge will be the primary factor impacting separation of ions. The change in total concentration generated by a potential difference between two points ($∆V$) can be calculated as:

$$∆V=K_c{Zq}_e{N}_A{\displaystyle \frac{∆C}{r}}$$

(10)

where Z is the ionic charge, q_e is the charge of an electron (1.602 × 10⁻¹⁹ C/eV), N_A is Avogadro’s number (6.023 × 10²³), and ∆C is the change in concentration from one point to another in mol/L. For a 100 kV source and a separation distance of 1 × 10⁻⁴ m, the predicted change in concentration is on the order of 10⁻¹² mol/L. This would seemingly make separation of this kind impractical without an excessively powerful potential source or minuscule length scale. However, this fact overshadows that, for a solution that is composed of many different ions of many different valencies, only the net charge and ionic strength of the solution must remain effectively constant. Ionic strength (I) is calculated using the following equation:

$$I={\displaystyle \frac{1}{2}}\sum _{i=1}^n{C}_i{z}_i^2$$

(11)

Ionic strength is simply a sum of ionic charges (z) and concentrations (C), and so long as the sum of charges and concentrations remains constant, the system can exist in a number of different configurations [22]. The system will end up in a configuration which minimizes its potential energy by arranging ions in a way that results in their effective ionic charge corresponding to the gradient of the electric field. This manifests as elements with higher positive charge moving further towards the potential source and those with lower charge diffusing to maintain a net zero change in ionic strength.

1.1.3. Advection and Mixing

Though the externally applied force term has been adequately defined, Equation (2) describes a force which works against a separation of ions, advection. While the forces described above can generate a concentration gradient in a solution, realizing that separation into two distinct fractions can be difficult because of mixing that will inevitably occur as one tries to physically separate them. Designing a device which would allow fluid to flow through the field in two laminar flows, a “top” flow and a “bottom” flow, would solve this problem. Designing the flow channels such that the flow is laminar will reduce turbulent mixing while having two channels, a top and a bottom, allows ions to be deflected from one stream into another and separated.

A balance of momentum in a flow carried by either inertial or viscous forces is described using the Reynolds number. For internal flow in a pipe, the Reynolds number (Re) is:

$$Re={\displaystyle \frac{\rho U{D}_H}{\mu }}$$

(12)

where ρ is the density of the fluid (kg/m³), U is the velocity of the flow (m/s), D_H is the hydraulic diameter (m), and μ is dynamic viscosity (Pa s) [23]. For internal flow, the critical Reynolds number is 2300 and a Re > 2300 denotes a transition from a laminar flow to a turbulent flow. Therefore, Equation (10) shows that to decrease the Reynolds number of a given flow, either the hydraulic diameter of the pipe can be decreased, or the dynamic viscosity of the fluid increased. For the intended separation, the Reynolds number is always going to be below 100. Therefore, the importance of the Reynolds number is not to tell whether the flow is laminar or not, as it will be laminar for every separation device tested, but instead, it will be mostly used to describe the magnitude of inertial forces in the flow which can drive even minor amounts of unintended mixing of the top and bottom streams on the boundary where they meet.

Another dimensionless number in fluid dynamics that can be used to evaluate the ratio of advective mass transfer to molecular (mass) diffusion is the Schmidt number (Sc):

$$Sc={\displaystyle \frac{\mu }{\rho D}}$$

(13)

A larger Sc indicates a flow with momentum transfer dominated by advective forces rather than the diffusive mass transfer [23]. The values for ions in water at room temperature are typically 200–1500.

Table 2. Diffusivities and Schmidt numbers for different metal ions.

Ion	D (×10−10 m2/s)	Sc	Reference
La3+	6.19	1438	[24]
Nd3+	6.16	1445	[24]
Li+	10.29	865	[25]
Fe3+	6.04	1474	[25]
Co2+	6.78	1313	[25]

All values are for water at 25 °C.

shows the Sc for a few different ions in water. This table demonstrates that most of these ions will have an Sc near the upper limit typical of a liquid–liquid system, meaning that general momentum in the stream is carried more by advective mass transfer than the back diffusion created by a concentration gradient. This is the motivation behind the design of the microchannel device because minimizing advective mass transfer is key to higher separations of the target metals. Additionally, facilitating diffusion between layers in the device is critical to maintaining a balance of charges in the system.

2. Materials and Methods

To control the flow of the testing solution such that it is laminar, a device to constrain the flow into many narrow channels was designed. This device consists of two hard, plastic layers with very thin flow channels on the surface of each. The two opposing layers are angled slightly and pressed together. The channels on each layer are spaced evenly and each channel is as close to parallel as possible. The device is then placed directly in a magnetic or electrostatic field and fluid is allowed to flow through the layers. The channels guide the fluid to allow it to flow without turbulence as separation in the field is taking place. The source of the magnetic field was a 4 cm × 4 cm × 1 cm N52 NdFeB magnet placed 1 cm from the flow. An electrostatic field of 100 kV was generated using a Van de Graaf generator placed 1 cm from the flow. Figure 1a is a schematic representation of the microchannel device and demonstrates how ions are separated by deflection from the top channel into the bottom channel. Figure 1b shows an alternative view of this process, where susceptible ions are preferentially concentrated in the bottom stream, separating them from non-susceptible and mildly susceptible ions.

Figure 2 show the setup of the magnetic and electrostatic separations, respectively. As an ion in solution passes through the magnetic or electric field, it is deflected from one stream into the other. The two streams flow out of the device into separate containers and are collected to be analyzed. To test the relative impact of different flow velocities and channel sizes, different channel widths were compared. The two channel widths that were tested were 170 µm and 320 µm. The testing solution was composed of 50 mg/L of the following trivalent REE chloride hexahydrate salts: La, Ce, Pr, Sm, Eu, Gd, Dy, Er (Sigma-Aldrich (Burlington, MA, USA), >99%), as well as 50 mg/L of selected transition and alkali metal chloride hydrate salts: Li (Alfa-Aesar (Haverhill, MA, USA), 99%), Fe, Ni, Co, Cu (Acros Organics (Waltham, MA, USA), 98%), and a background salt of 0.25 wt% NaCl (Macron Chemicals (Radnor, PA, USA), 99%). The solution was adjusted to a pH of 0.75 using concentrated HCl (Fisher Chemicals (Waltham, MA, USA), 38.0%). The addition of transition metals to the REEs was done in these tests in order to both demonstrate the magnetic properties of 3d ions in addition to the 4f lanthanides, but also to show the viability of this system for separating metals other than REEs. Ni, Co, and Cu are metals of significant interest and Fe is a common contaminant in REE purification processes. Another set of tests were performed on the same 170 µm microchannel device with the same 50 mg/L REE+TM test solution, but the device was oriented at a variety of different angles to modify the velocity of the fluid flowing through the device. The first solution tested with electrostatic separation consisted of 100 mg/L of the same FeCl₃, NiCl₂, LiCl, and KCl (Alfa-Aesar (Haverhill, MA, USA), 99%) salts with 0.25 wt% NaCl, adjusted to a pH of 0.75 using concentrated HCl. A different ES separation was performed on a solution consisting of 100 mg/L of LiCl, and 100 mg/L of K₂Cr₂O₇ (J.T. Baker, 99%) adjusted to either a pH of 2.0 or 10.0 using either concentrated HCl or KOH (Sigma-Aldrich (Burlington, MA, USA), 99%), respectively.

Lastly, an ES separation was done on a solution containing 50 mg/L of the selected trivalent REE chloride salts mixed with 25 mM of ethylenediaminetriacetic acid (EDTA) (Sigma-Aldrich (Burlington, MA, USA), 99%) and adjusted with concentrated NH₄OH (Fisher Chemicals (Waltham, PA, USA), 30.0%) to a pH of 6.5 and 9.5 [17]. The test solutions were allowed to flow through the microchannel device in a magnetic or electric field, the top and bottom portions were then collected, diluted in 5% HNO₃ (Fisher Chemicals (Waltham, PA, USA), trace metals grade), and analyzed with inductively coupled plasma optical emission spectroscopy (Agilent 5800 ICP-OES, Agilent Technologies, Santa Clara, CA, USA) to compare their various ion separations. pH was tested using a pH probe (Thermo Scientific Orion Ag/AgCl pH probe) for certain samples to gauge the magnitude of H⁺ diffusion. Theoretical speciation of ions in solution was calculated with the software Visual MINTEQ 4.0.

3. Results and Discussion

3.1. Microchannel Device Analysis

The primary factor affecting separation that was tested for the microchannel device was the diameter of the channels. The increase in channel diameter will lead to a lower density of channels, greater channel spacing, and a larger internal volume. This has the impact of decreasing residence in the field as well as increasing the flow rate through the device. Therefore, a poorer separation with a larger channel diameter is predicted from analyzing the Reynolds number of the flows in the two different devices. To do so, the channel width was calculated using channel density (channels/cm) to calculate the spacing between each channel wall.

Table 3. Flow parameters of devices with two different channel diameters.

Spacing	320 µm	170 µm
# Channels (per side)	104	184
Residence Time (s)	25.9	61.1
Flow Velocity (cm/s)	0.154	0.066
Re	54.6	12.3

shows the flow parameters through each device. As can be seen, the reduction in channel diameter from 320 µm to 170 µm has a significant impact on flow velocity, residence time, and, therefore, turbulence. The 170 µm channel device is about half the size of the 320 µm channel device, and this is the primary factor with contributes to the significant difference in performance between these devices. The Reynolds number for these two devices shows that while both flows should be demonstrating laminar characteristics, the 320 µm device’s flow will be more turbulent along the fluid layer separating the two top and bottom streams. This is a likely factor contributing to the inherently lower performance of the larger diameter channel devices. In addition, the residence time is approximately 41% of the larger channel device, thereby leading to a much shorter (2.4×) exposure time in the applied field, resulting in less separation.

With a Reynolds number determined, other mass transfer relationships can be calculated. The Sherwood number is a dimensionless constant in fluid dynamics that describes the ratio of the advective mass transfer coefficient to the diffusivity of the species over its diffusion length [23]. In practice, it represents the ratio of the two rates and incorporates Re into the calculation using the Froessling Equation:

$$Sh={\displaystyle \frac{k_{c}L}{D}}\cong 2+0.6\left({Re}^{{\displaystyle \frac{1}{2}}}{Sc}^{{\displaystyle \frac{1}{3}}}\right)$$

(14)

where k_c is the advective mass transfer coefficient, L is the diffusion length, Re is the Reynolds number, and Sc is the Schmidt number.

Table 4. Sherwood numbers for different ions in both the 170 µm and 320 µm microchannels.

	Sc	Sh170	Sh320
La3+	1437.803	25.761	52.018
Nd3+	1444.805	25.799	52.099
Li+	864.917	22.058	44.224
Fe3+	1473.510	25.956	52.429
Co2+	1312.684	25.051	50.523

shows the Sherwood numbers for a few selected ions and demonstrates that the actual magnitude of the difference between the advective and mass transfer is only roughly one order of magnitude, so both effects will be significant. Additionally, it is evident that the effects of advection are reduced significantly for the smaller microchannel device, making the impact of mass transfer due to diffusion more significant.

3.2. Magnetic Separation Performance

Magnetic separation was performed using the newly developed microchannel devices and the performance is summarized in Figure 3a. The magnetic nature of the concentration gradient created is confirmed by the lack of lithium mobility in the solution. Li⁺ was predicted to have no magnetic moment and be unresponsive to an inhomogeneous magnetic field, which makes it a good tracer to verify magnetic effects. Additionally, those ions with substantial magnetic moments were significantly separated from one stream to the other. Though slight, a trend in separation can be observed between each of the metals depending on the strength of their magnetic moments. LREEs with a small theoretical magnetic moment were moved from one stream to the other noticeably less than the HREEs with much larger magnetic moments. Figure 3b shows that at the low pH of 0.75, 99% of the metal in solution is present almost entirely uncomplexed with the exception of iron. This eliminates any doubt about the potential impact of differing speciation of metal ions in solution might create when analyzing the results.

Figure 4 shows the separation of each element plotted with respect to its magnetic moment strength. The correlation between these factors is imperfect; this is a result of mixing counter to the direction of separation. This applies to both those inherent to the system (such as the back-diffusion created by the induced concentration gradient) and those that come from the imperfections that result from construction of the microchannel devices. These work to mask the impact that the magnetic moment strength has on the total separation, but a clear trend can still be observed.

The 170 µm microchannel device was modified to allow for different fluid flow rates through the device. The impact of this is twofold: (1) to modify the residence time of the fluid in the magnetic field and (2) to modify the fluid flow velocity and therefore the flow parameters (such as Re). Figure 5 shows the separation of the same test solution as previously with multiple different residence times. As can be observed, the effect of residence time on separation is significant and consistent. In the 170 µm microchannel device, the Re is <15 for any system configuration, and therefore the impact on advection as a function of changing flow velocity is, in this set of circumstances, insignificant.

Table 5. Impact of fluid velocity on residence time and Reynolds number.

Device Angle	90°	45°	30°
Pump Rate (µL/min)	150	100	75
Residence Time (s)	61.11	91.67	122.22
Re	12.31	8.21	6.16

shows the flow parameters of the differently oriented devices. Therefore, in the smaller microchannel device, the primary factors influencing the separation of ions from one another are the force that an ion experiences in a magnetic field and the time that ion is exposed to that magnetic field for.

3.3. Electrostatic Separation Performance

Electrostatic separation was performed using the same channel devices developed for the magnetic separation and the performance shown in Figure 6a. As can be seen, separation based on valence of the individual ions was achieved, with the two most significantly separated ions being the Ni²⁺ and the Fe³⁺. Curiously, the Ni²⁺ seems to break this trend for the 320 µm device and the separation for the 170 µm device was poor. Figure 6b shows the relative percentage of each ion in solution as simulated from thermodynamics. In chloride media, it is likely that a larger portion of the iron was able to form complexes with chloride ions in solution compared to nickel. When comparing separation based on “effective” ionic charge, which is the weighted average of the charges of all the species of a given metal ion in solution, the trend is far more pronounced, as can be seen from Figure 7.

Further demonstration of the impact of complexation and effective ionic charge on separation is demonstrated in Figure 8. Here the same device was tested with two different solutions of LiCl and K₂Cr₂O₇ at a pH of 2.0 and 10.0. At a pH of 2.0, thermodynamics predicts ~95% of the chromium exists in solution as HCrO₄⁻, while at pH = 10.0, the 95% chromium forms CrO₄²⁻. Figure 8 demonstrates the clear disparity in separation due to this complexation effect compared to K⁺ and Li⁺ ions which remain relatively un-complexed in solution relative to pH. The ultimate effect of complexation in this context is to lower the effective charge of the ion in solution. By changing the pH from highly acidic to highly basic, the effective charge of chromium was halved from CrO₄²⁻ to HCrO₄⁻, and subsequently the separation seen between the two tests was halved as well.

The one aspect of this system not adequately described by chromium’s effective charge is the direction of movement in the field. Despite having an opposite effective charge to the alkali metals, chromium is concentrated in the same direction. This could be indicative of the chromate anions being dragged across from one stream to another by the movement of cations such as Li⁺. This is partly shown in the movement of chlorine anions in the system. A halving of the chromate movement results in a doubling of the movement of chlorine despite there being no observed impact of pH on the complexation of chlorine. It is therefore possible that the movement of chlorine is explained by the system’s inherent trend towards maintaining a balance of ionic strength in the system. The counter diffusion of chlorine balances the ionic strengths of both the top and bottom streams throughout the separation. This is a critical aspect of the viability of this manner of separation, as basic calculations on the allowed separation of ions in an electric field is only 10⁻¹² mol/L for this device, demonstrating that in general the amount of net charge on both sides of the separation should remain constant.

Table 6. Difference in ionic strength between the top and bottom streams for tests at different pHs.

		Li	K	H	Cr	Cl
pH 2.0	Zeff	1	1	1	−1	−1
	% Change	9.88	9.15	−17.50	8.98	−8.90
	% I change	−0.84%
pH 10.0	Zeff	1	1	1	−2	−1
	% Change	9.09	8.28	−7.15	3.70	−23.36
	% I change	−0.80%

shows the total change in ionic strength of both sides of the separation at different pHs when accounting for the migration of H⁺ ions in the form of pH change.

The change in ionic strength from top to bottom in the device is <1% and considered negligible. It shows the role the small, very mobile ions such as H⁺ and Cl⁻ play in maintaining a balance of charges and concentrations between the two streams of the device. At a low pH, large amounts of H⁺ can be observed moving counter to the direction of separation, and consequently a large amount of chromium in its anionic form is transported alongside its associated cations via electrostatic attraction. At a higher pH, the effective charge of the chromium was changed to −2 and part of the electrostatic attraction between it and the alkali cations moving across the boundary was partially overcome, meaning less of it was able to move across the boundary and be separated. However, its larger effective charge means that it will still have a significant impact on changing the ionic strengths of the top and bottom streams as it moves. Additionally, a higher pH means that less free H⁺ can move to balance charge in the two streams. This could explain the much larger movement of Cl⁻ and smaller movement of H⁺ at a high pH that was observed.

The separation of REEs in an electric field was done by utilizing a solution of lanthanides mixed with 25 mM EDTA. The EDTA complexes with the REEs to form anions and the degree of complexation for each lanthanide can differ depending on pH. A neutral and basic pH were selected to evaluate the impact of the increasing anionic nature of an ion on its separation. Work by J.I. Alonso and R.G. Fernández provides an experimental determination of the mechanism of complexation for these ions as well as their effective charge in solution as a function of pH [17]. The main favorable characteristic of EDTA in this system is that it generally complexes differently with LREEs than it does with HREEs, and the effect can be made more dramatic by changing the pH of the solution. If Y⁴⁻ can be considered the conjugate base of H₄Y which represents EDTA, then at a neutral pH the system has a propensity to form a LnY⁻ *(H₂O)_n (n = 3 for LREE, n = 2 for HREE). At a high pH of 9.5 the LREEs will form a mixture of LnY(OH)²⁻ *(H₂O)_2-3 and LnY(OH)³⁻ *(H₂O)_0-1 complexes, while the HREEs still preferentially form LnY⁻ in equilibrium with a small amount of LnY(OH)²⁻ [17]. This has the impact of making all the REE complexes have nearly the same effective charge of approximately −1 at a neutral pH, and at a higher pH, the effective charges vary between approximately −1 and −2.5 depending on the atomic weight of the lanthanide. Figure 9a shows the separation of the lanthanide elements in an electric field at differing pHs. As can be observed from the figure, the exact effect described above between the two different pHs is observed. The neutral pH test shows moderate overall separation with almost no separation between elements observed. However, at a high pH a clear difference in the separation of elements can be observed. The trend of separation is that it increased from top to bottom as atomic mass increased up until Gd, at which point the separation again begins to decrease. This trend agrees very well with the experimental effective charges found by Alonso and Fernández [17]. Figure 9b shows separation plotted against the effective charge of the complex at both high and low pH, and it clearly shows a strong trend of effective charge on separation.

The results of this experiment indicate that the formation of highly anionic EDTA–hydroxyl complexes is most prevalent in MREEs (Sm-Gd) and generally falls off increasingly as atomic mass increases or decreases. Additionally, a notable discrepancy between expectation and experiment can be noted for the separation of Dy and Er, which are the two points in Figure 9b that lie furthest from the line of best fit for pH = 9.5. The larger than expected separation is likely a result of the smaller radii of these HREE complexes because these elements typically form LnY⁻ with few to no waters of hydration, meaning that these elements are more mobile than their LREE counterparts which generally complex with 1 to 2 hydroxyl ions and have 2–3 waters of hydration. At a neutral pH, basically every ion is present as LnY⁻ and because the difference in effective charge as well as the separation between each element is relatively small, the effects of differing waters of hydration on the movement of these complexes is minor. This explains why in the pH = 6.5 case the effective charge of all of the ions cluster closely around −1 and similarly all the separations also fall tightly together around ~5%.

3.4. Discussion

The employment of FES was successfully demonstrated for separating metal ions in solution, in large part because the microchannel devices were effective at controlling the flow to minimize advective mass transfer while the fluid was subjected to the force field. This can be partially observed by comparing the separation of the most susceptible ions for different experiments to the Re for that particular set of testing conditions. A weak trend is present when looking at the separations presented in Figure 4a, Figure 5 and Figure 6a. This is because while Re can be used in conjunction with other dimensionless numbers such as Sc and Sh to describe the magnitude of advection relative to diffusion of ions in the force field, it is not the primary determining factor of total separation. The real effect that ties these experiments together is the correlation of total separation to residence time in the field, as might be initially expected. Figure 5 shines light on this particular effect best. In this experiment, a roughly 30 s increase in residence time is enough to increase the separation of most of the elements in solution by ~3–5% with each incremental increase. The decrease in residence time corresponds to increasing Re, explaining its weak correlation to separation.

A clear separation effect in the microchannel device was generated using magnetic fields generated by a strong permanent magnet. Though it leaves room for improvement, a stratification of elements on the basis of magnetic susceptibility as determined by the magnetic moment of each individual ion was clearly observed in between the top and bottom stream of the microchannel device. Between individual elements, for example Sm, Eu, and Gd, separations of 2–3% were observed. Additionally, increasing residence time maintains the observed stratification of elements even as concentration increases. While the osmotic effects of rapidly changing the concentration of solution were explored in the data presented in Figure 8 and Table 6, they were mostly neglected for these sets of experiments. This is due to the addition of a highly concentrated and non-magnetically susceptible background electrolyte (0.25 wt% NaCl). The high mobility of the salt paired with the very high ionic strength of the solution means that the magnetically susceptible ions should be free to migrate in the field without suffering the effects of back diffusion created by a chemical potential gradient.

Similarly, electrostatic separation experiments showed that ions can be separated in solution on the basis of effective charge. Figure 6 and Figure 7 describe this particular kind of separation. While complexation seems to have little effect on magnetic properties of 4f lanthanides, anions complexing with metals will work to lower its effective charge, and therefore how strongly it will respond in a field. This explains the seemingly anomalous separation behavior of Fe and Ni in this experiment because Fe complexes more strongly with Cl⁻ than Ni as predicted by thermodynamics. This effect can be used to improve separation between metals where it is known that their charges can be manipulated through selective complexation. Figure 8 and Figure 9 describe two experiments in which this effect was explored. In Figure 8, the effective charge of Cr was manipulated by changing pH which decreased its effective charge by −1 and subsequently halved its separation. Figure 9a,b describes a set of experiments wherein the pH dependent, selective complexation of REEs with EDTA was explored. It was demonstrated that EDTA can be used to create anionic complexes with REEs, and the degree of electronegativity exhibited by these complexes depended on pH, ionic radii, and coordination number. The combination of all of these factors means that medium to heavy REEs could be targeted with electrostatic separation by making them very anionic at high pHs.

4. Conclusions

This research describes the development of a new method of separation of rare earth and critical metals based on their response in magnetic or electrostatic fields, with the aid of flow-through microchannels. A device which constrained the flow of the test solution to many laminar streams and allowed the application of strong applied fields next to them to enable ion separations was designed and tested. The data demonstrated the following:

•

Significant concentration changes between the top and bottom stream of the microchannel device of 10–20% can be generated using magnetic and electrostatic fields;

•

Trends of ion mobility based on magnetic susceptibility and residence time in the field are observed, with individual element separations of 2–3% achieved per cycle;

•

Manipulating the effective charge in solution of metal cations by changing its pH allows them to be separated electrostatically;

•

The designed microchannel device sufficiently constricts flow to facilitate separation and minimize advective mixing.

While this method shows promise in separating both rare earths and critical metals in solution, in order for it to rise to meet the demand currently occupied by traditional methods of solvent extraction, further work to improve the efficiency of a single cycle of this process should be carried out to fully explore the potential of this hydrometallurgical separation technology.

5. Patents

This work has resulted in a patent application titled “Thin fluid layers and streams facilitated, force-based atom, ion, molecule, and fine particle separators and methods of using the same”, patent application number 18447171.