1

COMPUTATIONAL FLUID DYNAMICS (CFD) SIMULATIONS APPLIED

TO THE DESIGN OF PASSIVE MIXING MICROFLUIDIC SYSTEMS

by

SERGIO LEONARDO FLOREZ GONZALEZ

A thesis submitted to the Universidad de

los Andes in partial

fulfilment for the degree of

Master in Electronic Engineering

Supervised by Dr. Johann F. Osma and Dr. Juan Carlos Cruz

School of Engineering

Department of Electrical and Electronic Engineering

2020

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Abstract

Computational Fluid Dynamics CFD simulations of microfluidics and microsystems allow

to rapidly design and test the performance of multiple prototypes by identifying the

variables that impact the most the efficiency of the device for a particular task. This work

aimed at implementing multiphysics simulations for helping to prototype two different

microfluidic systems for passive mixing. First, a low-cost microsystem for the synthesis of

magnetite nanoparticles via chemical co-precipitation. Second, a toroidal microreactor to

conduct the continuous enzyme-based degradation of dyes in wastewater using magnetic

nanoparticles. The simulations show different changes in velocity profiles, shear rate, and

homogeneous mixing in each device tested. These variations in the behavior of the fluid can

improve the formation of nanoparticles by controlling their growth. Likewise, the torus

microsystem, with the implementation of a permanent magnetic field, increases the

retention time of the nanoparticles in the device, increasing the interaction and treatment of

the wastewater. The use of computational tools allows to quickly and economically

determine the impact of changes in the geometrical configuration of the systems on their

overall performance.

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Contents

1. Introduction .............................................................................................................................. 4

2. Materials and Methods ............................................................................................................ 5

2.1. Tutorial videos of Comsol Multiphysics simulations for microsystems .................. 5

2.2. Micromixer synthesis of magnetite nanoparticles: geometry design and

simulation ...................................................................................................................................... 6

2.3. Torus microreactor: geometry design and simulation ................................................ 8

3. Results and Discussion .......................................................................................................... 10

3.1. Tutorials videos .............................................................................................................. 10

3.2. Micromixer synthesis of magnetite nanoparticles ..................................................... 10

3.3. Torus Microreactor ......................................................................................................... 14

4. Conclusions ............................................................................................................................. 17

5. Acknowledgement ................................................................................................................. 18

6. Annexes ................................................................................................................................... 18

6.1. Comsol Introduction. ..................................................................................................... 18

6.2. Interface. .......................................................................................................................... 18

6.3. Pos-processing. ............................................................................................................... 18

6.4. CFD modeling focusing on microfluidics. .................................................................. 18

6.5. Mass transfer model focusing on microfluidics. ........................................................ 18

6.6. Heat transfer model focusing on microfluidics. ........................................................ 18

6.7. Supplementary information.......................................................................................... 18

7. References ................................................................................................................................ 18

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1. Introduction

Since the 1980s, with the advances in microelectromechanical systems (MEMS), the field of

microfluidics has had an exponential growth due to the development of easier and cheaper

ways of manufacturing at the microscale [1]. Today, this research field has reached an

important level of maturity and has been implemented by different industries including

food, pharmaceutical and biomedical [2]–[5]. One of the most attractive features of these

devices is that they can carry out chemical processes with low reagent consumption due to

their small sample volumes [1]. There are different device configurations to perform several

types of analysis and functions including sampling, preparation of the sample, analysis and

processing of the collected data. These systems are known as miniaturized Total Analysis

Systems, and an important number of them have been incorporated into in vitro testing

schemes of biological systems (µTAS) [1][6]. Moreover, an emerging trend is to assemble

microsystems capable of mimicking the performance of organs at the physiological level,

which are known as organs on a chip [7]. All these devices facilitate the processing of

samples, thereby reducing costs and processing times, which is very attractive for different

applications such as disease diagnosis [8], manipulation of materials at the micro- and nano-

scales [9][10], and the generation of complex and multifunctional nanocompounds and

encapsulates [11][12], among many others.

To design and test microsystems before their final manufacture, there are several in silico

tools including rapid and economic prototyping [13][14], hydraulic circuit analyses [15][16]

and Computational Fluid Dynamics (CFD) [17]–[22]. CFD simulations of the microsystems

allow to rapidly design and test the performance of multiple prototypes by identifying the

variables that impact the most the efficiency and overall performance of the device for a

particular task [17][19][20]. CFD simulations require to discretize the computational

domain, which can be done through several methods including Finite Difference Method

(FDM), Finite Volume Method (FVM) and Finite Element Method (FEM). In the case of

FDM, discretization relies on an approximation by Taylor series expansion[23]. FVM uses

an integral approach to solve the equations and discretizes the domains into volumes where

the equations are simultaneously solved [23] Finally, the Finite Element Method (FEM),

which also uses an integral scheme but in this case the domain is discretized into elements

that form intersections or nodes where the equations are solved [23]. All these methods

allow to solve partial differential equation systems through algebraic equations [24].

Commercial software packages have facilitated the implementation of FEM methods. A

popular one is Comsol Multiphysics®, which incorporates several physics that can be

coupled to investigate rather complex situations. Some authors have conducted

multiphysics simulations to optimize the performance of the systems. These improvements

vary depending on the type of microsystem but can range from the design of the

microsystem [25][26] to the mode of operation [27] and allow the integration of governing

equations for different phenomena such as fluid mechanics, heat transfer, mass transport,

reaction kinetics, electrochemistry, etc [28]–[30]. This means that the governing equations of

different physics can be solved simultaneously, allowing the multiparametric analysis of a

myriad of variables and their relationships [31][32].

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Microsystems geometries vary depending on their function. For instance, they can be

intended for the separation of particulate matter, for drop generation or for mixing

purposes. In the case of separators, they can be tailored to handle inorganic or polymeric

microparticles, cells, or in general any micro-object by exploiting differences in size or

density [33]–[35]. The drop generators can be operated to produce homogeneous size drops

for different applications ranging from encapsulation of pharmacological compounds to

aromas or fragrances with application in cosmetics or food industries [36]–[38]. Likewise,

the micromixers allow to carry out mixtures of different components or reagents involved

in chemical reactions, blend preparation or sample preparation [39][40]. A major challenge

when working with microfluidic systems is the difficulty to generate efficient mixing

patterns mainly due to the low Reynolds numbers (Re ≈ 1). To tackle this issue, it is necessary

to generate turbulence through special geometries such as Zigzag channels, 3-D serpentine

structures, and twisted channels [41]. Micromixing can be achieved either through active

mixing or passive mixing [42][43]. In the case of active mixing, integration of components is

accomplished via an external energy source such as ultrasound, acoustic vibrations, small

impellers, or electrokinetic instability. In contrast, passive micromixing requires a device to

intimately put in contact the components through disturbances in the mixing patterns.

These devices include chaotic flow configuration, flow recirculation configuration, colliding

jet, split and recombine flow configurations [42][43].

This work aimed atimplementing multiphysics simulations for helping to prototype two

different microfluidic systems for passive mixing. This approach was explored for two

different microsystems. First, a low-cost microsystem for the synthesis of magnetite

nanoparticles via chemical co-precipitation. The main objective was to evaluate whether this

synthesis was attainable in a continuous operation mode and that the obtained material

exhibited the appropriate size distribution and nanoscale morphology. This was

accomplished by coupling the CFD, chemistry and transport of diluted species modules.

Second, toroidal microreactor to conduct the continuous enzyme-based degradation of dyes

using magnetite nanoparticles. The objective was to evaluate the interaction of the magnetite

nanoparticles with the fluid and the residence time and retention within the system. In both

cases, the performance of the microsystems was determined in terms of mixing efficiency.

This was accomplished by coupling the CFD and particle tracing modules of Comsol

Multiphysics®.

2. Materials and Methods

2.1. Tutorial videos of Comsol Multiphysics simulations for microsystems

As part of the training for future students with interest in developing research on the field

of microsystems, we prepared a series of video tutorials for implementing Multiphysics

simulations in Comsol Multiphysics®. These videos explain in detail the steps to setup a

simulation. This includes the design of the geometry using CAD tools as well as the

processing and postprocessing of collected data. The pre-processing includes the definition

of physics, implementation of boundary conditions, initial conditions, properties, meshing

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and convergence criteria and solvers. In the case of post-processing, we discussed data

visualization, types of graphics, data operations, use of boundary conditions and exporting

data. All videos focused on evaluating the performance of the microsystems via coupling

the governing equations for transport of momentum, transport of species, chemical

reactions, and transport of thermal energy.

The first module is a brief introduction to multiphysics simulations, the finite element

method, governing equations, initial conditions, boundary conditions, symmetry and mesh

convergence. The second module studies the CAD tool of Comsol, materials, physics, mesh

and solvers. The third module studies post-processing, handling of large data sets, types of

graphics and data processing. The fourth module is a worked example of a microsystem

with a serpentine mixing topology. In this case, the governing equations of momentum

transport are introduced. Additionally, a parametric study was carried out in the

simulation. In the fifth module, mass transport was studied where the mass transport

governing equations were introduced, and the concepts of diffusion and convection were

explained. Finally, the sixth module is a microsystem heating system based on the Joule

effect. In this final study case, the energy transport equations were introduced.

2.2. Micromixer synthesis of magnetite nanoparticles: geometry design and simulation

Three micromixing geometries were proposed and analyzed via Comsol Multiphysics 5.3:

a serpentine-based topology (SB), a triangular-based topology (TB), and a 3D-based

topology (3DB) that involves sudden changes in flow direction by 90° elbows, allowing

turbulent mixing patterns (See Figure 1). The depth of systems was 1 mm. All microfluidic

systems were design to handle the same volume i.e., 300 mm3.

These 3 different geometries were implemented in Comsol by coupling the computational

fluid dynamics (CFD), laminar flow, chemical reaction engineering and chemical species

transport modules. To study both fluid flow and extent of reaction during the synthesis of

the nanoparticles, we coupled the Computational Fluid Dynamics (CFD), chemistry and

transport of diluted species modules. Eq.1 describes the chemical reaction to form magnetite

by the coprecipitation method.

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Figure 1. Microfluidic mixers geometry. A) Serpentine-based mixer, B) Triangular-based mixer, C) 3D-based mixer. (1-3.

Inflow for FeCl2 and FeCl3, 2. Inflow for NaOH and 4. Outflow)

𝐹𝑒𝐶𝑙2 + 2𝐹𝑒𝐶𝑙3 + 8𝑁𝑎𝑂𝐻 → 𝐹𝑒3𝑂4 + 8𝑁𝑎𝐶𝑙 + 4𝐻2𝑂 Eq.1

Also, the mixing phenomena were studied with the aid of the laminar flow and transport

of diluted species modules. In the former, the transport of momentum equation (Eq.2) is

solved to calculate the velocity profile. . In the latter, the conservation of species

was used (Eq.3). The velocity profile calculated by solving Eq.2 is input in the convective

term of Eq.3.

𝜌[(𝑉. ∇)𝑉] = −∇𝑃 + 𝜌𝑔 + 𝜇∇2𝑉 Eq.2

Where V is the vector velocity of the fluid, P is the pressure, ρ is the density of the

fluid, g is the gravity and μ is the viscosity of the fluid

∇(−𝐷𝑖∇𝑐𝑖) + 𝑉∇𝑐𝑖 = 𝑅𝑖

Eq.3

Where Di is the diffusion constant of each species, ci is the concentration of each species and

Ri is the reaction rate for each species.

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All the simulation parameters are summarized in the Table 1. The 3 geometries were

subjected to a mesh convergence analysis to determine the minimum number of elements

necessary to obtain a stable solution . For this study, 5 random measurement points were

selected along the computational domain and the change in magnitude of speed was

evaluated as the number of mesh elements increased. As a convergence criterion, it was

determined that the velocity magnitude change obtained for a meshing level and the next

one was below 3%. An unstructured mesh with tetrahedral elements was

generated. A stationary study was run with the direct solver PARDISO that allows to

parallelize processes solving large symmetric or structurally symmetric dispersed linear

systems of equations in shared memory multiprocessors [44].

Table 1. Parameters of reaction simulations

Parameters Value Units

Density of the fluid 1000 Kg/m3

Viscosity of the fluid 1 mPa.s

Rate constant 1*10-24 m30/(s*mol10)

FeCl2 molar mass 0.199 Kg/mol

FeCl3 molar mass 0.270 Kg/mol

NaOH molar mass 0.040 Kg/mol

Fe3O4 molar mass 0.232 Kg/mol

NaCl molar mass 0.058 Kg/mol

H2O molar mass 0.018 Kg/mol

FeCl2 inflow concentration 100 mM

FeCl3 inflow concentration 200 mM

NaOH inflow concentration 800 mM

Central inlet normal inflow rate 1 ml/min

Lateral inlets normal inflow rate Outlet

0.5

1

ml/min

Atm

2.3. Torus microreactor: geometry design and simulation

Three different geometries were studied in silico via Comsol Multiphysics 5.3® for the torus

microreactor. Figure 2 shows such geometries, namely, one-loop, two-horizontal-loop, and

two-vertical-loop microreactors. Each microreactor was equipped with a cylindrical

neodymium magnet with a diameter of 5 mm and a height of 6 mm. The magnet was directly

inserted in the hole created by the loop (Figure 2). The channel width of each microreactor

is 0.5 mm while its depth is 1 mm in the sections previous to the loop. Then, in the section

where the magnet is inserted the depth increases to 2 mm. Finally, it is reduced again to a

height of 1 mm as the fluid exits the loop. This device was conceptualized by considering

its prototyping through the assembly of layers of PMMA. For each case, the Computational

Fluid Dynamics (CFD) (Eq. 4) and Magnetic Field, no current (MF) (Eq. 5-6) modules of

Comsol were coupled. To evaluate the impact of magnetic fields on the transport of the

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magnetite nanoparticles, the Particle Tracing (PT) module was implemented solely for the

one-loop microreactor.

Figure 2. Simulation geometries for the studied microreactors. A) One-loop, B) Two-horizontal-loop and C) Two-vertical-

loop. The numbers 1, 2 and 3 in the figure represent the inputs, outputs, and the neodymium magnet, respectively.

The laminar flow module (Eq. 4) was used here to describe the fluid flow due to the low

Reynolds number (Re) calculated for the microreactors (Re = 4.4). The inflow to the

microreactor was 12 mL/h while the output pressure was set to 1 atmosphere. Density and

viscosity of water were assumed as the properties of the flowing fluid. The non-slip

boundary condition was imposed at the walls of the microchannels. The boundary

conditions are summarized in Figure 3.

0 = −𝛻𝑃 + 𝜇𝛻2𝑉 Eq. 4

𝐵 = 𝜇0𝜇𝑟𝐻 Eq. 5

𝐵 = 𝜇0𝜇𝑟𝐻 + 𝐵𝑅 Eq. 6

Where ∇𝑃, is the pressure gradient in the fluid, µ is the viscosity of the fluid and 𝑉 is the

velocity of the fluid. For the equations of MF, 𝐵 is a magnetic flux density, 𝜇0 is the magnetic

permeability of the vacuum, 𝜇𝑟 is the magnetic permeability of the fluid, 𝐻 is the magnetic

field and 𝐵𝑅 is the remanent flux density of the neodymium magnet. The PT module was

used to study the dynamics of the magnetic particles within the microreactor. The particle

diameter was assumed as 1.2 µm with a density of 5180 kg/m3. The particle size was decided

according to previous experimentation and small agglomerations of NPs forming clusters.

Additionally, the magnetic permeability of the particle was set to 5000 H/m. The particles

were delivered at the main inlet of the device. The PT was solved in a time-dependent study

for 10 seconds using 0.1s steps. In this case, a projected conjugate gradient iterative solver

was chosen due to the high demand for computational resources. Also, a parametric

analysis was performed to evaluate the impact of the remanent flux density of the

neodymium magnet on the particles transport. Equations Eq.7 to Eq.10 describe the forces

experienced by a particle. This study considered the interactions between the particles and

the fluid (drag force) and the magnetic attraction between particles. Particle-particle

interactions, lifting force and Brownian motion were disregarded due to the complexity of

the model and the need for extra computational resources:

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𝐹𝐷 =1

𝜏𝑃𝑚𝑃(𝑈 − 𝑉) Eq. 7

𝜏𝑃 =𝜌𝑃𝑑𝑃

2

18𝜇 Eq. 8

𝐹𝑚𝑝 = 2𝜋𝑟𝑝3𝜇0𝜇𝑟𝑘∇𝐻2 Eq. 9

𝑘 =𝜇𝑟𝑝 − 𝜇𝑟

𝜇𝑟𝑝 + 2𝜇𝑟 Eq. 10

Where 𝐹𝐷 is the drag force, 𝑚𝑃 is the mass of the particle, 𝑈 is the velocity of the particle, V

is the fluid velocity, 𝜌𝑃 is the density of the particle and 𝑑𝑝 is the particle diameter. 𝐹𝑚𝑝 is

the magnetophoretic force, 𝑟𝑃 is the particle radius and 𝜇𝑟𝑝 is the magnetic permeability of

the particle. As described before, the meshing was subjected to a convergence analysis to

determine the minimum number of elements necessary to arrive to a meaningful solution.

Figure 3. Boundary conditions and mesh for simulation.

3. Results and Discussion

3.1. Tutorials videos

The annexes section includes 6 introductory videos to multiphysics simulations in Comsol

Multiphysics. Each presentation includes a video tutorial, the video presentation and the

example model implemented in Comsol Multiphysics 5.3®.

3.2. Micromixer synthesis of magnetite nanoparticles

Figures S1, S2 and S3 in supplementary information show the mesh convergence analysis

for SB, TB and 3DB, respectively. In the case of SB, converge was achieved with 300,000

mesh elements. For TB, this was achieved with 200,000 mesh elements while for the 3DB

400,000 were required. All simulations were performed on a computer with an AMD Ryzen

5 2100 Mhz processor, 4-core and 16 GB of RAM.

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Although all the input flows to the systems are the same, they develop different velocity

and shear rate profiles due to the differences in geometries. Figure 4 show the velocity

profile for each micromixer. The SB microsystem shows no noticeable zones of dead

volume. However, the TB and 3DB microsystems have zones of dead volumes along sharp

corners of the geometries. This could be due to low pressure areas of the microsystem where

reagents or air bubbles will begin to accumulate in the corners [45][46]. The SB and TB

microsystems achieved higher maximum velocities compared to the 3DB. Also, the TB

developed a velocity profile that resembles that of the SB system. This is due to the

sinusoidal flow pattern that we can see in Figure 4.B. Due to the generation of the dead

zones described above, the fluid tends to move to areas with less hydrodynamic resistance,

generating such flow pattern.

Figure 4. Velocity profiles for the three studied micromixers. A) Serpentine-based mixer, B) Triangular-based mixer, C)

3D-based.

Figure 5 shows a shear rate in each microsystem. The SB and TB developed shear rate values

that approached similar maximum values of about 15 s-1. In contrast, the 3DB system has

some areas with high shear rate (around 80 s-1). This is due to the smaller width of the

channels and the abrupt changes in flow direction along the path. All these phenomena

affect the formation of NPs and their growth rate [47][48]. Although there is a lack of studies

relating the formation of nanoparticles and the shear rate, some studies suggest that by

increasing the shear rate in the system the energy barrier to form crystalline structures

increases as well [48]. This suggests that the nucleation rates strongly depend on the shear

rate. At low shear rates the nucleation rate increases due to the increase in advective

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transport while at high shear rates the opposite occurs [48]. The competition between these

two processes results in an intermediate regime where a maximum nucleation rate might

be expected [48].

Figure 5. Shear rate values for the studied micromixers. A) Serpentine-based mixer, B) Triangular-based mixer, C) 3D-

based.

Figure 6 shows the concentration of NPs along the microchannels. NPs tend to accumulate

in the corners of the TB and 3D geometries. This zones match those of the previously

identified dead volumes, which can be seen in Figure 4. The TB system exhibits the highest

accumulation level of NPs in the corners, which can be attributed to inefficient mixture of

reagents. The SB system shows more efficient mixing as evidenced by the absence of dead

volumes. Finally, the 3DB system, although it has several dead volume zones, the abrupt

changes in the flow direction appears to promote a better interaction between the reacting

species. It is important to note that all 3 configurations arrive to similar concentrations of

NPs (i.e., SB= 23.22 mM, TB= 22.43 mM and 3DB= 23.18 mM). This suggests that the flow

rates, dimensions, and channel features are adequate to produce the magnetite NPs.

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Figure 6. Fe3O4 NPs concentration after the reaction for each of the studied micromixers. A) Serpentine-based mixer, B)

Triangular-based mixer, C) 3D-based mixer.

The magnetite NPs synthesis process can be studied using a thermodynamic nucleation

model [47][48]. Nucleation is the first step to obtain a new thermodynamic (solid) phase.

The classical theory of nucleation (CNT) is based on the changes of Gibbs free energy during

the reaction (Eq.11). Where ∆𝐺 is a Gibbs free energy of the cluster, 𝑟 is a radio of the cluster,

|∆𝐺𝑣| the difference in Gibbs bulk free energy per unit volume and 𝛾 the surface energy per

unit area [47]. relating the favorable binding and formation energy of the NP cluster per unit

of volume (bulk free energy) and surface energies that disfavored the stability of such cluster

[48].

∆𝐺 = −4

3𝜋𝑟3|∆𝐺𝑣| + 4𝜋𝑟2𝛾 Eq. 11

When a critical size is reached in the cluster after overcoming the energy barrier, the

assembly becomes a stable crystal and the growth process begins by aggregating more

precursors from the solution [47]. If this energy barrier is not overcame, it is most likely that

the cluster fails to form a stable crystal, and eventually disintegrates into its precursors [47].

This suggests that by increasing the shear rate during the synthesis reaction, their nucleation

process is affected, and therefore, their final size. One probable explanation for this

phenomenon is that, by increasing the energy barrier, we prevent cluster formation very

quickly, which would lead to a process of growth by inducing aggregation [48][47]. There

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are a few studies where this phenomenon has been already described, but in some of them

it has been suggested that the shear rate is directly related to the aggregation rates [48].

According to this notion, only particles that manage to overcome this energy barrier to

remain stable in the suspension.

3.3. Torus Microreactor

Figure S4 in supplementary information shows the convergence plot for a one-loop

microreactor. In this case, the system reaches convergence with 60,000 mesh elements for

the fluid domain. To preserve the convergence in the other simulation domains, the element

size was kept constant (0.18 mm).

The velocity profiles and magnetic field fluxes for the 3 proposed devices are shown in

Figure 7 and Figure 8. Dead zones of low velocities (blue color) are observable in the 3

configurations, however, the two-vertical-loop microreactor shows a larger dead zone

compared with the other 2 devices. This can be explained by the relatively important

changes in height as the fluid passes through the loops. In addition, the fluid decelerates as

a result of changes in the cross-sectional area of the microchannels.

Figure 7. Velocity profile for the three different configurations under study. A) One-loop, B) Two-horizontal-loop

and C) Two-vertical-loop.

The magnetic field flux results show a uniform distribution around the magnet for the case

of the single loop (Figure 8.A). For the two magnets arranged in a horizontal configuration

(Figure 8.B), there is no interaction between the field lines produced by the magnets. Finally,

the configuration of two-vertical-loop (Figure 8.C) showed the greatest field interaction.

Figure 8. Magnetic field flux for the three different configurations under study. A) One-loop, B) Two-horizontal-

loop and C) Two-vertical-loop.

The time evolution of the particle's transport within the one-loop microreactor was studied

under varying intensities of the applied magnetic field (i.e., 0, 50, 100, 200, 300, 350, 500, and

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1000 mT). The simulations were ran for a total time of 30 seconds with data collection at 1,

5, 15 and 25 s (See ¡Error! No se encuentra el origen de la referencia.9). For these

simulations, each particle trajectory is random and driven by the exerted drag and

magnetophoretic forces. As the particles are attracted to the magnet and due to the interplay

of involved forces in the loop, they follow a parabolic trajectory until they finally stick to

wall of the microreactor channel. For some particles, the magnetic field will not be enough

to retain them within the loop. This unique trajectories have been exploited by others for the

separation and manipulation of magnetic particles within microchannels [49][50]. In our

case, the movement is enough to perturb the laminar flow, thereby generating mixing

patterns that are useful to promote the intimate interaction of the nanoparticles with other

components present in solution. This was also evidenced by a better suspension of the

nanoparticles as the magnetic field was increased.

Total retention of the particles was achieved for the fields of 500 and 1000 mT, as the particles

remain statically attached to the walls of the microreactor. To support this result, the

particle's loss and retention ratio were analyzed by counting the particles leaving the system

through the microreactor's outlet during the 30 seconds of simulation (See Figure 1010). The

experimentally applied magnetic field by the magnet was of 349.23 mT, which is close to the

one simulated at 350 mT. In this case, the particles retention approached 96.83% while the

loss ratio was 3.17%. The actual particles loss ratio obtained experimentally was between 13

- 20%, which was closer to the results obtained in silico at 300 mT where the retention ratio

was 82.67% and the loss ratio approached 17.33%. The reduction in the actual strength of

the magnetic field can be explained by the marked difference in the medium surrounding

the fluid computationally (i.e., air) and the actual medium (i.e., PMMA walls), which

attenuates the applied magnetic field.

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Figure 9. Particle distribution in the One-Loop device at a magnetic field intensity: A) 0mT, B) 50mT, C) 100mT, D)

200mT, E) 300mT, F) 350mT, G) 500mT and H) 1000mT.

17

Figure 10. Particles (■) loss and (■) retention ratio analysis at the microreactor's outlet after 30 seconds of

simulation.

4. Conclusions

The use of multiphysics simulations is a very useful tool for rapid prototyping of

microsystems. Given the impossibility of manufacturing complex and expensive devices,

mathematical models allow experimentalists to give a prediction regarding performance

that is close to reality. This is accomplished by coupling several physics that account for the

interplay of different physical phenomena occurring simultaneously. The success of the

simulation, however, depends on the availability of physicochemical properties, numerical

method selected, mesh size and convergence, the proper definition of boundary and initial

conditions, among many others. The prepared video series accompanying this document

presents several study cases where the physical situations are properly modeled and

simulated in Comsol. The obtained results are also plotted according to the investigated

variable interactions to withdraw compelling conclusions and make sound predictions.

Here we illustrate the use of Multiphysics simulations to study the performance of several

microfluidic devices in silico prior to their prototyping. According to our studies, on the one

hand, we identified the presence of dead volumes in geometries with sharp edges, however,

the achieved shear rate values appear sufficient for the synthesis of nanoparticles with

homogeneous size distributions and morphologies. On the other hand, the torus

microreactor configuration equipped with a magnetic field source prolongs theresidence

time of the nanoparticles within the system without inducing detrimental perturbations in

the mixing patterns. This leads to a longer contact time between the nanoparticles and other

substances present in the medium. Even though the predictions might be closer to reality,

often the complexity of the real system adds extra phenomena that are not necessarily

addressed by the Multiphysics modeling. For this reason, it is always advisable to calibrate

the models with experimental data prior to the next round of prototype manufacture and

testing. Likewise, other aspects must also be considered when manufacturing the

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microsystems such as their cost, ease of manufacture and instrumenting, and manufacturing

precision required.

5. Acknowledgement

The authors would like to thank the Clean Room laboratory of the Department of Electrical

and Electronic Engineering, for access to their facilities laboratories and license of the

software is gratefully acknowledged.

6. Annexes

6.1. Comsol Introduction.

6.2. Interface.

6.3. Pos-processing.

6.4. CFD modeling focusing on microfluidics.

6.5. Mass transfer model focusing on microfluidics.

6.6. Heat transfer model focusing on microfluidics.

6.7. Supplementary information.

7. References

[1] N. Convery and N. Gadegaard, “30 years of microfluidics,” Micro and Nano Engineering,

vol. 2. Elsevier B.V., pp. 76–91, Mar. 01, 2019, doi: 10.1016/j.mne.2019.01.003.

[2] M. Tokeshi, Ed., Applications of Microfluidic Systems in Biology and Medicine, vol. 7.

Singapore: Springer Singapore, 2019.

[3] M. Aa, A. Sa, and Adali T, “Mekonen et al Microfluidics Devices Manufacturing and

Biomedical Applications,” J Biosens Bioelectron, vol. 10, p. 1, 2019, doi: 10.4172/2155-

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