Design and experimental investigation of a novel spiral microfluidic chip to separate wide size range of micro-particles aimed at cell separation

Graphical abstract Isolation of microparticles and biological cells on microfluidic chips has received considerable attention due to their applications in numerous areas such as medical and engineering fields. Microparticles separation is of great importance in bioassays due to the need for smaller sample and device size and lower manufacturing costs. In this study, we first explain the concepts of separation and microfluidic science along with their applications in the medical sciences, and then, a conceptual design of a novel inertial microfluidic system is proposed and analyzed. The PDMS spiral microfluidic device was fabricated, and its effects on the separation of particles with sizes similar to biological particles were experimentally analyzed. This separation technique can be used to separate cancer cells from the normal ones in the blood samples. These components required for testing were selected, assembled, and finally, a very affordable microfluidic kit was provided. Different experiments were designed, and the results were analyzed using appropriate software and methods. Separator system tests with polydisperse hollow glass particles (diameter 2–20 µm), and monodisperse Polystyrene particles (diameter 5 & 15 µm), and the results exhibit an acceptable chip performance with 86% of efficiency for both monodisperse particles and polydisperse particles. The microchannel collects particles with an average diameter of 15.8, 9.4, and 5.9 μm at the proposed reservoirs. This chip can be integrated into a more extensive point-of-care diagnostic system to test blood samples.


Introduction
Isolation of bio-components is of particular importance for identifying and studying bio-particles for detection, improvement, or treatment of diseases and the improvement of health status. Separation of Biological elements can also have a specific role in the sampling process, studying the impact of treatment, medical diagnosis, and the desired tests. Separation of microparticles can be used for study and research in cases such as biosample preparation steps in the molecular analysis, including chemical and biological analyses such as food and chemical processing and also environmental assessment automotive and electronics industries. [1][2][3] Moreover, the separation of biological elements is also used at different stages of understanding diseases, treatment processes, and medications. Blood cell separation, and applications such as preparation of biological samples are just some of the applications of particle separation in the medical field. [4][5][6][7] Isolation of circulating tumor cells (CTCs) from blood samples is one of the most critical applications of bio-particle isolation. CTCs are cancer cells circulating in the bloodshed from primary tumors and flow through the bloodstream to other parts of the body. Moreover, CTCs isolation and analysis are also essential for investigation of cancer and required to monitor post-treatment in many types of cancer therapy. [8][9][10] Nowadays, with the advancement of microfluidics science, the number of studies on the isolation of bioparticles on microfluidic chips has increased, this will result in a comprehensive examination of the common diseases in the world in the medical and engineering fields. Due to the weaknesses of conventional methods, there has been a profound interest in using techniques that take advantage of microscale technologies and the inherent properties of cells for improved mechanization and reduced cost. 11,12 Microfluidic talks about the science that arranges with the behavior, precise control, and manipulation of fluids and particles in the scale of 10-100 mm. With the appropriate length scale that matches the scales of cells, microfluidics is well suited to contribute significantly to cell biology. This scale provides an interface for manipulating single cells and accessing these forces in various ways, including for kinetic, equilibrium, and elution separation. They will also possibly reduce sample volume and cost and are potentially portable. 13 Therefore, as an essential step in many biological and medical analysis, the need for efficient cell separation has led to the recent development of numerous microfluidics separation techniques.
The application of microfluidics-based technologies for cell separation offering numerous advantages, including reduced sample volumes; reduced sample preparation procedures and leading to faster sample processing and reducing analysis time; high sensitivity and spatial resolution; increasing detection accuracy; reducing odds of sample contamination; The potential for the designs that are sufficiently compact for integration into point-of-care systems for clinical diagnostics, and the potential to be highly integrated and automated to reduce human intervention and errors as well as device errors. [14][15][16][17][18] Therefore, efficient microscopic separation methods can provide greater control over cell size distribution, increasing the importance of the realization of many on-chip laboratory systems.
Mechanical and physical properties, including size, shape, density, adhesion, and deformability, are common markers for differentiation. In microfluidic separation science, separation methods are classified as active, passive, and combined methods. The active separation methods use external forces to exert force. Magnetic, dielectrophoresis, and acoustophoresis separation techniques are examples of active methods that separate particles by applying external force. 17,19,20 In the passive separation method, in contrast to the active methods, external force fields are not used, and therefore, using properties such as channel geometry and inherent hydrodynamic forces is significant. In passive methods, techniques such as inertia, pinch flow fraction, deterministic lateral displacement, filtration, etc. are used for separation. 17,[21][22][23] Depending on how it works, the basis of passive separation is either the difference in particle size or density.
Moreover, since passive isolation techniques do not use external force, these techniques are simpler to use in comparison to the active techniques, and by using passive techniques for separation, cell viability will significantly decrease. In microfluidics, passive cell separation techniques have been extensively studied. This is due to the fact that these techniques utilize simple channel geometries and pressurized flows to achieve and enhance separation. There has always been a trade-off between separation efficiency and operating power, 24 and this has led the researchers to the combined methods. In the combined separation method, active and passive separation methods simultaneously improve separation and sorting performance.
Due to the simplicity of passive separators and since it causes less damage to cells in this method, the development of inertial separation techniques, one of the passive methods, has been the focus of recent years.
Inertial microfluidic techniques work in the intermediate Reynolds number range (;1 \ Re \ ;100) between Stokes and turbulent regimes. In this intermediate range, both inertia and fluid viscosity are finite and bring about several intriguing effects that form the basis of inertial microfluidics. On the other hand, according to Reynolds number of flow, inertial microfluidic systems are expected to critically impact highthroughput separation applications in fluids processing such as particle separation. The inertial displacement was first expressed by Segre´and Silberberg 25 in the 1960s. This migration behavior takes advantage of hydrodynamic forces that act on particles, localize them within the flow caused by the balance of lift forces arising from the parabolic velocity profile (the shear-induced inertial lift), and the interaction between particles and the channel wall (the wall-induced lift). 24 In recent years, extensive researches have been done on inertial separation technique, and inertial devices can be divided into three general categories: straight channels, straight channels with pillar arrays or multi orifice structures, and spiral channels. 14 Creating a secondary flow by channel curvature or orifice structure will help improve inertial migration and alter the final equilibrium positions. Due to this reason, the design and use of curved microchannels have received considerable attention. Recently, many investigations have been done on curved microchannels in the fields of different geometries, different cross-sections, and different applications for separating particles of diverse diameter with appropriate separation rates and efficiency. 26,27 It has also been used in some cases to increase the separation and efficiency rates of multi-channel systems in series or parallel with each other. 28,29 However, passive microfluidics methods have an inherent limitation, in which it is difficult to separate cells of the same size and researchers have to adopt a sorting strategy which leads to a trade-off either sacrificing purity for high recovery rate or sacrificing recovery for high purity. [30][31][32][33] Therefore, in the present work, we designed an integrated system for microparticle separation to overcome the limitations of the inertial method, using a combination of inertial and magnetic techniques by considering dominant factors of separation microchannels. Since fewer studies have been done on separating polydisperse particles, we have used the designed spiral microchannel as an inertial separator to isolate both monodisperse and polydisperse particles with sizes range correspond to the biological cells. The experiment of particles with variable dimensional distribution is essential because biological cells have a size distribution similar to polydisperses particles compared with single size ones. The spiral channels can be produced at a meager cost and with a high resolution utilizing PDMS casting; they can also be operated using a double syringe pump, facilitating automation.

Physics and equations
In order to design a separation system, it is necessary to examine the physics of the problem and the forces involved in the flow. As mentioned, passive separation methods sort particles only on the basis of their mechanical properties, such as size and shape, using their micro-channel or flow geometries and inherent hydrodynamic forces. Passive techniques were also the basis of the first attempts to Miniaturize segregation, as researchers logically tried first to produce principles on a smaller scale that were well known and valid on a large scale. The forces acting on the particles in the channels, including the shear lift force and the wall effect, occur according to the ratio of particle to channel dimensions, which is also observed in macro dimensions. Therefore, a micro-sized channel should be used to separate the microparticles. Because the shear gradient of a microscale stream is approximately one order of magnitude larger than that of a macro-scale flow, particles can migrate rapidly in a small Re stream. 34,35 It can also be said that in microchannels, the surfaceto-volume ratio is higher than in macrochannels, and the forces associated with wall effects are amplified, so wall effects are more effective in fluid flow and particle motion.

Inertia isolation
The inertial separation technique utilizes the lift force to balance the particles in distinct transverse positions at the microchannel cross-section, which owes to different transverse positions due to particle size ratio to microchannel dimensions. Floating particles flow in the microchannel under the influence of lift forces, migrating to different positions along with the channel range.
The key parameters in controlling the magnitude and orientation of lift forces and particle positionings, such as channel dimensions, aspect ratios, particle diameter, and flow velocity, 4,36 can be discussed with connection to the relevant equations.
For a particle, located in a direct wall-bounded Poiseuille flow, in addition to a viscous drag force along the axis (according to equation (1)), there are four lateral forces in the particle that operate: Magnus force due to slip-rotation, Safman force due to slip shear, the shear force due to disturbance in the flow field around particles from the wall, and shear gradient lift force due to the curvature of the undisturbed fluid velocity profile (Poiseuille profile). Among these four lift forces, the Magnus force and the Safman force in microfluidics problems are often minimal and negligible. 5 Thus, as shown in Figure 1, particle focusing along channel cross-section is dependent on the balance of the shear-induced lift force (arising from the parabolic velocity profile) and the wall-induced lift force (arising from interactions with channel walls), based on their size relative to the microchannel dimensions, thus achieving separation. 26,37 In the case of the effect of wall-induce lift force for a particle moving near the channel wall, the interaction between the particle and the wall will stop the particle from tracking the fluid flow. Besides, the shrinkage of flow between the particle and the channel wall causes the fluid flow to accelerate to the top of the particle as more flow streamlines diverge. This creates less relative pressure than the ''sidewall'' of the particles and lifts force away from the wall (equation (2)). In the case of shear-gradient lift force, due to the parabolic velocity profile of the in-channel flow, the velocity magnitude varies on each side of the particle, resulting in a pressure difference between the upper and lower sides of the particle. Due to the pressure difference, a shear-gradient lift force is applied to the particles that drive toward the channel wall (equation (3)). 15 Where d is particle diameter, m is the viscosity of the fluid, and U is the velocity of fluid flow.
Where D h is the hydraulic diameter of the channel and f(R c , x) is the lift coefficient, which depends on the particle position within the channel (x) and the channel Reynolds number (Re c ). As a result of these two opposing lifting forces, the particles are balanced at predetermined positions around the microchannel margin. This effect is leading the particles with a size comparable to microchannel dimensions'd=h ø 0:07. The magnitude of F L is given by equation (4): where C L is the lift coefficient, which is a function of the particle position across the channel cross-section while assuming an average value of 0.5, and G is the shear rate of the fluid. The average value of G for a Poiseuille flow is assumed by G = U max =D h , where U max is the maximum fluid velocity and can be estimated as 23U F .
As depicted in Figure 1(d). The focus of particle equilibrium positions due to inertia lift depends on the symmetry of the channel. Interestingly, as the ratio of the channel dimensions becomes larger and becomes a rectangular channel in a very wide or very long channel, symmetry is followed, and mainly two equilibrium positions in the long channel are reduced.

Physics of secondary flow and application
As stated, the inertia separation technique utilizes the lift force to balance the particles in distinct lateral positions at the microchannel cross-section, which is due to the ratio of particles size to microchannel dimensions. However, the microchannel's shape can be used to apply the flow properties as inertia separators. The secondary flow on the cross-sectional plane of the channel, which William Dean first reported in 1928, 38 occurs in a curved microchannel and happens because the fluid pressure at the inner wall is slightly higher than that of the outer wall. Furthermore, as shown in Figure 2(a), in curved microchannels, the viscous drag force consists of two components: the mainstream direction due to the axial velocity difference between the fluid and the suspended particles, and the cross-section direction, due to the secondary flow induced by the channel curvature. These pressure and velocity gradient imbalance caused by Dean instability results in secondary flow defined by a non-dimensional number called the Dean number that can be calculated by equation (6): 39 where r is the fluid density, U F is the average flow velocity, m is the viscosity of the fluid, R C is the radius of curvature of the path of the channel, D h is the channel hydraulic diameter, and Re is the flow Reynolds number. Stokes' law also gives the magnitude of Dean drag force: In equation (7), U Dean is the velocity depending on the Dean number and can be calculated as follows: According to equations (6)-(8), the parameters that influence the secondary flow and, consequently, Dean force in a curved channel are Dean number, Reynolds number, and aspect ratio of the channel. 5 Subsequently, the magnitude of F D can be equal to, larger, or smaller than F L depending on the flow rate and geometry. At meager flow rates, when Re is low, all the particles occupy equilibrium positions at the center of the channel, as the Re increases, drag force caused by Dean Vortices becomes gradually stronger than the centrifugal force, and the particles tend to move inward of the channel radially. As a result, small particles move closer to the inner wall, while bigger particles remain at their original equilibrium positions. In curved channels, when inertia is of the highest importance, the faster movement of liquids near the center of the channel tends to continue externally, and in order to maintain mass, more stagnant fluid circulates inwardly near the walls. These two anti-rotation vortices create a perpendicular motion to the mainstream direction. 4 (b) Schematic of the spiral microparticle separator. The randomly dispersed particles equilibrate at different equilibrium positions along the inner wall (IW) of the spiral microchannel under the influence of F L and F D . The separation between individual particle streams is enhanced by connecting the spiral section into a diffuser section before conducting the individual streams using multiple outlet ports. 40 Consequently, larger particles are concentrated and aligned near the inner wall, while smaller particles are located near the outer wall. The inertia lift force is effective for larger particles of size comparable to the microchannel dimensions (d=h ø 0:07 the particle diameter and channel height). 41 Whereas the effect of secondary flow on smaller particles is noticeable and contributes to their concentration on the outer wall. Therefore, the device height, particle sizes, and outlet positions can be designed to match a single outlet to each stream containing target-bound beads of a single size, which can thus be separated (Figure 2(b)).

Design principles
As mentioned, using magnetic separation in addition to the inertial technique, as a combined method, will likely increase the purity of the isolated particles. Therefore, in the present chip design, it is attempted to use a combined method of magnetic separation along with inertial separation to take advantage of both active and passive methods.

Conceptual design
In magnetic separation, the sample cells are first labeled with magnetic beads by antibodies. Then, a magnetic field gradient is used to separate cells with magnetic beads. During the sorting of magnetic cells by crossing the microchannel, cells that get attached to the magnetic beads are deflected in one direction and follow the path of the magnetic lines, whereas cells that are not labeled follow the flow direction. Magnetic separation techniques is usually used to distinguish two types of target cells, and it also can be said that it depends on just one single parameter. 42 As shown in Figure 3, the fluid containing the particles enters from one side and the buffer fluid on the other, and then by magnetic field effect on the labeled particles, these particles are diverted and separated.
The magnitude of the magnetic force applied to the floating particles in the flow can be calculated by (equation (9)): 43 whereas m is the magnetic permeability, m 0 is the permeability of free space, R p is the radius of particles, and H is the amount of magnetic field.

Detailed design
The designed chip uses an inertial isolation technique for size-based separation of tumor cells and WBCs that are equal in size to CTCs from the whole blood, and then uses microfluidic magnetophoresis to isolate circulating tumor cells. It is currently composed of two separate chips, used serially (in-line). Therefore, this chip can be designed for negative enrichment, where the target cell was unlabeled, and all other cells were labeled with one or more antibodies. As the sample passed through this chip in a flow-through manner, other cells were captured. One of the advantages of negative selection is that a label is not needed for the target cell. Negative enrichment will continue to be an area of interest for CTC collection, as the unlabeled CTCs can readily be used in downstream analyses. 44 This Negative selection strategy provides tumor antigenindependent enrichment performance, and as a result, it applies to cells disseminated from virtually any tumor type. 28 In the designed separation system, as shown in Figure 4, initially, red blood cells and primary white blood cells with a size smaller than the cancer cells were separated by a spiral microchannel. Then, the desired output from the microchannel, which contains circulating Tumor cells and some white blood cells that are equal in size to CTCs, enters the second chip and is combined with magnetic beads. Given that at this stage, there are only two types of cells (circulating cancer and white blood cell), isolation can be done by negative selection. In this way, the magnetic beads are labeled on white blood cells, which enables active separation in a designed system, which is cheaper and more efficient and independent from antigens and can be used for a variety of circulating cancer cells. Each chip has a different manufacturing procedure, and these two chips can be considered separately. In the present work, we will perform the relevant experiments for the first chip.
As mentioned earlier, in a curved or spiral microchannel, the curved geometry gives rise to the dean force. The particles are guided by the secondary flow and the effect of the dean force, from the upper and lower walls to the inner and outer walls (in the transverse section). Thus, in the spiral microchannel with the rectangular cross-section, resulting in a possible balance of force for focusing, the identical particles become in a single position. 45 Regarding the irregular cross-sections, such as the microchannels with the trapezoidal crosssection, due to the secondary flow intensification, can be suitable for separating particles according to their size. 46,47 However, these channels are suitable for separating just two kinds of particles with different size. 48 Furthermore, size-based enrichment techniques are often unable to recover smaller CTCs. 28,41 Therefore, in the designed microchannel, a rectangular cross-section is considered to take advantage of the desired effects of geometry on the microchannel crosssection. To avoid entrainment of particles in the dean vortices, the microchannel dimension should be d/ D h \ 0.07. 42 Therefore, the larger side of the rectangular section of the microchannel (microchannel width) is 500 mm, and the smaller side of the microchannel crosssection (microchannel depth) is considered 130 mm in order to influence the particles better. For construction considerations, the depth of all microchannel sections is 130 mm. The particles are randomly distributed at the inlet and move through the loops, moving toward the equilibrium position in the spiral channel, 49 thus in the passive separation part of the system, To ensure that the particles reach the desired equilibrium position, the spiral microchannel consists of four loops. The number of loops in spiral microchannels can be variable, with less pressure drop in the microchannels with fewer loops, but in more loops, higher flow rates can be used for the sample fluid. 50 The first loop is 2 cm in diameter, and the distance between the spirals is 500 mm. In the microchannel manifold, two inlet plugs are provided for the sample fluid and buffer fluid, with a width of 250 mm, which will create an angle of 90°between the two plugs. In the microchannel output section, a 500-mm microchannel width is pre-outputted to an 800-mm transverse section to achieve better separation using layer flow profiles at the outlet that open to five outputs of equal width at the termination it ends. Besides, the opening at the microchannel termination reduces the velocity near the output that can allow better imaging of the particles. Due to the manufacturing constraints in the microchannel dimension, to allow more accessible construction of the microchannel, the distance of both consecutive outputs is assumed to be 40 mm, and the width of each output is 128 mm.
The magnetic part of the separation system, which is a direct microchannel, is considered to be consists of two inputs and two outputs. The cross-section of the magnetic section is a rectangle measuring 280 mm and 130 mm with a depth of 130 mm. The length of the direct microchannel is 20 mm. At the magnetic section inlet, the fluid containing the particles will be taken from the output of the first section of the system, the symmetric geometry of the buffer fluid entering the microchannel. Within 1 mm of the direct microchannel, the permanent magnet is positioned, causing the magnetic field to deviate the labeled particles with magnetic beads, and then, the separated particles will exit the two different outlets.

Experimental methods
Due to the progress in manufacturing micro/nanofluidic devices by lithographic methods, 51 to produce the microchip, the soft lithography method was used and the fabrication process was as follows: The microchannel was fabricated in polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning), using soft lithography techniques. A mixture of PDMS prepolymer and its curing agent (Sylgard 184; Dow Corning, MI) in the ratio of 10:1 was poured on the SU8 2100 (with 2000 RPM) photoresist molds and cured for pre-bake: 5 min at T = 65°C and 30 min at T = 95°C; post bake: 5 min at 65°C and 12 min at 95°C; hard bake: 2 min at 150°C. Following curing on a hotplate for 2 h at 80°C. Irreversible bonding was made between a PDMS replica and a glass slide, treating both with an oxygen plasma (1.2-2 mbar, 180 W, 2 min). Then both PDMS and glass slide was put together and heated at 90°C for 15 min on a hot plate. The dimensions and angles of the microchannels can be determined by Dinocapture2.0 software from the microscope manufacturer ( Figure 5). Figure 6, the experimental setup consists of several parts, the most important of which are: syringe pump: to move the fluid with the desired flow rate, designed microfluidic chip: its performance is examined, reservoirs: to collect fluid from different outlets, microscope: to imaging fluids collected in reservoirs, and computers and software: to analyze and examine microscopic images.

As shown in
To perform experiments, after preparing the different parts of the system, first to observe possible leaks from the joints and also to eliminate air bubbles that are formed inside the microchannels, a fluid stream without particles such as pure water is introduced into the microchip. Then, by examining all the areas of the microchip under a microscope, the remaining bubbles inside the channels should be removed by manual pumping. In the next step, the syringe containing the desired suspension is placed inside the syringe pump and the syringe pump is set to the desired flow rate obtained from the range calculated in the microchip design. It takes a few minutes for the flow to reach a steady state in all areas of the microchip and the  suspension to come out of the microchip output. The fluid flow inside the microchannel can then be imaged. All the above steps are repeated for different experiments so that the optimal flow rate for particle separation can be obtained using the analysis of the results.
For imaging and image analysis, the Dino-lite Microscope was used to image the reservoirs embedded in the various microchip outputs, and the recorded images were analyzed using ImageJ1.52a software, powerful software for microscopic image analysis. This software can calculate the distance, cross-section, location, and number of particles, which is why it is used to analyse microscopic images.
In Diverse experiments, different monodisperse and polydisperse particles which are soluble in pure water are used. Monodisperse particles with diameters of 5 and 15.6 mm are made of polystyrene and manufactured by BS-Partikel. Polydisperse particles with diameters of 2-20 mm and an average diameter of 10 mm are made of Hallow-glass manufactured by Dantec. In order to prevent the effect of the particles on the flow of fluid and other particles, the permitted concentration of the particulate samples should be such that the interaction of the particles in the prepared suspension is minimized. In order to provide a homogeneous suspension with appropriate concentration of the particles, consider the particles in the suspension as shown in Figure 7.
Assuming that the particles have the same size and spacing, the geometrical location of the particles in the fluid is assumed to be the prisms of the triangle whose sides are equal to L. The particle spacing should be higher than the permissible distance from the simulation studies to avoid interactions between the particles. 52 The volume of each prism is: Since each particle has four prisms in common and each prism has four vertices, the volume of the constituent of the mixture can be subdivided into prisms. To calculate the numerical concentration of the particles, we have: Where N is the total number of particles, and n is the numerical concentration (number per volume unit). The minimum dimensionless distance must be greater than 10 for the particle to be independent. Therefore, the concentration of the dimensionless dimension can be calculated: 52 Where x is the dimensionless distance for the particles, and it is equal to: x = L=D. Then, the results of these calculations determine the allowable concentration of particles in the sample fluid containing the particles to avoid the effects of hydrodynamic coupling. In order to ensure one-way coupling between particles and fluid flow, x is considered to be 15 in tests, and for this purpose, the suspensions are diluted with pure water.

Results and discussion
As mentioned, the fabricated devices consist of a fourloop spiral microchannel with two inlets and five similarly spaced outlets. The spiral designs have an initial diameter of curvature of 2 cm, with spacing between the successive spiral loops fixed at 500 mm. The microchannel's width was fixed at 500 mm, and the microchannel height is 130 mm. There are two inputs at the beginning, one for the fluid containing particles and the other for the buffer fluid, which is used as a sheath flow to focus on small particles. At the outlet, the 500 mm width channel is opened into an 800 mm wide section to increase the spacing between particle streams before splitting into five 128 mm width outlets. In polydisperse particle experiments, the average particle diameter at each output was calculated by the Image-J software after completing the process. This can show how effective the designed microchip separation is in an experiment where we have a wide range of particles with different dimensions and demonstrates the ability to separate. Given that the cells in the blood, RBCs, WBCs, and CTCs are not all the same size, and  with good approximation, they can be considered as polydisperse particles, these tests can confirm the effectiveness of the system. In the monodisperse particle test, the particles are less dispersed, and particles of the same diameter can be easily distinguished from other particles. In order to evaluate the separation efficiency of monodisperse particles, the number of desired particles in the desired outlets was counted and divided by the number of all types of particles in all outlets so that the separation efficiency for the desired particles can be expressed as a percentage.
In this work, we take advantage of differences in particle sizes so that with the difference in the ratio of F L and F D in the spiral channel to separate monodisperse and polydisperse microparticles. In the first test, polydisperse HGS particles of 2 to 20 mm diameter with an average diameter of 10 mm were used. The sheath flow rate is 900 mL/min, and the flow rate of Particle Suspension is 300 mL/min. Figure 8 and Table 1 give details of the results of this test. By imaging the reservoirs embedded in the outputs, it can be derived that for large particles, the lift force ongoing to dominate over the Dean force, and obviously, the particles would be focused on the inner wall of the channel. As a result, larger particles in size have been gathered in the first outlet. On the other hand, it is evident from Figure  8(c) and Table1 that in the spiral microchannel, for small particles, Dean drag forces are always dominated over the lift forces, which means that these particles are likely to enter the Dean's vortex and circulate along the fluid stream. Accordingly, smaller particles in size are focused closer to the centerline of the microchannel and will exit from the third output.
For further studies, similarly, polydisperse HGS particles of 2-20 mm diameter with an average diameter of 10 mm were used, the flow rate of Sheath flow is 1200 mL/min, and the flow rate of Particle Suspension is 300 mL/min. As shown in Figure 9(a), it is clear that also in this test, larger particles in size have been collected in the first outlet. Table 2 shows the results of   In the third outlet, the average diameter of output Particles is equal to 5.9 mm, which indicates that Particles of different sizes are collected from the desired outlets. As shown in Experiments 1 and 2, this microchip can separate polydisperse particles with an average diameter of 2-20 mm with good accuracy in dimensions similar to the dimensions of biological cells. Tables 1  and 2 show the average diameter of the particles released from each output, which shows that the average diameter of the particles released in the desired output is approximately equal to the average diameter of the bioparticles, and therefore it can be claimed that this system is for separating bioparticles. It will be efficient.
For further analysis, microparticle separation with the spiral microchannel, monodisperse polystyrene particles of diameter 5 and 15.6 mm were tested, and separation efficiency of microchannel was described. Separation efficiency is defined as the number of one type of particles collected at a specific outlet versus the total number of the same type of particles collected at all the outlets. Separation efficiency can show the efficiency of a particular type of particles from a whole sample. The flow rate of Sheath flow is 900 mL/min, and the flow rate of flow containing particles is 300 mL/ min. By imaging the reservoirs embedded in the outputs, as demonstrated in Figure 10, it is observed that particles larger in size have gathered in the first outlet, and smaller particles will exit from the third output.
Moreover, considering that different types of particles will exit from the different outputs in this experiment, the separation efficiency for this state is shown in Figure 11, which illustrates that 15.6 mm particle separation efficiency would be about 86% and 5 mm particles separation efficiency would be about 72%.
To further analyze, the impact of the sheath buffer flow rate on separation efficiency is investigated. Monodisperse polystyrene particles of diameter 5 and 15.6 mm were tested when the flow rate of Sheath flow is 1200 mL/min, and the flow rate of particle suspension is 300 mL/min. By imaging the reservoirs embedded in the outputs, separation of microparticles is demonstrated in Figure 12, and consequently, Figure 13    shows the amount of separation efficiency. It can be said that the effect of Dean forces has made the separation efficiency of 5 mm particles go up. The separation efficiency for this state is shown in Figure 13, which illustrates 15.6 mm particle separation efficiency would be about 84%, and 5 mm particle separation efficiency would be near 80%.
As can be seen in Experiments 3 and 4, for monodisperse particles, particles of the same size and scattering of small diameter changes in the outputs can be clearly observed and easily separated. Therefore, the number of particles with similar dimensions in each output can be counted by the software and the separation percentage can be calculated by dividing the number of one type of particle in the desired output by the total number of that type of particle in all outputs. It can be seen that microchip can provide more than 80% efficiency.
It is important to mention this point below, that experiments show that with increasing shear stress, cell viability and cell proliferation decrease, so increasing shear stress has a direct effect on reducing cell viability. 53,54 Therefore, since high shear rates could affect cell viability, simulation of laminar flow is performed on the numerical study of fluid shear rate when the flow rate of sheath flow is 1200 mL/min. As shown in Figure 14, the magnitude of shear rate is less than 2310 4 (1=s) along almost all the microchannel, so it could be said the amount of shear rate is in a safe area. 54

Conclusions
We report an inexpensive microfluidic separator with an easy interface based on inertial focusing. We did various experiments with monodisperse and polydisperse particles to show that the designed microchip has acceptable performance for microparticle separation. For polydisperse HGs particles, at optimal flow conditions, the microchannel collects particles with an average diameter of 15.8, 9.4, and 5.9 mm at the Intended output. For monodisperse polystyrene particles, the spiral chip achieved an overall separation efficiency of 86% for 15.6 mm particles and about 80% for 5 mm particles. As can be seen, this microchip can separate polydisperse particles with an average diameter of 2-20 mm with good precision in dimensions similar to the dimensions of biological cells. Also, the separation results for monodisperse particles are quite acceptable. With these outstanding separation performances, this low-cost and user-friendly setup could be used for various microparticle separation applications such as cell separation in biological assays.

Author's contributions
All the authors have done all the steps together.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.

Consent for publication
All authors agreed to submit this study.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.