Numerical Study of the Electrothermal Effect on the Kinetic Reaction

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Numerical study of the electrothermal effect on kinetics reaction of immunoassay for a microfluidic biosensor Marwa Selmi, mohamed hichem gazzah, and Hafedh Belmabrouk Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02637 • Publication Date (Web): 15 Nov 2016 Downloaded from http://pubs.acs.org on November 15, 2016

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Numerical study of the electrothermal effect on kinetics reaction of immunoassay for a microfluidic biosensor Marwa Selmi a,b1 , Mohamed Hichem Gazzaha, Hafedh Belmabrouk a,c a

Laboratory of Electronics and Microelectronics, Faculty of Science of Monastir, University of

Monastir, Environment Boulevard, Monastir, 5019, Tunisia. b

Department of Radiological Sciences and Medical Imaging, College of Applied Medical

Sciences, Majmaah University, 11952, Saudi Arabia. c

Department of Physics, College of Science AlZulfi, Majmaah University, 11932, Saudi Arabia.

KEYWORDS: Heterogeneous Immunoassay, Microfluidics, Numerical Simulation, Binding Kinetics, Electrothermal, C-reactive protein

ABSTRACT In this work, we simulate the binding reaction of C-reactive protein in a microchannel of a biosensor. A problem that arises in this device concerns the transport the analyte towards the

1

Corresponding author : [email protected] )

(E-mail :

[email protected],

[email protected]

ACS Paragon Plus Environment

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reaction surface of the biosensor, which is of very small dimensions. The limitation of mass transport causes the formation of a diffusion boundary layer and restrains the whole kinetic reaction. To enhance the performance of a biosensor by improving the transport, an applied AC electric field and flow confinement are used to stir the flow field. The numerical simulation of these mechanisms on the binding reaction is performed using finite element method. Swirling patterns are generated in the fluid. They enhance the transport of the analyte and confine it near the reaction surface. The location of the electrode pair on the walls of the microchannel for the design of the biosensor has been studied to find out the effects of varying geometric configuration on the binding efficiency. The best performances of the biosensor are obtained when the electrodes are placed in the same wall of the microchannel as the reaction surface. For the best case, under only the effect of the applied electric field, the enhancement factors can be raised up to 2.46 and 2.10 for the association and dissociation phases, respectively. In contrast, under the effect of the electric field with flow confinement, the enhancement factors of the association and dissociation jump to 3.43 and 2.97, respectively, for 30:1 flow confinement (ratio of confining to sample flow).

Introduction In the last decade, the emerging field of microfluidic seeks to take advantage of biology in union with the growth of the micro/nanotechnologies in a wider context encompassing, for example, microfluidic biosensors for health-care applications (e.g. immunoassays), DNA sequencing, nanoparticles detection, protein separation and other biomedical clinic diagnostics techniques 1. The advantages of the microfluidic devices are tremendous, including high throughput, short analysis time and the ability to operate with small samples and high sensitivity 2

. These devices employ low sample volumes, make available fast reaction rates due to the


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smaller diffusion distances, are easy to fabricate and can include integrated sensors to provide label-free analysis 3,4. Devices, with channels on the size of tens of microns, are being developed for use in a variety of applications such as enzymatic analysis,5,6. DNA analysis,7 proteomics analysis,8, and nano-particle fabrication 9. Rapid advances in nanotechnologies have given thrust to the development and conception of microfluidic biosensors for health-care applications, such as immunoassays. Recently, miniaturization of the microfluidic systems have attracted a lot of attention to integrate advanced biosensors into lab-on-a-chip systems 10,11. The biosensor contains of three components, namely quantum dot-enzyme conjugates, hydrogel microstructures, and a set of microchannels. These components are integrated into a microfluidic device. Lee et al. developed a chip based microfluidic device that has a multi-channel configuration to detect microarray immunoassay samples based on a SPR detection system 12. The lab-on-chip systems have proven to be a promising approach for diagnoses several human diseases, allowing accurate detection of low-concentration disease marker proteins or biomolecules. For example, C-reactive protein (CRP) is a biomarker of inﬂammation increases rapidly in response to tissue infection or inflammation, especially in cases of cardiovascular disease 13. In addition, serum CRP concentrations can be used to assess the risk of cardiovascular diseases 14. Fractal analysis is used for the binding and the dissociation of prion proteins to biosensor surfaces. It provides a quantitative measure of the degree heterogeneity on the biosensor surface 15. The surface plasmon resonance (SPR) sensor16, the quartz crystal microbalance (QCM) sensor17, and the immunoassays are the principal methods used in the most cases for the detection of biomolecules. Although the processes of detection are different, they all implicate the same kinetics of specific binding of analytes, and immobilized ligands. More specifically, the system mixes a small concentration of a biological analyte, such as C-reactive


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protein (CRP) or immunoglobulin G (IgG), with the fluid in a microchannel where the reaction surface is located on the channel walls. The flow velocity perpendicular to the surface is so small that the analyte is transported mainly by diffusion. The rate of the binding reaction on the surface is usually large enough to bind practically all analyte molecules appearing there. Thus, the kinetics reaction is said to be transport limited and it usually causes the formation of a diffusion boundary layer 18. The development of the diffusive layer provokes the limitation of the response time and the performance of the biosensor. In order to increase the reaction rate, several methods were developed. Most of these methods use the AC electrokinetic forces to enhance the rate of transport of reactants to a reaction surface on the wall of a microchannel. AC electrokinetics can be classified into three kinds of force: dielectrophoresis, electrothermal force, and electroosmosis 19, 20. In the last decade, several experimental and theoretical studies that used the AC electrokinetics, have been developed to improve the response of microfluidic biosensors 21-24. In our previous study, we have demonstrated the relevance of the flow confinement effect on the binding reaction in order to enhance efficient mass transport 25. The flow confinement is achieved as follows: a sample flow is joined with a perpendicular makeup flow of water or sample medium. The makeup flow confines the sample into a thin layer above the sensing area. In the present work, we expand the investigation of the effect of the flow confinement with the effect of the electrothermal force on the binding reaction in order to enhance efficient mass transport. The coupled, Navier-Stokes, the energy, the Laplace equations and the kinetic reaction are solved using the finite element method. The location of the electrode pair on the walls of the microchannel for the design of the biosensor has been studied to find out the effects of varying geometric configuration on the binding efficiency. The combination of the effect of the electrothermal and the flow confinement on the biosensor performance is also investigated.


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Theoretical formulation Geometrical and physical parameters Our main purpose is to compute the rate of the kinetic binding reaction between an analyte A (such as C-reactive protein) and a ligand B (anti-CRP). The analyte A is carried by a fluid towards a sensitive membrane in which the ligands are immobilized. The originality of the present work consists to control the biosensor response by two means, namely the application of an electrical field that produces an electrothermal force and the flow confinement. The investigated device is a rectangular microchannel containing a sensitive membrane on the top wall. A pair of electrodes is located on the bottom in order to generate an electric field which yields an electrothermal force. The geometry is assumed to be two-dimensional. The dimensions of the reaction surface and the microchannel are 40 µm × 3 µm, and 500 µm × 150 µm, respectively. The thickness of the electrodes are neglected, the length of each electrode is 60 µm. In this work, we consider four different arrangements of the geometric locations of the electrodes as presented in Figure 1. Type 1

Type 2 +Vrms/2

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Inlet Reaction surface Reaction surface +Vrms/ 2 +Vrms/2

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Figure 1: Sketch of four types of biosensors with an applied external electric field.


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The computation of the concentration of the complex [AB] requires the determination of the analyte concentration [A]. This parameter depends on the fluid flow velocity, which is affected by the electrothermal force and the temperature. Then, the problem presents a coupling between the transport phenomena (convection-diffusion) with the adsorption reaction of the molecules on the reaction surface. ሬሬԦ Compute the potential ࣐ and the electrical field ࡱ ሬԦ (without its In the framework of quasi stationary regime approximation, the electrical field E instantaneous value) is obtained by solving Poisson equation for the electrical potential ߮. Since the fluid is electrically neutral and the dependence of the permittivity versus temperature may be omitted in the Poisson equation, we obtain: ∆߮ = 0 and ‫ܧ‬ሬԦ = −ߘ߮

(1)

The boundary conditions for the electrostatic problem are as follows: at the left and right electrodes, the electric potential ߮ = ±߮௠௔௫ is applied, and at the other boundaries, the electric insulation condition is adopted. Compute the temperature and the velocity fields We assume that the dependence of the specific thermal capacity ܿ௣ and the thermal conductivity ߣ versus temperature can be neglected in the energy equation. This equation reads as follows: ሬԦห ߩܿ௣ ‫ݑ‬. ߘܶ = ߣ߂ܶ + ߪห‫ܧ‬

ଶ

(2)


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Here we have neglected the viscous dissipation term26, which is of the order of 10-8 times smaller than the Joule effect ߪห‫ܧ‬ሬԦ ห. The flow velocity field in the microchannel is obtained by the Navier-Stokes equations. The fluid is assumed to be Newtonian and incompressible. The flow is laminar and steady but is not isotherm. The continuity and motion equations can be written as: ∇.u=0

(3)

ߩሺ࢛. ߘሻ࢛ = −ߘ‫ ݌‬+ ߤߘ ଶ ࢛ + ‫ܨ‬௘

(4)

࢛ is the velocity vector field in the 2D cartesian coordinates (u, v) and p is the pressure. The fluid properties such as the kinematic viscosity and the density are assumed to be constant. The kinematic viscosity is µ=10-3 m2/s, and the fluid density is ρ=1000 kg/m3. When an external electric field is applied across the electrodes, there will be a temperature variation due to Joule heating. Gradient temperature in the fluid gives rise to local changes in permittivity and conductivity. These inhomogeneties lead to create a bulk electrothermal force causing fluid motion. The general expression for this force ሬሬሬԦ ‫ܨ‬௘ reads 19, 24, 27, 28 ሬԦ

ଵ ఇఙ ఇఌ ሬሬሬԦ ሬԦ ఌா మ − ଵ ߘߝห‫ܧ‬ ሬԦ ห ‫ܨ‬௘ = − ଶ ቀ ఙ − ఌ ቁ . ‫ܧ‬ ଵାሺఠఛሻ ସ

ଶ

(5)

where σ and ε are the electrical conductivity and the relative permittivity of the medium, τ is its charge relaxation time, ߱ = 2ߨ݂ is the angular frequency and ‫ܧ‬ሬԦ is the electric field. According to Green et al. 29, for aqueous media at 293 K, we have:


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1 ߘߝ ߘߝ 1 ߘߝ = −0.004 ⇒ = ߘܶ = −0.004ߘܶ ߝ ߲ܶ ߝ ߝ ߲ܶ 1 ߘߪ ߘߪ 1 ߘߪ = 0.02 ⇒ = ߘܶ = 0.02ߘܶ ߪ ߲ܶ ߪ ߪ ߲ܶ Therefore, the electrothermal force is given by: ሬሬሬԦ ሬԦ ൯ ‫ܨ‬௘ = −0.012൫ߘܶ. ‫ܧ‬

ሬԦ ఌா

ଵାሺఠఛሻమ

ଶ

ሬԦห ቁ ߘܶ + 0.001 ቀߝห‫ܧ‬

(6)

The inlet fluid flows in the longitudinal direction x, with a parabolic velocity profile along the ௬

௬

direction ‫ݒ‬ሺ0, ‫ݕ‬ሻ = 4‫ݒ‬௔௩௘ ሺ1 − ுሻ, where ‫ݒ‬௔௩௘ is the average inlet flow velocity and H is the ு

microchannel height. The outlet of the channel is open to the atmosphere. We apply non-slip velocity boundary conditions at all solid boundaries. The fluid is assumed to be at rest initially. At the entrance section, the temperature is equal to the ambient temperature. The outlet section is set to the heat flux condition. Since the electrodes may be assumed as perfect heat conductors, they remain at the ambient temperature T0. The other parts of the walls are supposed thermally insulated. Compute the analyte [A] and the complex [AB] concentrations The binding reaction: The analyte diffused fraction towards the sensitive membrane reacts with the antibody ligand immobilized on the reaction surface. The binding reaction gives rise to a complex AB: ሾ‫ܣ‬ሿ௦௨௥௙௔௖௘ + ሾ‫ܤ‬ሿ ⇌௞௞೚೙ ሾ‫ܤܣ‬ሿ ೚೑೑


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where ሾ‫ܣ‬ሿ௦௨௥௙௔௖௘ is the analyte concentration at the surface, [B] is antibody concentration, [AB] is the complex concentration. The association and dissociation rate constants are respectively denoted by ݇௢௡ and ݇௢௙௙ . We assume that the antibodies B and the complex AB are immobilized on the surface and do not diffuse. The binding reaction between immobilized ligand and analyte is assumed to follow the first order Langmuir adsorption model

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. The reaction rate is then described by the following

chemical kinetics equation. డሾ஺஻ሿ డ௧

= ݇௢௡ ሾ‫ܣ‬௦௨௥௙ ሿሼሾ‫ܤ‬଴ ሿ − ሾ‫ܤܣ‬ሿሽ − ݇௢௙௙ ሾ‫ܤܣ‬ሿ

(7)

where ሾ‫ܤ‬଴ ሿ is the concentration of free antibodies. The association and dissociation constants, i.e. ݇௢௡ and ݇௢௙௙ for CRP-anti-CRP binding interactions are 107 M-1s-1 and 2.6×10-2 s-1, respectively. Analyte transport model: To obtain the analyte concentration ሾ‫ܣ‬௦௨௥௙ ሿ at the sensitive surface, we have resolved the convection-diffusion analyte equation. Indeed, the fluid contains a small concentration of a biological analyte, such as C-reactive protein (CRP). A fraction of this analyte is convected towards the sensitive membrane. The transport equation of the analyte reads: డሾ஺ሿ డ௧

+ ࢛. ߘሾ‫ܣ‬ሿ = ‫∆ܦ‬ሾ‫ܣ‬ሿ + ‫ܩ‬

(8)

where u is the flow velocity, D (D=2.175×10-11 m2/s) is the analyte diffusion coefficient and G denotes the reaction rate. Here G equals to zero because no reaction takes place in the fluid bulk.


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For the simulation of the convection-diffusion equation, different boundary conditions are applied. The inlet boundary is set to a constant concentration ሾ‫ܣ‬଴ ሿ. We adopted the condition ߘሾ‫ܣ‬ሿ = 0 at the outlet, it is assumed that the remaining concentration leaves the system by convection, at the reaction surface, a diffusive flux is imposed. It is given by:

−‫ܦ‬

߲ሾ‫ܣ‬ሿ = ݇௢௡ ሾ‫ܣ‬ሿ௦௨௥௙௔௖௘ ሼሾ‫ܤ‬ሿ଴ − ሾ‫ܤܣ‬ሿሽ − ݇௢௙௙ ሾ‫ܤܣ‬ሿ ߲‫ݐ‬

The other parts of the walls are impermeable and do not interact with the analyte. Initially, the analyte concentration is equal to zero. For the binding reaction (i.e. Eq. 7), only an initial condition is required. This condition reads ሾABሿሺt = 0ሻ = 0. Numerical method and mesh sensitivity analysis The system of the transport equations coupled with the first Langmuir adsorption model is solved using the finite element method (FEM) with the Galerkin approach 30. To find the numerical solution to these equations, a computer code was developed 31. Firstly, the 2D domain is divided in triangular elements. The regions nearby the reaction surface and the electrodes are refined with a better mesh quality. Secondly, all variables are approximated by a polynomial in each element. To ensure that the convergence has been reached and the computed results are independent of the mesh size, several mesh grids have been tested. The results presented hereafter are obtained with a total number 15000 elements and a refined mesh grid near the sensitive surface. Figure 2 presents a synoptic scheme of the algorithm used. First, we solve the electrostatic equation to calculate the magnitude of the electric field. Then, the steady Navier-Stokes


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equations and the energy equation are solved together to obtain the velocity, the pressure and the temperature fields. Finally, we solve the analyte transport equation coupled with the complex concentration equation. These two equations are time-dependant. The total concentration accumulated at the capture area can be found by integrating the local concentration over the

Steady simulation

whole reaction surface.

Geometrical parameters

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H, L, l, LE

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ρ, ν, v0

Tapez une équation ici

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kon, koff, [B0]

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Analyte concentration [A](x,y,t)

Bound Complex [AB](x,t)

Figure 2: Synoptic scheme of the numerical algorithm. Results and discussion Heterogeneous immunoassays based on the interaction between a free target analyte (antigen/antibody) and an immobilized biological receptor ligand (antibody/antigen) on the


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reaction surface, which can be quantified to determine the presence and concentration of the analyte, have been well defined and modeled within the literature 22, 23, 32. A crucial factor that affects the binding reaction (analyte-ligand) is the mass-transport limitation in the microdevices. The limitation mass transport restrains the whole reaction kinetic in the immunoassay biosensor and leads to the growth of the diffusion boundary layer 18, 33-35, which limits the overall biosensor performances. To overcome this problem in the microfluidic device, we will study the AC electrothermal force and the flow confinement effects on the binding reaction. Electrothermal effect In this section, we investigate only the effect of the electrothermal force on the kinetic binding reaction. Four types of biosensors with different arrangements of the electrodes are considered in this study. The inlet flow velocity is 100 µm/s and the applied voltage is 15 V with an operating frequency of 150 kHz. The electrothermal force is used to enhance the rate of the diffusion limited reaction. It results from the application of a non-uniform AC electric field in the microchannel through the two electrodes. Indeed, when the electric field is applied, the fluid warms up due to the Joule effect. The inhomogeneous heating of the fluid induced by the electric field creates local variations in conductivity and permittivity. These gradients of the conductivity and the permittivity are the main cause behind the electrothermal force causing fluid motion. Further, the electrothermal force can generate a vortex field to stir the flow and reduce the thickness of the diffusion boundary layer which leads to the enhancement of the reaction rate 19. In addition, the largely accelerated flow over the reaction surface causes the efficient transport of analyte to the reaction surface and considerably increases the association and dissociation velocity.


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Figure 3 presents the simulated curves of the binding reaction of CRP for the four configurations of the biosensor with 0 V and 15 V. The characteristic behaviors in the association phase or the dissociation phase are different for the four types of biosensor. It is clear that the response time of the CRP is apparently faster for the type 2 than the other types. The binding reaction with the applied voltage is apparently faster than without. This may be explained by the increase of the flow velocity due the electrothermal effect. Indeed, the electrothermal is used to produce a stirring fluid motion that enhances the transport of the analyte in the bulk of the microchannel of the biosensor. -8 10 2

Average surface complex concentration (mol/m )

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0V type 1, (15 V) type 2, (15 V) type 3, (15 V) type 4, (15 V)

1,0

0,8

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0,4

0,2

0,0 0

1000

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4000

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Figure 3: Temporal evolution of the complex concentration for the four types of biosensors for 0 V and 15 V.

To quantify the difference between the binding curves of the four types of biosensor, we defined a factor called enhancement factor defined as the ratio of the initial slope of the binding reaction curve with an applied voltage of 15 V to the initial slope without applying a voltage. Table 1


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shows the enhancement factors in the association and dissociation phases for CRP. We found that the enhancement factor of the association phase is higher than in the dissociation phase. In addition, the enhancement factors of the association and dissociation curve of the type 2 are the largest factors and are equal 2.33 and 1.89, respectively. It is noted that the pair electrodes of the type 2 of biosensor are located on the same wall as the reaction surface. Indeed, the electrothermal force induced by the AC electric field is more efficient and enhances the binding reaction for the type 2 of biosensor than the others. Table 1: Enhancement factors due to electrothermal effect. Type

Enhancement factor (association)

Enhancement factor(dissociation)

Type-1, (15 V)

1.11

0.96

Type-2, (15 V)

2.23

1.89

Type-3, (15 V)

0.67

0.68

Type-4, (15 V)

1.92

1.67

0V

The left and right panel of Figure 4 presents the velocity field and temperature rise distribution, respectively, for the four types of biosensors and for 15 V applied voltage. Indeed, the left panel depicts clearly that the flow pattern is far from a unidirectional flow with a parabolic profile and it contains some vortices induced by the applied electric field. This figure also shows that the position of vortex patterns depends on the position of the electrodes. As shown in this figure that the temperature rise distribution is non-uniform and the largest value appears close to the electrodes. In addition, the largest electrothermal flow velocity occurs at the upper region of the small gap between the electrodes. It arises where the temperature gradient is the largest. The higher velocity is found for the type 2 and it is about 0.6 mm/s. Furthermore, the largest


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temperature rise is 2.4 K. Hence, the type 2 is the best case of biosensor and therefore gives better performances. Consequently, some conditions should be considered in the biosensor design. The numerical result agrees quite well with the results performed by Huang et al. 26. Type 1

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Figure 4: Velocity field (left panel) and temperature rise distribution (right panel) in the microchannel for the four types of biosensor for 15 V applied voltage.


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We study also in this section, the effect of the inlet flow velocity on the binding reaction. Figure 5a and 5b present the initial slope of the association and dissociation phases respectively, for various inlet flow velocity for a biosensor of type 2, with different applied voltage namely, 0, 5, 10 and 15V. a)

-11

Initial slope of assocition phase x(10 )

4,2 3,6 3,0

0 V 5 V 10 V 15 V

2,4 1,8 1,2 0,6 0,0 0

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Inlet flow velocity (µm/s)

b) 0,0

0 5 10 15

-11

Initial slope of dissociation phase x(10 )

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-0,5

V V V V

-1,0 -1,5 -2,0 -2,5 -3,0 -3,5 0

200

400

600

800

1000


Figure 5: Initial slope versus inlet flow velocity for the CRP-Anti CRP binding reaction curves (a) association, (b) dissociation for type 2 for 0, 5, 10 and 15 V. We see that the initial slope increases when we increase the inlet flow velocity. This increase is more important with an applied voltage of 15 V than 5 and 10 V. Therefore, higher inlet flow velocity enhances the mass transport of the analyte and leads to an increase of the initial slopes.


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However, the enhancement factor of both association and dissociation phases decrease versus the inlet flow velocity increases, as shown in Figure 6a and 6b. It means that the electrothermal force is less efficient for higher inlet flow velocity. In addition, when velocity of the particle of the analyte is faster, the probability of the interaction between the analyte-ligands is too lower.

Enhancement factor (association)

a) 5 V 10 V 15 V 10

1

0

200

400

600

800

1000


b)

Enhancement factor (dissociation)

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5 V 10 V 15 V

10

1

0

200

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Figure 6: Enhancement factor versus inlet flow velocity for the CRP-Anti CRP binding reaction curves: (a) association, (b) dissociation for type 2 for 0, 5, 10 and 15 V.


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Electrothermal with flow confinement effect In this section, based on our previous study 25, we combine an active mechanism (electrothermal force) with a passive mechanism (flow confinement) 36, 37. The main flow is confined into a thin layer above the reaction surface by a secondary flow having a perpendicular direction to the first. Figure 7 presents the curves of the binding reaction for the four types of the biosensor under both effects of the flow confinement and the electrothermal force. It compares the binding reaction of the C-reactive protein without any external effect (0V) and the two effects of electrothermal force and the confinement. The applied voltage is 15 V, the inlet flow velocity of the main flow is 100 µm/s and the velocity of the second flow of the confinement is about 10 times of the first flow. We observed that the binding reaction appears always faster with the type 2 than the others types. The makeup flow confines the sample into a thin layer above the sensing area. Therefore, the velocity flow increases to improve the binding rate. The enhancement of the binding reaction may be explained by local collect of the analyte above the reaction surface. Indeed, the confinement flow constricts the microchannel height and leads to an increase of the velocity in the vicinity of the sensitive membrane. Table 2 lists the enhancement factors corresponding to the curves presented in Figure 7. The enhancement factor is defined as the ratio of the initial slope of the binding curve with the applied of the electric field and the flow confinement to the initial slope without applying electric field and without flow confinement. For instance, the largest enhancement factors for the association and dissociation are 2.46 and 2.10, respectively. The effect of the electrothermal with the flow confinement is much appeared when we are compared the enhancement factors associated to the binding reaction. For example, e.g., for the only flow confinement effect, the initial slope for the association phase could be increased from


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1.8 to 2.33, and for the dissociation phase, the initial slope increases from -1.4 to -1.8 for 10:1 flow confinement (ratio of confining to sample flow), which leads to improve the binding reaction with an enhancement factor equal to 1.28. 25. Whereas, the binding reaction is more improved by the combination of the flow confinement with the electrothermal, and the enhancement factor is around 1.34.

10 2


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-8

0V type 1, (15 V) type 2, (15 V) type 3, (15 V) type 4, (15 V)

1,0

0,8

0,6

0,4

0,2

0,0 0

1000

2000

3000

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5000

Time (s)

Figure 7: Temporal evolution of the complex concentration for the four types of biosensors for 0 V and 15 V and with the confinement effect.

Table 2: Enhancement factors of the association and dissociation phases due to electrothermal and confinement effects. Type

Enhancement factor (association))

Enhancement factor(dissociation)

Type-1, (15 V and with flow confinement)

1.81

2.07

Type-2, (15 V with flow confinement)

2.46

2.10


1.34

1.34


2.30

2.09

0 V (without confinement)


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Figure 8 shows a comparison study between our present simulations and experimental data performed by Hofmann et al. 38. It shows the completion time defined as the beginning of the state steady of the binding reaction for different velocities of flow confinement with 0, 5, 10 and 15 V applied voltage. It is clear, that the completion time of our simulation is apparently faster than that obtained by Hofmann et al. 38. The main reason is that the values kon and koff of CRP are greater than those of Cy5-labeled anti-rabbit IgG. The other reason is due to the beneficial effect resulting from the application of an electrical field and the flow confinement. Indeed, the electrothermal effect generated by the applied electrical field and the confinement flow enhance the binding reaction by confining the analyte above the reaction surface and increasing its velocity. Thus, the confinement flow leads to limit the expansion of the boundary layer and contributes to orientate the bulk analyte to the sensitive surface in the microchannel and to enhance the binding reaction.

1800

Hofmann et al. [38] 0V 5 V 10 V 15 V

1600 1400

Detection time (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1200 1000 800 600 400 0

5

10

15

20

25

Uconfinement/Usample

Figure 8: Evolution of the completion time.


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Conclusion Electrothermal and the confinement effects on heterogeneous immunoassays have been investigated in two dimensional simulations, and are identified as a promising approach to increase mass transport at the level of the sensitive surface of a biosensor. They raise considerably the enhancement factor of the binding reaction. The changing of the location of electrode pair on the walls of the microchannel has been studied to find out the effects of varying geometric configuration on the binding reaction. The results show that the electrothermal effect on the binding reaction of a biosensor occurs when placing the electrodes on the same side of the microchannel with the reaction surface. Our results demonstrated the benefit of the effect of the electrothermal flow to enhance the binding reaction. The analysis of the flow confinement with the applied electrothermal force gives a further improvement for the binding reaction. References (1) Reyes, D. R.; Iossifidis, D.; Auroux, P. A.; Manz, A. Micro Total Analysis Systems. 1. Introduction, Theory, and Technology. Anal. Chem. 2002, 74, 2623-2636. (2) Lin, C-C.; Wang, J-H. ; Wu, H-W.; Lee, G-B. Microfluidic Immunoassays. J. Assoc. Lab. Autom. 2010, 15, 253-274. (3) Hong, J.; Edel, J. B.; deMello, A. J. Micro- and nanofluidic systems for high-throughput biological screening. Drug Discovery Today. 2009, 14, Numbers ¾, 134-146. (4) Yang, W.; Woolley, A. T. Integrated Multiprocess Microfluidic Systems for Automating Analysis. J. Assoc. Lab. Autom. 2010, 15, 198-209. (5) Hansen, C. L.; Sommer, M. O. A.; Stephen, R.; Quake, S. R. Systematic investigation of protein phase behavior with a microfluidic formulator. PNAS., 2004, 101, 40, 14431-14436.


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(6) Zhang, H.; Fu, X.; Liu, L.; Zhu, Z.; Yang, K. Microfluidic bead-based enzymatic primer extension for single-nucleotide discrimination using quantum dots as labels. Anal. Biochem. 2012, 426, 30-39. (7) Ben-Yoav, H.; Dykstra, P. H.; Bentley, W. E.; Ghodssi, R. A microfluidic-based electrochemical biochip for label-free diffusion-restricted DNA hybridization analysis. Biosens. Bioelectron. 2012, 38, 114-120. (8) Sanders, G. H. W.; Manz A. Chip-based microsystems for genomic and proteomic analysis. trends in analytical chemistry, 2000, 19, 6, 364-377. (9) Jahn, A.; Vreeland, W. N.; Gaitan, M.; Locascio, L. E. Controlled Vesicle Self-Assembly in Microfluidic Channels with Hydrodynamic Focusing. J. Am. Chem. Soc. 2004, 126, 26742675. (10) Haeberle, S.; Zengerle, R. Microfluidic platforms for lab-on-a-chip applications. Lab Chip. 2007, 7, 1094-1110. (11) Konry, T.; Bale, S. S.; Bhushan, A.; Shen, K.; Seker, E.; Polyak, B.; Yarmush, M. Particles and microfluidics merged: perspectives of highly sensitive diagnos tic detection. Microchim Acta. 2012, 176, 251-269. (12) Lee, K-H.; Su, Y-D.; Chen, S-J.; Tseng, F-G.; Lee, G-B. Microfluidic systems integrated with two-dimensional surface plasmon resonance phase imaging systems for microarray immunoassay. Biosens. Bioelectron. 2007, 23, 466-472. (13) Pepys, M. B.; Hirschfield, G. M. C-reactive protein: a critical update. J. Clin. Invest. 2003, 111, 12, 1805–1812.


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(14) Myers, G. L.; Rifai, N.; Tracy, R. P.; Roberts, W. L.; Alexander, R. W.; Biasucci, L. M.; Catravas, J. D.; Cole, T. G.; Cooper, G. R.; Khan, B. V.; Kimberly, M. M.; Stein, E. A.; Taubert, K. A.; Warnick, G. R.; Waymack, P. P. CDC/AHA Workshop on Markers of Inflammation and Cardiovascular Disease Application to Clinical and Public Health Practice. Circulation. 2004, 110, e545-e549. (15) Taneja, R.; Shelton, K. C.; Sadana, A. Fractal Analysis of Binding and Dissociation Kinetics and Interactions of Cancer Markers on Biosensor Surfaces. Journal of Receptors and Signal Transduction, 2007, 27(2-3), 167-87. (16) Kanda, V.; Kariuki, J. K.; Harrison, D. J.; McDermott, M. T. Label-Free Reading of Microarray-Based Immunoassays with Surface Plasmon Resonance Imaging. Anal. Chem. 2004, 76, No. 24, 7257-7262. (17) Pascal-Delannoy, F.; Sorli, B.; Boyer, A. Quartz Crystal Microbalance (QCM) used as humidity sensor. Sens. and Actuators. 2000, 84, 285-291. (18) Hibbert, D. B.; Gooding, J. J.; Erokhin, P. Kinetics of Irreversible Adsorption with Diffusion: Application to Biomolecule Immobilization. Langmuir. 2001, 18, 1770-1776. (19) Ramos, A.; Morgan, H.; Green, N. G.; Castellanos, A. Ac electrokinetics: a review of forces in microelectrode structures. J. Phys. D: Appl. Phys. 31, pp. 2338-2353, January 1998. (20) Sigurdson, M.; Wang, D.; Meinhart, C. D. Electrothermal stirring for heterogeneous immunoassays. Lab. Chip. 2005, 5, 1366-1373. (21) Han, D.; Park, J.-K. Optoelectrofluidic enhanced immunoreaction based on opticallyinduced dynamic AC electroosmosis. Lab Chip, 2016, 16, 1189-1196.


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(22) Hart, R.; Lec, R.; Noh, H. Enhancement of heterogeneous immunoassays using AC electroosmosis. Sens. and Actuators B. 2010, 147, 366-375. (23) Huang, K-R.; Chang, J-S.; Chao, S. D.; Wu, K-C.; Yang, C-K.; Lai, C-Y.; Chen, S-H. Simulation on binding efficiency of immunoassay for a biosensor with applying electrothermal effect. J. Appl. Phys. 2008, 104, 064702-11. (24) Feldman, H. C.; Sigurdson, M.; Meinhart, C. D. AC electrothermal enhancement of heterogeneous assays in microfluidics. Lab Chip, 2007, 7, 1553-1559. (25) Selmi, M.; Echouchene, F.; Gazzah, M. H.; Belmabrouk, H. Flow Confinement Enhancement of Heterogeneous Immunoassays in Microfluidics. IEEE Sensors J. 2015, 15, 12, 7321-7328. (26) Huang, K-R.; Chang, J-S. Three dimensional simulation on binding efficiency of immunoassay for a biosensor with applying electrothermal effect. Heat Mass Transfer. 2013, 49, 1647-1658. (27) Chen, D. F.; Du, H. Simulation studies on electrothermal fluid flow induced in a dielectrophoretic microelectrode system. J. Micromech. Microeng. 2006, 16, pp. 2411-2419. (28) Green, N. G.; Ramos, A.; Gonzalez, A.; Castellanos, A., Morgan, H. Electrothermally induced fluid flow on microelectrodes. J. Electrostat. 2001, 53, 71-87. (29) Castellanos, A. (Ed.), Electrohydrodynamics, Springer, New York, 1998, (Chapter 4). (30) Chen Z., Finite Element Methods and Their Applications (Scientific Computation). Berlin, Germany: Springer-Verlag, 2005.


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(31) Nasri, F.; Ben Aissa, M.F.; Gazzah, M. H.; Belmabrouk, H. 3D thermal conduction in a nanoscale Tri-Gate MOSFET based on single-phase-lag model. Applied Thermal Engineering. 2015, 91, 647-653. (32) Yang, C-K.; Chang, J-S.; Chao, S-D.; Wu, K-C. Effects of diffusion boundary layer on reaction kinetics of immunoassay in a biosensor. J. Appl. Phys. 2008, 103, 084702-10. (33) Chaiken, I.; Rosé, S.; Karlsson, R. Analysis of Macromolecular Interactions Using Immobilized Ligands. Anal. Biochem. 1992, 201, 197-210. (34) Friedrich, D.; Please, C.; Melvin, T. Optimisation of analyte transport in integrated microfluidic affinity sensors for the quantification of low levels of analyte. Sens. and Actuators B. 2008, 131, 323-332. (35) Kim, D. R.; Zheng, X. Numerical Characterization and Optimization of the Microfluidics for Nanowire Biosensors. Nano Lett., 2008, 8, No. 10, 3233-3237. (36) Negri, P.; Jacobs, K. T.; Dada, O. O.; Schultz, Z. D. Ultrasensitive SERS Flow Detector Using Hydrodynamic Focusing. Anal. Chem., 2013, 85 (21), 10159-10166. (37) Bailey, M. R.; Pentecost, A. M.; Selimovic, A.; Martin, R. S.; Schultz, Z. D. Sheath-Flow Microfluidic

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Electrochemical Detection. Anal. Chem. 2015, 87, 4347-4355. (38) Hofmann, O.; Voirin, G.; Niedermann, P.; Manz, A. Three-Dimensional Microfluidic Confinement for Efficient Sample Delivery to Biosensor Surfaces. Application to Immunoassays on Planar Optical waveguides. Anal. Chem., 2002, 74, No, 20, 5243-5250.


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Table of Contents ABSTRACT .................................................................................................................................... 1 Introduction ..................................................................................................................................... 2 Theoretical formulation .................................................................................................................. 5 Geometrical and physical parameters ......................................................................................... 5 Compute the potential φ and the electrical field E ..................................................................... 6 Compute the temperature and the velocity fields ....................................................................... 6 Compute the analyte [A] and the complex [AB] concentrations ................................................ 8 Numerical method and mesh sensitivity analysis ......................................................................... 10 Results and discussion .................................................................................................................. 11 Electrothermal effect ................................................................................................................. 12 Electrothermal with flow confinement effect ........................................................................... 18 Conclusion .................................................................................................................................... 21 References ..................................................................................................................................... 21


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Abstract Graphic

Antigen Antibody

Antigen-Antibody

kon

+

10 2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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koff

-8

0V 15 V, with flow confinement

1,0

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0,6

0,4

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Numerical Study of the Electrothermal Effect on the Kinetic Reaction

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