Development of spiral square coils for magnetic labelling detection in microfluidic systems

ABSTRACT


INTRODUCTION
Microelectromechanical systems (MEMS) are miniaturized devices that integrate electrical and mechanical components at a micronic or submicronics scale.They can include sensors, actuators, and electronic conditioner, withing the same components, and are able performing a wide range of functions such as sensing, actuation, and manipulation of biological cells or tissues in biomedical-microelectromechanical systems (Bio-MEMS) applications.The development of the microfluidic systems components is associated with the microtechnology based on silicon materials.They were developed after the discovery of deep etching and bonding methods [1], [2], which allow to realize microchannels in silicon [3], [4], glass [5], [6], polymer material polydimethylsiloxane (PDMS) [7], [8] and SU-8 [9].
The superparamagnetic particles are tiny magnetic particles (form of microbeads), they exhibit unique magnetic properties, are used by lab-on-chip [10]- [12], for applications in biotechnology, pharmaceuticals, medicine and industry.This type of device was born thirty years ago and is now experiencing tremendous development, through miniaturization of biosensors [13], [14].Their micronic and nano size and their  ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 13, No. 6, December 2023: 6037-6046 6038 manipulation by a magnetic field make them highly required for analysis and diagnosis in biology and medicine [15]- [17].
In the medical field, microbeads can be used to target cells to separate or mark them [18].Several applications use different ways of transporting the microbeads [19] under the effect of the magnetic field created by a magnet [20] or an electromagnet [21].The latter allows us to better control the magnetic flux density and to build an integrated microsystem [22], [23] as shown in Figure 1.The aim is to model and simulate a magnetic flux density using the COMSOL Multiphysics software to study the magnetic flux density generated by different square spiral microcoil structures and to study the effects of geometrical and electrical parameters on the behavior of the magnetic flux density.
In general, when using micro-electromagnets for especially magnetic labelling, suffers from many problems, such as coils size and Joule effect heating which are major concerns.Despite these thermal issues, the thermal design of microcoils is scarcely studied.We propose in this paper a new approach in designing microcoil with developed by adding a ferromagnetic core of a nickel-iron material (NiFe) to the inner center for order to increase the magnetic flux density and avoid the effect of the temperature by avoiding increasing the value of the electric current.
This paper is organized into five sections as follows.Section 2 presents the utilization of microbeads for the magnetic labelling detection; it includes the way of manufacturing microbeads for the sake of magnetic labelling functions and so to separate the targeted cells in microfluidic systems.In section 3, we descript the way of designing the microcoil with a demonstration of the different geometrical features, such as the width of the mains input of the injected current, the number of turns, the copper wire section and inter-wire space and the ferromagnetic core.After the designing process by COMSOL Multiphysics software, we made a suitable condition for simulating the magnetic flux density by including the mathematical equations of the microcoil which has been presented in section 4. Finally, section 5 presents the obtained values of the magnetic flux density from the microcoils of different geometrical shapes, along with a discussion of these results.Figure 1.Simple structure of procedural sequences for tagged cell by magnetic bead in the microfluidic system

MICROBEADS FOR THE MAGNETIC LABELLING DETECTION
The magnetic labelling detection offers a powerful and versatile tool for sensitive and rapid detection of analysis in various biological and environmental samples.For instance, its usage can extend to every part of the body (blood, saliva, or urine) and are also used by more invasive diagnostic methods (tissue samples) to allow the early diagnosis of disease [24], [25], one of these methods is to use of magnetic beads in the bodily fluids.Protocols involving magnetic microbeads in conventional biological laboratories for capturing proteins, enzymes, ribonucleic acid (RNA) and deoxyribonucleic acid (DNA) are widely used.It is very important to use microbeads in the process of separation in any diagnostic body fluid or target those cells for biomarking (the monocytes in the blood for example), as shown in many works [26], [27], because these magnetic beads are flexible due to the ability of modifying the surface chemistry and the straightforward capturing method by a permanent magnet configuration [28].This is done in three basic steps.In the first step, in the mixing zone, the antigen of the cells to be targeted is implanted on the surface of the magnetic microbeads and the magnetic microbeads are put into solution to target these cells.Then, in the second step, the target (antigen) contained in the sample is recognized by the probe and adsorbs specifically on the surface of the microbeads (monocyte biomarkers) [29].Finally, in the separation zone, the magnetic microbeads and labeled monocytes are trapped by a magnetic field generated by permanent magnets [30] or a specially designed microelectromagnet [31].In the case of permanent magnets, it is possible to structure the magnets in the form of lines and it is also possible to use in the microelectromagnet the microcoils integrated in microfluidic systems [32] with vertical or horizontal separation [33].

MODELING OF PLANER SPIRAL SQUARE COILS
Since the magnetic flux density is an essential element in this microfluidic application, and as we are interested in microcoils of squared spiral type, it is important to do predictive calculations concerned with this application.Thus, our purpose is to study the influence of different parameters (number of turns "N", width of the mains input of the injected current "d", copper wire section "S", inter-wire space "a", width of the wire being "r" and the thickness of the wire is "e") on the distribution of the magnetic flux density by using the help of the finite element method (FEM) numerical by COMSOL Multiphysics software in order to evaluate device behavior and to optimize its design.The geometry of the studied model shown in Figure 2 consists of a microcoil of square spiral type with the following geometrical characteristics.

METHOD OF CALCULATION
The application of the magnetic flux density B generated by the coils is based on Maxwell's laws, as shown in (1): This law states that the total magnetic flux through a closed surface is zero.The relationship between the magnetic field H and current density  is given in expression (2): The Biot-Savart law defines the magnetic field H generated at some point in space by a current I, passing in a wire of finite length dl: where r is the distance from that point to the finite straight wire, u is the displacement vector from the element dl to the point.The relationship between the magnetic field H and the magnetic flux density B is given by ( 4): with µ 0 = 4π x 10 −7 H.m -1 is the permeability of vacuum and µ  is the relative permeability.

RESULTS AND DISCUSSION
Our first study consists in optimizing of the magnetic flux density for different geometries and then evaluating the magnetic flux density of a selected coil at different heights (h) and electrical parameters (I).The geometries of the models consist of the square spiral type microcoils; their geometric characteristics are shown in Figure 3, which allows us to study the effects of different shapes and dimensions of every coil on the value of the magnetic flux density.To study the impact of the width of the turns on injected current "d", we used the coil in Figure 3

Effect of design on the magnetic flux density
In this paper, we will discuss the effect of the width of the main input of the injected current and the effect of the number of turns by comparing the magnetic flux density resulting from the coils.Moreover, we will study the effect of the copper wire section and the inter-wire space effect through the values obtained from simulating the magnetic flux density.Finally, we will also examine the effect of the ferromagnetic core on the magnetic flux density value.

Effect of the width of the turns on injected current "d"
The geometrical shape of the microcoil has a crucial effect of the magnetic flux density.For this, we will study the influence of the width of the injected current, we modeled and simulated the magnetic flux density B by two microcoils shown in Figures 3(a After modeling and simulating the magnetic flux density  by two microcoils with different injected current widths, we obtained the maximum magnetic flux density results presented in Table 1.We specifically chose heights of 5 and 50 μm above the microcoil to indicate the respective thicknesses of the channel containing the microfluidics and the microbeads.We note that the variation of the width of the electrical input d results in a weak and negligible increase in the value of the magnetic flux density   and   .

Effect of the number of turns "N"
We then study the effect of another factor in the coil's geometric shape on the magnetic flux density values, namely the number of turns.To do this, two microcoils are optimized with the same geometrical and electrical characteristics, but with a different number of turns for each coil, with  = 3 and  = 5.In this case, Figure 5 shows the obtained values of the magnetic flux density components   and   , the current is fixed at 100 mA at different heights from 5 to 50 µm above the microcoil.The maximum values of the magnetic flux density components   and   are reported in Table 2.
The number of turns in the microcoil significantly effects of the magnetic flux density.We notice that increase in the number of turns, improves the values of the magnetic flux density components   and   .Thus, when the number of turns increases from 3 to 5, we observe an increase of 1.2 times for the "X" component (3.31 to 3.97 mT), and 1.4 times for the "Z" component (4.49 to 6.36 mT).

Effect of the copper wire section "S"
Varying the dimensions of the coil cross section has a strong effect on the magnetic flux density of the microcoils.Figure 6 represents the results obtained for the two values of section of the coil (10×5) µm 2 and (5×5) µm 2 .The current is fixed at 100 mA at different heights from 5 to 50 µm above the microcoil.
The values of the magnetic flux density components   and   increase with the decrease of the conductor width from 10 to 5 µm.This is due to the current density which is twice as high between these two structures.A current density of 2 × 10 9 A/m 2 is injected in the 10 µm wide segment versus 4 × 10 9 A/m 2 in the 5 µm wide segment.The values are reported in Table 3.

Effect of the inter-wire space "a"
To investigate the effect of the inter-wire space on the magnetic flux density, we have taken into account two special square microcoils of 5 turns made of copper wire section (10×10 µm) and inter-wire space of 5 and 10 µm as shown in Figures 3(g) and 3(h).The variations of the   ,   components at different heights above the microcoil will be shown in Figure 7.The maximum values of magnetic flux density components   ,   are presented in Table 4.
This simulation has allowed us to recognize the importance of the inter-wire spaces to determining the value of the magnetic flux density.We notice the values of the magnetic flux density components   ,   increase weakly for the inter-wire space of the microcoil from 10 to 5µm.Indeed, when the inter-wire space decreases from 10 to 5 µm, the impact of the magnetic flux density component Bx increases by about 1.25 times, and that of the magnetic flux density component   by about 1.10 times.

Effect of the ferromagnetic core
The geometrical shape of the microcoil is an important factor in enhancing the magnetic flux density.However, the values of the magnetic flux density may not be sufficient for labelling and separating the cells in microfluidic systems.To address this, we can enhance the coils by incorporating a ferromagnetic core.The comparison between the magnetic flux density variations of the two microcoils is shown in Figure 8.A simulation using COMSOL software was conducted to study the influence of the ferromagnetic core located in the middle of the microcoil center represented in Figure 8(a).The ferromagnetic core is a cube-shaped nickeliron (NiFe) material with a thickness of 20 µm.This microcoil has the same geometrical and electrical properties as the microcoil without core in Figure 8(b).The current is fixed at 100 mA at different heights from 5 to 50 µm above the microcoil.The maximum values of magnetic flux density components   ,   are presented in Table 5.The magnetic flux density values obtained in Table 5 confirm that the incorporation of a ferromagnetic core in the center of the microcoil plays a crucial role to obtain an efficient magnetic flux density.We notice that the addition of the ferromagnetic core allowed the increase of the value of the magnetic flux density for   , and for   .In fact, the impact of the magnetic flux density   increases around 1.07 times, and the component of the   increases around 1.45 times.On the other hand, we notice that in Figure 8, the shape of the magnetic flux density is not modified.

CONCLUSION
In this paper, we have investigated the effects of different geometrical properties of spiral square microcoils type on the induced magnetic flux density.This study allows us to give a preview of the geometric characteristics of the coil that must be manufactured to have an effective magnetic flux density on the level of the microchannel systems for magnetic labeling's sake and for separating targeted cells.We have also studied the effects of current input and ferromagnetic materials.The calculations have been carried out with the help of COMSOL Multiphysics software.
We have noted that changing the width of the mains input of the injected current gives just a small, non-considerable variation in the value of the magnetic flux density.We noted that an increase in the number of turns, leads to a significant increase in the components of the magnetic flux density   and   .When we vary the copper wire section, the values of the magnetic flux density remain approximately constant for different sizes when the height is higher (50 µm), but for a low height (5 µm), the magnetic flux density maxima are greater for lower size.The influence of the inter-wires space seems also to be insignificant for great height (50 µm), but not for low heights (5 µm) for which, the components of the magnetic flux density increase with decreasing the inter-spacing turns between each conductor line.We have proposed a new technique for designing and optimizing of the microcoil with introduction of a ferromagnetic core of a nickel-iron (NiFe) material that leads to a significant increase of the magnetic flux density.This new approach in designing of microcoil is considered the best to obtain a fast trapping of the microbeads and highly sensitive detection of biological elements and to avoid the effect of temperature in microfluidic systems.

Int
Development of spiral square coils for magnetic labelling detection in microfluidic … (Abdelhadi Feddag) 6039

Figure 2 .
Figure 2. Tridimensional representation of a square spiral microcoil with different parameters

Figure 4 .
Figure 4. Variation of the magnetic flux density for the two microcoils along of the microcoil with a 5 µm and 40 µm width of the injected current, the current is fixed at 100 mA

Figure 5 .
Figure 5. Variation of the magnetic flux density for two microcoils in the 3 and 5 turns with the different heights above the coil, the current is fixed at 100 mA

Figure 8 .
Figure 8. Variation of the magnetic flux density component   ,   , for two microcoil, (a) variation of the magnetic flux density by micro coil with ferromagnetic core and (b) variation of the magnetic flux density by microcoil without core, the current is fixed at 100 mA

Table 4 .
The maximum values of magnetic flux density components   ,   with different in the inter-wire space, the injected current  = 100 mA

Table 5 .
The maximum value of magnetic flux density component   and   for two microcoils with ferromagnetic core in the first coil, the current is fixed at 100 mA