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The introduction of functionalized magnetizable particles for the purification of enzymes or for the multi-use of pre-immobilized biocatalysts offers a great potential for time and cost savings in biotechnological process design. The selective separation of the magnetizable particles is performed for example by a high-gradient magnetic separator. In this study FEM and CFD simulations of the magnetic field and the fluid flow field within a filter chamber of a magnetic separator were carried out, to find an optimal separator design. The motion of virtual magnetizable particles was calculated with a one-way coupled Lagrangian approach in order to test many geometric and parametric variations in reduced time. It was found that a flow homogenisator smoothed the fluid flow, so that the linear velocity became nearly equal over the cross section in the direction of flow. Furthermore the retention of magnetizable particles increases with a high total edge length within the filter matrix.

The use of functionalized magnetizable particles in combination with a high-gradient magnetic separator is an efficient way to perform a solid/solid/liquid separation in one step. Functionalized magnetizable particles with a diameter in the nano- or micron-range for various applications are described in some publications [

Within the total number of publications regarding the usage of magnetizable particles and magnetic separation in bioengineering, only a little fraction is focused on the design of the separator itself. The reason for this could be that the separation in bench-scale was very simple and practicable with a permanent magnet. Normally, when the separation takes place in milliliters, either the magnet or the suspension container is removed manually for resuspension of the magnetic particle deposits. But when magnetic separation is conducted for several liters, a magnetic filter is required. The fluid is pumped through a filter chamber in which a matrix insert of highly magnetizable stainless steel is placed [

Until now the magnetic yoke of the separator was not varied and analyzed for optimization. The air gap of the magnetic yoke can be varied with different steel pole plates, which decrease the distance of the pole surfaces to each other. Herewith the separator could be modified for the process requirements. In this study the distance and the surface area of the pole plates were varied to determine the effect of different geometries on the magnetic flux density in the middle of the air gap.

The magnetizable matrix inserts in the filter chamber were mainly made of stainless steel wool. Hereby the rinsing of the filter chamber was not efficient and the optimization of the filter matrix was the focus of some studies [

Therefore, in this study the optimization of a high-gradient magnetic separator was performed using Finite Element Method (FEM) and Computational Fluid Dynamic (CFD) simulations. On this basis, trajectories of virtual magnetizable particles were calculated to quantify the effects of the geometric variations. The use of a flow homogenisator was tested to quantify the distribution of the linear fluid velocity and the particle distribution on a cross-section near the filter matrix in the filter chamber. The retention of magnetizable particles on filter matrices with different geometries was tested to find the optimal cutouts in the filter plates.

Previous studies on the behavior of magnetizable particles in a magnetic field and a fluid flow field were based on different approaches. A simple and easy to compute approach is the Lagrangian one-way coupled simulation. Hereby the magnetic field and the fluid flow field are calculated at first and the Newtonian particle motion is calculated on the basis of the two previous fields. The particles do influence neither the fluid flow field nor the magnetic field [

The geometries constructed in this study were made with the Computer Aided Design (CAD) software NX^{TM}8 from Siemens AG in a 1:1 scale. In

Between the filter plates of the filter matrix a highly inhomogeneous magnetic field with magnetic flux density gradients at the corners of the matrix filaments is generated. The filter is constructed for a placement of quartz sight glasses. Herewith optical checks can be performed during filtrations. In

The CAD models were imported in a step 214 format into the simulation software Comsol Multiphysics^{®} 4.3a. Within the simulation software the fluid flow with particles and the magnetic field were calculated. The magnetic field and the fluid flow were calculated stationary. The particle motion was calculated time dependent. Hereby water was used as the fluid with standard properties at room temperature. The magnetic flux densities were measured at the magnetic pole surfaces and then used for an input of the magnetic field simulation. In the following the equations are shown which are used by the software Comsol Multiphysics^{®} 4.3a. For further reading a look at the user’s guide of Comsol Multiphysics^{®} 4.2a is advised. The Interface “Magnetic Fields, No Currents” in the software Comsol uses the equations 1 to 4 for modeling of magnetostatics in the absence of electric currents, with µ_{0} = vacuum permeability, µ_{R} = relative permeability, V_{m} = magnetic potential, H = magnetic field, B = magnetic flux density and n = surface normal.

Furthermore at the boundaries with an inward magnetic flux density B_{n} the Equation (3) was set.

On the rest of the boundaries magnetic shielding was set with the Equation (4).

For the fluid field simulation the Navier-Stokes equations were used. The continuity equation (see Equation (5)) describes the conservation of mass for the incompressible fluid. Equation (6) represents the momentum conservation of the laminar simulation. Hereby ρ = density, u = linear velocity, p = pressure, ν = dynamic viscosity, F = Force, U_{0} = average linear inlet velocity, I = unit vector and T is used as an indicator for matrix transposition. For the turbulent simulation of the fluid flow, the equations of the k-ε-model described in Shaikh et al. [

At the boundaries the velocity was zero for the laminar simulation. The inlet boundary condition is represented by Equation (7).

The time dependent motion of the virtual particles is described by Equations (8) to (10), whereby m_{P} = mass of the particle, v = linear particle velocity, F_{D} = drag force, F_{M} = magnetic force and M = specific saturation magnetization.

It was assumed that the calculated amount of particles at the filter outlet, which is only accurate for low particle concentrations, provides information on the performance of the magnetic filter. When more and more particles attach to these primary deposits during the filtration, a filter clogging arises and CFD/Discrete Element Method modeling is required to describe the process. This approach was previously studied by Lindner et al. [

The experiments for the evaluation of the simulation results were carried out with a high-gradient magnetic separation laboratory plant which consists of a magnetic separator, a pump and a flow meter. The devices are controlled by a process control system realized with National Instruments^{®} LabView^{™} 8. The peristaltic pump of the type Ismatec^{®} MCP from the company IDEX Health & Science GmbH is equipped with a pumphead type Easy-Load 2 from the company Masterflex^{®} SE, whereby the pump tubing is C-Flex with an inner diameter of 4.8 mm. The tubing of the pilot plant is realized with polyurethane tubes with an inner diameter of 6 mm and quick connectors made of polyoxymethylene from the company Riegler & Co. KG. The high-gradient magnetic separator type HGF10 from the company Steinert Elektromagnetbau GmbH is equipped with N42 permanent magnets, which can be rotated by an electrical motor. Hereby the magnetic field within the magnetic yoke can be switched on and off [

The polyvinyl alcohol based magnetizable particles (M-PVA magnetic beads) used in this study, were produced by PerkinElmer chemagen Technologie GmbH with a polydispersed diameter distribution ranging from <1 µm to 10 µm. The particles consisted of equal proportions of magnetite and polyvinyl alcohol and had a dry density of 2 kg∙dm^{−3}. The particle concentration in the filtrate was measured at the outlet of the magnetic filter with an UV/VIS spectrometer Ultrospec 2100 pro from the company GE Healthcare equipped with a flow through cell. The measurement is explained in detail in Shaikh et al. [

For the manufacturing of flow homogenisator prototypes, 3D-printing was used with the printer types Objet Eden260VS (material VeroClear-RGD810 for flow homogenisator 1 - 4) and Mojo (material ABSplus for flow homogenisator 5) from the company Stratasys^{©} Ltd.

For the optimization of the magnetic field between the magnetic pole surfaces, the flux density was measured and simulated. By connecting north- and south-pole plates (stainless steel AISI 430) tightly to the yoke, the air gap volume was decreased and the magnetic flux density could be increased (see

In

The force acting on a magnetic particle is dependent inter alia on the gradient of the magnetic flux density. It can be seen that the curves in ^{3}] within the volume was calculated for a 3 µm magnetic particle with a wet density of 1200 kg∙m^{−3} and a magnetization of 40 A∙m^{2}∙kg^{−1}. This value was divided by the value of the volume around the matrix. Hereby the average magnetic force in the filter volume was calculated as a scalar value. When the matrix was placed in the yoke B this force was 0.12265 nN and for yoke C it was 0.12881 nN respectively. With the modified pole plate the average magnetic force could be increased by 5%.

In a simulation with a varied magnetic pole plate thickness of type B, it was found that the magnetic flux density in the center of the air gap rose exponentially with a decreasing distance. The distance of the pole surfaces was varied from s = 5 mm to 40 mm. Equation (11) calculates the magnetic flux density B with the distance s in millimeters (with R² = 0.95).

For the magnetic pole plates of type C with a distance of 26 mm, the tapering was varied in another simulation with a final surface ranging from 10 mm by 10 mm to 70 mm by 90 mm. The calculation revealed that for this case no significant changes of the magnetic flux density occur in the center of the air gap. In summary the distance of the pole surfaces to each other has the greatest impact on the maximum of the magnetic flux density in the air gap. But the magnetic flux density gradients at the edges of the surfaces represent the areas with the magnetic force maxima. In this context the reduction of the pole surface area increase the magnetic force within the filter chamber.

The inlet of the magnetic filter was constructed in one piece with a flange connection to the filter chamber (see

identical to the inlet. The transition area from circular to rectangular could be produced with a maximum length of 20 mm in Z-direction, due to the milling cutter diameter of 8 mm. Herewith the linear fluid velocity is highly inhomogeneous at the start of the filter matrix. The fluid has a high linear velocity in the center of the cross section. At the boundary areas the velocity is low. This means that the particles have a higher velocity in the areas where the magnetic force is the lowest and vice versa in the front part of the filter matrix. So the deposits of the magnetic particles build up inhomogeneously.

In order to obtain information on how the velocity maximum changes with a varying milling depth, a set of fluid flow simulations were carried out. The length of the transition part was varied from 10 mm over 20 mm to 30 mm, while the volume flow was set to 100 mL∙min^{−1}. The maximum linear fluid velocities at the end of the inlet were 59 mm∙s^{−1}, 48 mm∙s^{−1} and 43 mm∙s^{−1} respectively. When the volume flow was adjusted to 400 mL∙min^{-1} the maximum flow velocities and slopes were nearly 4-fold greater. The fluid flow profile has a parabolic shape at the center of the cross section. So a solution for the inlet problem could be an increased inlet length. But due to the limitations in manufacturing and otherwise rising costs, this was not further pursued. Additionally, an enlarged inlet would increase the mean residence time of the particles, which was also not favored. In order to homogenize the velocity profile of the fluid flow the installation of a flow homogenisator was regarded as a better solution due to the compact geometry and simple manufacturability. The flow homogenisator length in Z-direction was adjusted to 24 mm. Within this piece of rectangular channel, crossbars with a length of 26 mm in X-direction were placed, so that the fluid was divided into the direction to the magnetic pole surfaces (see

In a first laminar simulation the amount of crossbars was varied in Y- and Z-direction. In Y-direction the amount of crossbars was adjusted up to 5 (with a thickness of 1.5 mm) and in Z-direction up to 6. In X-direction the length of the crossbars was 26 mm, which was identical to the filter chamber length in X-direction. The height of each crossbar in Z-direction was calculated by the ratio between the sum of crossbar heights and the length of the flow homogenisator (24 mm). Hereby quotient values of 0.25, 0.5 and 0.75 were adjusted. The ratio calculation was carried out with Equation (12). Hereby r = ratio, d_{A} = distance between crossbars in Z-direction, d_{C} = length of crossbars in Z-direction. d_{C} and d_{A} are identical when the ratio is adjusted to r = 0.5. d_{C} has a higher value than d_{A} in case of r = 0.75 and vice versa in the case of r = 0.25.

The first prototype of the geometry was manufactured via 3D-printing with 5 horizontal and 6 vertical crossbars with a ratio of 0.5 (see

In ^{−1} on two crossbred X- and Y-cut lines. These lines are running through the center of the rectangular filter channel. For a clear presentation the pictured results were limited to the following combinations: h = 2 and 6 (amount of horizontal crossbars), v = 2, 4 and 6 (amount of vertical crossbars), r = 0.25, 0.5 and 0.75 (ratio of crossbar height). The abscissa in

Magnetic filtrations with threefold repetition were carried out with the manufactured flow homogenisator to check its effect. A dense magnetic particle suspension with a concentration of 5 g∙L^{−1} was filtrated with a volume flow of 100 mL∙min^{−1} by an exemplary matrix of eight stacked filter plates. In

inlet mass on the abscissa. Furthermore the standard deviation for each data point is plotted as a gray colored error bar. The filtration with the flow homogenisator shows the desired more evenly development. In the range from 3.5 g to 4 g cumulative particle inlet mass the filtration without the flow homogenisator is clearly worse than with a flow homogenisator. In both cases a filter breakthrough could be measured, but in case of a flow homogenisator the breakthrough appeared after 4.3 g of particle input rather than 3.5 g. It was assumed the filter clogging was built up more evenly by using a flow homogenisator. Herewith the amount of re-released particle fractions from the filter clogging was lower than in case without a flow homogenisator. So the experiments confirm the simulated results.

In a further simulation study supplemental flow homogenisator geometries were simulated in terms of the particle retention. The variation was focused on the crossbar constellation. The crossbars were aligned in two patterns: 1) behind and 2) shifted to each other (see

introduced to analyze the flow velocity without crossbars.

The turbulent volume flow of water was adjusted to 400 mL∙min^{-1}_{.}Within this simulation 10,000 virtual magnetizable particles were used with a uniformly distributed diameter from 0.2 µm to 10.2 µm. The magnetization was adjusted to 40 A∙m^{2}∙kg^{−1} and the release of the particle was located at the inlet of the filter. After a simulation time frame of 60 s the amount of particles at the outlet was counted and used for the ratio calculation between the amounts of particles flowing in and out.

An experimental setup, which was very similar to the simulation conditions, was used to measure the filtrate particle mass in real filtrations. Therefore 1 mL of a particle suspension with a concentration of 20 g∙L^{−1} was injected with a syringe into the tubing at the inlet of the magnetic filter, while the feed pump was out of action. The particles used for the experiments had a median diameter of 5.4 µm but a significantly lower amount of small size particles (with a diameter smaller than 2 µm) in comparison to the particle size distribution in the simulation. After injection the pump was started with a volume flow of 400 mL∙min^{−1}. To ensure a complete particle run-through with an expected mean residence time of 20 s, the pumping was applied for 240 s. At the outlet of the filter chamber the concentration of particles was measured according to Shaikh et al. [

It can be seen that the amount of particles in the filtrate is significantly higher in the simulation than in real filtrations. During high-gradient magnetic separation the impact of the drag force on smaller particles is greater than the impact of the magnetic force. This means that smaller particles could pass the magnetic filter easier. Consequently the median particle diameter of the particles in the experiment, which passed the magnetic filter, was below 3.56 µm in all cases (in comparison to 5.4 µm in the feed). Therefore the difference between calculations and experiments can be explained with the different particle size distributions. But the simulations as well

as the experiments pointed out that the flow homogenisator types 3 and 4 had the best performance in particle retention.

Interestingly, the highest amount of particles at the outlet of the filter was measured in the experiment with the flow homogenisator type 5 (see

After finding an optimum geometry of the flow homogenisator crossbars, the research was continued with an analysis of the particle retention on filter matrices with cutouts. By cutting out pattern in the filter plates, the magnetic flux density field becomes strongly inhomogeneous and at the corners of the cutouts the magnetic force maxima build up.

The time dependent simulation of particle retention on a filter matrix, consisting of 8 stacked filter plates with a thickness of 0.75 mm, a X by Z dimension of 26 mm by 80 mm and a relative permeability of 1000 was performed with a laminar volume flow of 200 mL∙min^{−1}. The amount of virtual magnetizable particles was adjusted to 1000 particles with a wet density of 1200 kg∙m^{−3}. The particle diameter was uniformly distributed between 0.2 µm and 10.2 µm. After a simulation time frame of 45 s the amount of particles at the outlet was counted. Furthermore the motion of non-magnetizable particles, which could retain on the matrix due to hindrance, was also simulated and used for the ratio calculation.

The plates of the filter matrix inserted into the center of the filter chamber had different plate patterns. The design of the cutouts was matched to result in a constant plate volume of 870 mm^{3}. For reference a plate without cutouts and a plate volume of 1440 mm^{3} was used. In

The total edge length of all corners of a filter plate could be identified as the major parameter, which affects the particle retention. The total edge lengths of the filter plates (widthwise: 2582 mm, circular: 1924 mm, square: 2084 mm, lengthwise: 2589 mm, without: 416 mm) are in good accordance to the simulated retention performances of the filter plates.

The analysis of the median particle diameter at the outlet of the magnetic filter showed that the magnetizable particles had different d_{50} values (widthwise: 0.89 µm, circular: 6.21 µm, square: 5.96 µm, lengthwise: 0.69 µm, without: 5.56 µm). In all simulations the non-magnetizable particles at the outlet of the magnetic filter had the same median particle diameter of 5.4 µm. In case of the simulation of width- and lengthwise cutouts only very small magnetizable particles flow through the magnetic filter in comparison to the median particle diameter of the ingoing particles (d_{50} = 5.2 µm). This shows again the good retention performance of those two geometries.

For an experimental testing of the filter matrix geometry, filtrations with filter matrices of 8 stacked filter plates, each with either widthwise or square cutouts, were carried out. The suspension had a particle concentration of 5 g∙L^{−1} and the volume flow was adjusted to 100 mL∙min^{−1}. In

concentration (including gray colored error bars) in the filtrate is plotted along with the time dependent cumulative particle inlet mass.

After a total inlet of 2 g magnetizable particles the particle concentration in the filtrate begins to rise significantly in case of square cutouts. At this point the retention within the filter begins to decrease. The use of widthwise cutouts results in a constant retention up to 3 g of magnetizable particles, which represents a retention improvement of 50%.

Computational methods to study the effects of geometric variations of magnetic filters have a great potential to reduce time and costs. The one-way coupled Langrangian approach represents a simple way to calculate the particle motion within the magnetic field and the fluid flow field. The geometry of the filter matrix should have as much as possible total edge length to maximize the particle retention.

It could be shown that the inlet profile of the fluid flow had an impact on the retention of magnetizable particles in the filter matrix as well. The linear fluid velocity should be homogenous at the start of the filter matrix, otherwise the particle deposits are built up irregularly on the filter plates. In this case, the concentration of particles in the filtrate rises faster while the magnetic filtration takes place. This means that the retention within the filter decreases with an increasing velocity distribution at the inlet cross section. When a flow homogenisator is installed prior to the filter matrix, the particle retention can be improved and stays constant over a longer filtration time.

The authors acknowledge financial support received from the German Federal Ministry of Education and Research (BMBF) (Project reference No: 0316057B). Furthermore the authors thank Jonas Wohlgemuth, Karlsruhe Institute of Technology, Institute of Functional Interfaces for the 3D-printing of the flow homogenisator prototypes.

Yonas S. Shaikh,Christian Seibert,Percy Kampeis, (2016) Study on Optimizing High-Gradient Magnetic Separation—Part 1: Improvement of Magnetic Particle Retention Based on CFD Simulations. World Journal of Condensed Matter Physics,06,123-136. doi: 10.4236/wjcmp.2016.62016