Magnetic separation technology has been a hot area of research with its advantages of low cost, low energy consumption, high efficiency, ease of use, and so on.^[1,2] In recent years, magnetic separation has made great progress and has a broad application prospect in many fields. It can be used to separate target samples mixed with magnetic nanoparticles, as the pretreatment of many analytes such as biological macromolecules, cells, antibodies, organic compounds, and so on.^[3–6] The high gradient magnetic separation technology is proved to be useful in the removal of magnetic particles and lubricant pollution in sticky oil.^[7] Magnetic separation technology can be applied to the environment when using magnetic nanoparticles as carriers to remove heavy metal ions or organic dyes in aqueous solutions.^[8–10] Besides, by studying the feasibility of removing algae in fish ponds and the separation of binary mixtures of sorbitol and sucrose, it is proved that magnetic separation also has applications in ecology and food processing.^[11,12]

In recent years, the research starts from the magnetic solid particles^[13] to the magnetic nanoparticles,^[14–18] and in the research progress, particles become smaller gradually with the improvement of research and applications. Nevertheless, few experimental studies of magnetic separation of molecules and ions under continuous flowing conditions have been reported.^[19–24] Currently, the research objects of magnetic separation are mainly superparamagnetic nanoparticles represented by Fe₃O₄. These magnetic particles usually have large magnetic susceptibility and size, which makes the magnetic force large enough under the gradient magnetic field of thousands of Gausses (G). Compared with magnetic particles, the magnetic moment of molecules and ions is much smaller (for example, the magnetic susceptibility of a ferric chloride molecule is about 12 orders of magnitude smaller than that of a Fe₃O₄ particle). Thus, the magnetic force of molecules or ions is very weak under the same conditions. Besides, molecules or ions are very different from nanoparticles, and there are many obstacles such as a variety of interactions in the separation process. It is very difficult to achieve the magnetic separation of molecules and ions by common methods.

The separation of molecules or ions is needed in many potential applications with the development of science and technology. In the rectification column, for example, magnetic separation technology can be used as an assistant for the separation of liquid oxygen and liquid nitrogen. In the applications of industry, how to improve the recovery rate and reduce the energy consumption of the rectification column has been a common concern. As the temperature and pressure of the rectification column are difficult to control, complete separation is impossible. The residual liquid flowing from the bottom of the rectification column often leads to a waste of energy. However, the target liquid in the residual liquid can be further separated and enriched by using magnetic separation technology. When putting the residual liquid into the rectification column for cyclic utilization, the recovery rate will be improved. Correspondingly, the waste of energy is avoided. Moreover, flow behavior is always the key point in the research of magnetic separation technology. Therefore, it is a challenging and important scientific issue to research the magnetic separation of molecules and ions.

In this work, the ferric chloride (FeCl₃) solution was used to study the possibility of magnetic separation at the ionic level in a homogeneous mixed solution. FeCl₃ molecules are paramagnetic, and the magnetic susceptibility^[25] is χ_m = 13450 × 10⁻⁶ cm³ · mol⁻¹. FeCl₃ molecules mainly exist in the form of Fe³⁺, Cl⁻, and hydrated ions like [Fe(H₂O)₆]³⁺ in an aqueous solution.^[26] The magnetic susceptibility of molecules or ions is much smaller than that of magnetic nanoparticles, thus the magnetic force is very weak in a normal strength gradient magnetic field. Besides, many hindering factors such as diffusion exist in the separation, and the movement and diffusion of ions are greatly influenced by the flow state. Therefore, it is hard to confirm whether the magnetic separation of FeCl₃ solution can be achieved. In this research, a magnetic field device with large magnetic field gradient and a “layered” flow channel that can easily achieve laminar flow were designed to study the possibility of the magnetic separation of FeCl₃ solution. This study also built a segregation model to discuss the segregation behavior as well as the factors that may affect the magnetic separation, which could provide theoretical and experimental basis for magnetic separation at the molecular and ionic level in homogeneous mixed solution.

The concentrations in the two outlets when the flow channel is located in area I and area II respectively are shown in Fig. 3. The initial concentrations of FeCl₃ solutions are about 13% and the flow rate is 2 ml/min (the flow velocity is about 0.67 mm/s). When the channel is located in area II where the magnetic field gradient is larger on the side of outlet 2, the concentrations in outlet 1 are less than that in outlet 2. When the channel is located in area I where the magnetic field gradient is larger on the side of outlet 1, the concentrations in outlet 1 are greater than that in outlet 2. It can be seen that the concentration is greater in the area with larger magnetic field gradient, which indicates that the direction of the movement and enrichment of Fe(III) ions is consistent with that of the magnetic force. The results of the concentrations in the two outlets are just the opposite when the flow channel is located in area I and area II, respectively. However, the concentration difference is almost the same. The opposite results of concentration and the same concentration difference indicate that the action of the Lorentz force can be ignored, the magnetic force is the major driving force in the magnetic separation of FeCl₃ solution.

Fig. 3.

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	Fig. 3. The concentrations in the two outlets when the flow channel is located in different areas, with the initial concentration of the solution of (a) 12.6% and (b) 13.2%.

The results of the concentration difference between the two outlets versus different flow velocity when the flow channel is located in area I are shown in Fig. 4, where the mass fraction of FeCl₃ solution is respectively 15%, 17%, 20%. It can be found that the concentration difference between the two outlets increases first and then decreases with the increase of the flow velocity. The concentration difference is the result of Fe(III) ions’ movement and enrichment to the area with larger magnetic field gradient under the effect of the magnetic force, as shown in Fig. 5. The flow channel can be divided into two equal parts, area 1 and area 2. Assume that the number of Fe(III) ions in each of the two equal areas at the initial state is N₀, and the number of Fe(III) ions which can be enriched in the solution is N. Then N₀ + N and N₀ − N is respectively the number of Fe(III) ions in area 1 and area 2 at the steady state. Assuming that t₀ is the time which is needed for achieving the maximum enrichment (when Fe(III) ions move from one side to another side of the channel, t₀ is maximum), t₀ does not change with the flow velocity because there is no transverse flow in the solution and the magnetic force of the Fe(III) ions is independent of the flow velocity. Thus, there is a critical flow velocity v₀. When v ≤ v₀, all the Fe(III) ions that can be enriched will move and accumulate in area 1, and in this case N = N_max is unchanged. When the flow velocity is greater than v₀, there is not enough time for some Fe(III) ions to move to area 1. Therefore, N will be decreased with the increase in the flow velocity.

Fig. 4.

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	Fig. 4. The separation effect with different inlet flow velocities. (a) 15%, (b) 17%, (c) 20%.

Fig. 5.

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	Fig. 5. Segregation of Fe(III) ions in the flow channel. Fe(III) ions move from area 2 to area 1 under the effect of magnetic force. There is a critical flow velocity v0. When v ≤ v0, all the Fe(III) ions that can be enriched will move and accumulate in area 1. When v > v0, the number of segregated Fe(III) ions will decrease.

The enrichment of Fe(III) ions leads to the increase of the chemical potential. The chemical potential can be expressed^[31] as , which is the change of Gibbs free energy when the change of the amount of components is 1 mol. Since each of the components in the solution is Fe(III) ions, the chemical potential can be written as

The magnetic field gradient is far greater at the exit position than that in the channel because of the sudden disappearance of the magnetic field at the exit of the channel. The Fe(III) ions are intercepted by greater magnetic force at the exit position, and only a few Fe(III) ions can flow out. Therefore, a certain accumulation of Fe(III) ions is formed (accumulation area in Fig. 5), which makes the concentration distribution very different from that in the channel.

The volume of the two equal areas in the flow channel is expressed by V₀, then the concentration of Fe(III) ions in area 1 and area 2 can be expressed respectively as

According to Eq. (2), we have the following relationship between the concentration of Fe(III) ions in accumulation area and the flow velocity (detailed derivation process is shown in Appendix A):

When Fe(III) ions are accumulated in the accumulation area, the viscous resistance pointing to the outlet will have an effect. The accumulation of Fe(III) ions also leads to the change of the chemical potential, which causes Fe(III) ions to be affected by the chemical potential driving force pointing to the outlet. At the steady state, the accumulated Fe(III) ions are balanced by the intercepted magnetic force, the chemical potential driving force and the viscous resistance at the exit position

According to Eq. (9), the chemical potential driving force can be written as

According to Eq. (7), the concentration difference between the two outlets is determined by N and ΔN, which are respectively the number of Fe(III) ions that can be enriched in the solution and the number of the accumulated Fe(III) ions in the accumulation area. The change of N and ΔN versus the flow velocity is shown in Fig. 6. When v ≤ v₀, N = N_max is unchanged, and ΔN is decreased when increasing the flow velocity. Thus the concentration difference between the two outlets is increased with the increase of the flow velocity. When v ≥ v_A, N is decreased when increasing the flow velocity and ΔN = 0, thus the concentration difference decreases. When v₀ < v < v_A, there must be a flow velocity which makes the concentration difference maximum. As a consequence, the concentration difference between the two outlets increases first and then decreases with the increase of flow velocity, and there is an optimum flow velocity which makes the maximum separation.

Fig. 6.

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	Fig. 6. The change of N and ΔN versus the flow velocity.

It has been shown that the flow velocity v_A which makes ΔN = 0 is constant, and the change of ΔN with the flow velocity v is determined by the constants F and λ. Therefore, the optimum flow velocity which makes the maximum separation be dependent on the critical flow velocity v₀, according to Fig. 6.

The optimum flow velocity of 15%, 17%, and 20% FeCl₃ solution are shown in Fig. 7. It can be found that the optimum flow velocity is increased with the increase of the initial concentration of the solution. When the initial concentration of the solution is increased, the initial number of Fe(III) ions increases. Correspondingly, there are more Fe(III) ions surrounding the enrichment area. These Fe(III) ions always have greater magnetic force compared with the Fe(III) ions farther away from the enrichment area. Therefore, the Fe(III) ions surrounding the enrichment area will move and accumulate to the enrichment area faster. However, N_max, the maximum number of Fe(III) ions that can be enriched is unchanged. As a result, the enrichment area can reach saturation more quickly. It indicates that when increasing the initial concentration of the solution, the time which is needed for achieving the maximum enrichment, t₀, is decreased. Correspondingly, the critical flow velocity v₀, which can achieve the maximum enrichment in the channel, is increased.

Fig. 7.

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	Fig. 7. The optimum flow velocity of different concentration of the solution.

It has been shown that the optimum flow velocity is dependent on the critical flow velocity v₀. When increasing the initial concentration of the solution, v₀ is increased. Therefore, the optimum flow velocity is also increased.

The magnetic separation of magnetic ions has been achieved by the magnetic field device with larger magnetic field and gradient as well as the flow channel that can easily achieve laminar flow. The magnetic force is the major driving force, which plays an indispensable role, leading to the segregation of magnetic ions. The maximum number of the segregated ions is determined by the joint action of the chemical potential and magnetic force. The flow velocity also has an effect on the segregation behavior. When the flow velocity increases to a certain degree, the number of the segregated ions in the channel will start to reduce. As a consequence of the interception at the exit position of the channel, segregated ions accumulate. The number of the accumulated ions will be decreased when the flow velocity increases. As a result, the separation effect increases first and then decreases with the increase of the flow velocity. There is an optimum flow velocity which makes maximum separation. In this experiment, the optimum flow velocity is related to the initial concentration of solution, the higher the concentration, the larger the optimum flow velocity.

This study has some guiding significance for the magnetic separation of liquid oxygen and liquid nitrogen. It indicates that magnetic force plays a decisive role in the maximum separation effect when the flow velocity is optimum. Improving the performance of the magnetic device, such as using superconducting magnets, can greatly improve the magnetic force. Therefore, the separation effect will be improved to a certain extent. When using magnetic separation technology as an assistant for the separation of liquid oxygen and liquid nitrogen in the rectification column, the liquid oxygen in the residual liquid will be enriched greatly. As a consequence, the recovery rate will be improved when putting the residual liquid into the rectification column for cyclic utilization. Correspondingly, the energy is also saved. Besides, the equipment of magnetic separation technology is reusable, and no more energy consumption exists. Therefore, magnetic separation technology has great potential application in the separation of liquid oxygen and liquid nitrogen in the rectification column.