3. Modeling and simulation of microdevices

The popularity of six sigma DMAIC (define, measure, analyze, improve, and control) approach has made more companies to embrace extensive modeling and simulation in order to save cost and time. In the production of chip-based disease diagnostic platforms, numerical computation is seen as an important process step as it affords the flexibility of exploring how various parameters affect device performance without the need for extensive experimental research. In cases where experimental activities are needed to improve numerical computations, the utilization of the design of experiment principles is usually a wise choice. In the design of experimental principles, ability to obtained related factors, which can be confounded optimally is a key component of the cost and time-saving strategy. Microfluidic devices for disease diagnostics can be operated using AC or DC sources. Discussion in this section will be based on DC operations. Details of AC-operated designs have been given elsewhere [11–13].

flow equations in stationary mode. The electric current module requires that the electric potential be specified in addition to electrical insulating boundaries. The spatial distribution of the electric field strength with the channel reveals that when

uniformity in field strength. This non-uniformity is usually seen using, in COMSOL Multiphysics for instance, color pallet or legend. As theory suggests, dielectrophoretic force acts only at the region with field gradient (i.e. at the constriction(s)). Suffice it to say that the solved electric current equations in iDEP systems usually

After solving the fluid and electric current equations in stationary mode to obtain the distributions of velocity, pressure and electric field within the diagnostic device, it is expedient to visually and quantitatively verify if the sorting or trapping process results in the desired output. Two approaches are possible; (1) using Fick's law of diffusion to classify the components of the mixture as unique tubes through the transport of diluted species module or (2) using a balance of viscous drag and dielectrophoretic force through particle tracking module. In the former, it is expected that the concentration gradient between the inlet and the outlet ports may cause diffusion and when the electro-osmotic flow is initiated for bulk fluid motion, convective flux also comes into play. This implies that the total particle flux can be

Ni ¼ �Di∇ci <sup>þ</sup> <sup>u</sup> <sup>þ</sup> <sup>μ</sup>EP,i <sup>þ</sup> <sup>μ</sup>DEP,i∇E<sup>2</sup> ci (8)

! is the hydrodynamic velocity vector, Di is the diffusivity of the particle,

<sup>p</sup>ε<sup>m</sup>

where dp is the particle diameter and η is the medium viscosity. In the latter, the

Microdevice fabrication has traditionally been through the lithographic and etching process. In iDEP devices constructed with polymer, a combination of lithography, etching and rapid prototyping is usually utilized. While lithography prints the patterns on the substrates (glass or silicon wafers), etching creates the grooves on those patterns and rapid prototyping transfers the substrates patterns to polymer. The lithography process starts with the printing of the patterns made in the modeling and simulation stage. Usually, the patterns assisted by laser or electron-beam (and other process steps) are printed on a transparent-opaque pair plate which could further transfer the printed patterns to a resist-coated substrate in

þ ∇:Ni ¼ Ri (9)

<sup>12</sup><sup>η</sup> <sup>f</sup> CM (10)

mpð Þ u � v which is balanced with the DEP equa-

constrictions are placed within a uniform microchannel, the effect is non-

Applications of Electrokinetics and Dielectrophoresis on Designing Chip-Based Disease…

DOI: http://dx.doi.org/10.5772/intechopen.82637

include Ohm's law, electric displacement and the charge conservation.

expressed as the sum of diffusive, EP, DEP and convective flux:

∂ci ∂t

is the electric field applied, and μEP and μEP are the EP and DEP motilities respectively. The DEP mobility is a function of CM factor and for a spherical

<sup>μ</sup>DEP <sup>¼</sup> <sup>π</sup>d<sup>2</sup>

2ρpr<sup>2</sup> p

and

where u

tion (Eq. 3).

61

particle it is expressed as:

drag force is given as; Fdrag <sup>¼</sup> <sup>9</sup><sup>η</sup>

4. Microdevice fabrication

E !

In DC models for disease diagnostics, electro-osmosis and dielectrophoresis are usually the electrokinetic mechanism that governs the transport phenomena prior to the region of electric field non-uniformity within the channel [14]. At the region of non-uniform electric field, the dielectrophoretic force is combined with these electrokinetic forces to bring about the desired particle differentiation either through trapping (pDEP) or streaming (nDEP). A smart idea, then, is to locate the exit channels close to the region immediately following the field gradient so that sorted bioparticles can be collected appropriately. Failure to do this might result in the recombination of streamlines, which tend to restore the separated cells to their ab initio states.

Models of the envisaged diagnostic devices are usually drawn to scale using any suitable software. (AutoCAD, SolidWorks, etc.). These models are then interfaced with multi-physics simulation software such as COMSOL Multiphysics, FLUENT, to explore parameter dependence and their effects of targeted outcomes. It is not uncommon to draw the models using the functionalities available in the simulation software themselves. One requirement to emphasize here is the sound knowledge of the physics governing the operations of the diagnostic device. These inexhaustible physics are discussed in this section. For insulator-based (iDEP) diagnostic devices, the physics usually involve momentum transport (Newton's Law), mass transport (Fick's Law), energy transport (Fourier's Law) and charge transport (Maxwell's Laws/Ohm's law) [15].

Momentum transport involves the transfer of momentum from one particle to another. This transfer results in the continuous change in fluid's positional space leading to the concept of fluid dynamics (hydrodynamics for liquids). Depending of the focus of any project, momentum transport can be explored in 1D, 2D or 3D. One good approximation in iDEP devices is that the complexity of 3D consideration can be avoided by using 2D analysis provided the channel's width-to-depth ratio is about 5:1. The 3D to 2D approximation is also good on the basis that turbulence is not a common occurrence in micron-sized devices. The governing equations for momentum transport are generally the Navier-Stokes and mass continuity equations [16] (Eqs. 8 and 9). Navier-Stokes equation is usually reduced to Stokes equation when the continuity equation is applied at static conditions under the assumption that the Reynolds number is very low. This makes the computer solve, numerically, for the pressure and velocity distributions within the channel. Prior to obtaining the pressure and velocity profiles, appropriation boundary conditions are utilized to completely define the system. In iDEP operations, electroosmotic wall is specified in lieu of the 'no-slip' wall condition. This is because, in electro-osmotic flow, the bulk motion of the fluid is driven by the wall effects - a phenomenon termed electro-osmotic pumping. Electro-osmotic pumping makes the use of external pumping mechanism unnecessary. The boundary mainly utilizes the electric field solution obtained from the second physics (electric current node in, for instance, COMSOL Multiphysics) which is usually solved together with the fluid

Applications of Electrokinetics and Dielectrophoresis on Designing Chip-Based Disease… DOI: http://dx.doi.org/10.5772/intechopen.82637

flow equations in stationary mode. The electric current module requires that the electric potential be specified in addition to electrical insulating boundaries. The spatial distribution of the electric field strength with the channel reveals that when constrictions are placed within a uniform microchannel, the effect is nonuniformity in field strength. This non-uniformity is usually seen using, in COMSOL Multiphysics for instance, color pallet or legend. As theory suggests, dielectrophoretic force acts only at the region with field gradient (i.e. at the constriction(s)). Suffice it to say that the solved electric current equations in iDEP systems usually include Ohm's law, electric displacement and the charge conservation.

After solving the fluid and electric current equations in stationary mode to obtain the distributions of velocity, pressure and electric field within the diagnostic device, it is expedient to visually and quantitatively verify if the sorting or trapping process results in the desired output. Two approaches are possible; (1) using Fick's law of diffusion to classify the components of the mixture as unique tubes through the transport of diluted species module or (2) using a balance of viscous drag and dielectrophoretic force through particle tracking module. In the former, it is expected that the concentration gradient between the inlet and the outlet ports may cause diffusion and when the electro-osmotic flow is initiated for bulk fluid motion, convective flux also comes into play. This implies that the total particle flux can be expressed as the sum of diffusive, EP, DEP and convective flux:

$$N\_i = -D\_i \nabla c\_i + \left(\mu + \mu\_{EP,i} + \mu\_{DEP,i} \nabla E^2\right) c\_i \tag{8}$$

and

simulation in order to save cost and time. In the production of chip-based disease diagnostic platforms, numerical computation is seen as an important process step as it affords the flexibility of exploring how various parameters affect device performance without the need for extensive experimental research. In cases where experimental activities are needed to improve numerical computations, the utilization of the design of experiment principles is usually a wise choice. In the design of experimental principles, ability to obtained related factors, which can be confounded optimally is a key component of the cost and time-saving strategy. Microfluidic devices for disease diagnostics can be operated using AC or DC sources. Discussion in this section will be based on DC operations. Details of AC-operated designs have

In DC models for disease diagnostics, electro-osmosis and dielectrophoresis are usually the electrokinetic mechanism that governs the transport phenomena prior to the region of electric field non-uniformity within the channel [14]. At the region of non-uniform electric field, the dielectrophoretic force is combined with these electrokinetic forces to bring about the desired particle differentiation either through trapping (pDEP) or streaming (nDEP). A smart idea, then, is to locate the exit channels close to the region immediately following the field gradient so that sorted bioparticles can be collected appropriately. Failure to do this might result in the recombination of streamlines, which tend to restore the separated cells to their

Models of the envisaged diagnostic devices are usually drawn to scale using any suitable software. (AutoCAD, SolidWorks, etc.). These models are then interfaced with multi-physics simulation software such as COMSOL Multiphysics, FLUENT, to explore parameter dependence and their effects of targeted outcomes. It is not uncommon to draw the models using the functionalities available in the simulation software themselves. One requirement to emphasize here is the sound knowledge of the physics governing the operations of the diagnostic device. These inexhaustible physics are discussed in this section. For insulator-based (iDEP) diagnostic devices, the physics usually involve momentum transport (Newton's Law), mass transport (Fick's Law), energy transport (Fourier's Law) and charge transport (Maxwell's

Momentum transport involves the transfer of momentum from one particle to another. This transfer results in the continuous change in fluid's positional space leading to the concept of fluid dynamics (hydrodynamics for liquids). Depending of the focus of any project, momentum transport can be explored in 1D, 2D or 3D. One good approximation in iDEP devices is that the complexity of 3D consideration can be avoided by using 2D analysis provided the channel's width-to-depth ratio is about 5:1. The 3D to 2D approximation is also good on the basis that turbulence is not a common occurrence in micron-sized devices. The governing equations for momentum transport are generally the Navier-Stokes and mass continuity equations [16] (Eqs. 8 and 9). Navier-Stokes equation is usually reduced to Stokes equation when the continuity equation is applied at static conditions under the assumption that the Reynolds number is very low. This makes the computer solve, numerically, for the pressure and velocity distributions within the channel. Prior to obtaining the pressure and velocity profiles, appropriation boundary conditions are utilized to completely define the system. In iDEP operations, electroosmotic wall is specified in lieu of the 'no-slip' wall condition. This is because, in electro-osmotic flow, the bulk motion of the fluid is driven by the wall effects - a phenomenon termed electro-osmotic pumping. Electro-osmotic pumping makes the use of external pumping mechanism unnecessary. The boundary mainly utilizes the electric field solution obtained from the second physics (electric current node in, for instance, COMSOL Multiphysics) which is usually solved together with the fluid

been given elsewhere [11–13].

Bio-Inspired Technology

ab initio states.

Laws/Ohm's law) [15].

60

$$\frac{\partial\_{ci}}{\partial t} + \nabla.\mathbf{N}\_i = \mathbf{R}\_i \tag{9}$$

where u ! is the hydrodynamic velocity vector, Di is the diffusivity of the particle, E ! is the electric field applied, and μEP and μEP are the EP and DEP motilities respectively. The DEP mobility is a function of CM factor and for a spherical particle it is expressed as:

$$
\mu\_{\rm DEP} = \frac{\pi d\_p^2 \varepsilon\_m}{12\eta} f\_{\rm CM} \tag{10}
$$

where dp is the particle diameter and η is the medium viscosity. In the latter, the drag force is given as; Fdrag <sup>¼</sup> <sup>9</sup><sup>η</sup> 2ρpr<sup>2</sup> p mpð Þ u � v which is balanced with the DEP equation (Eq. 3).
