**3.3 Velocity and concentration profile visualization**

As mentioned earlier, there are two physics interface models that were solved in this work which are laminar flow (LF) and transport of diluted species (TDS). The LF interface model considers the fluid flow of the system with inlet velocity ranging from 1 to 10,000 μm/s chosen as input parameter. The LF interface model is solved independently. However, the TDS interface model is solved by obtaining a data of velocity field from the solution of the LF interface model. This is the reason why both physics interface models are used together. **Figures 5** and **6** show the velocity profile from the top view (XY view) of the geometric configuration comprised of corrugated and straight microchannel, respectively. The color gradient shows the maximum velocity of the microchannel at the middle of the channel which can be

seen in red color, while the blue color represents the low velocity value which is at the domain wall. This phenomenon indicates laminar parabolic flow where the velocity varies parabolically across the discharge slit with the maximum velocity at

*Velocity profile of straight microchannel from XY-axis view.*

*Computational Fluid Dynamics of Mixing Performance in Microchannel*

*DOI: http://dx.doi.org/10.5772/intechopen.89928*

*Concentration profile of corrugated microchannel for various inlet velocities.*

Visualization of mixing process in this work can be seen clearly by the plotted concentration profile of the species in which the different color gradients represent the species before and after the mixing process. In particular, the unmixed species is represented by blue and red colors, and the green color represented the mixed one. **Figures 7** and **8** shows the concentration profile of the corrugated and straight microchannel respectively for all the inlet velocities studied in this work. Both geometric domains have similar dimension of length and width but different configuration of microchannel. The mixing starts when the fluids with different concentrations denoted as blue and red enter the discharge slit. A clear separation of the

the center.

**Figure 7.**

**111**

**Figure 6.**

**Figure 5.** *Velocity profile of corrugated microchannel from XY-axis view.*

*Computational Fluid Dynamics of Mixing Performance in Microchannel DOI: http://dx.doi.org/10.5772/intechopen.89928*

#### **Figure 6.** *Velocity profile of straight microchannel from XY-axis view.*

seen in red color, while the blue color represents the low velocity value which is at the domain wall. This phenomenon indicates laminar parabolic flow where the velocity varies parabolically across the discharge slit with the maximum velocity at the center.

Visualization of mixing process in this work can be seen clearly by the plotted concentration profile of the species in which the different color gradients represent the species before and after the mixing process. In particular, the unmixed species is represented by blue and red colors, and the green color represented the mixed one.

**Figures 7** and **8** shows the concentration profile of the corrugated and straight microchannel respectively for all the inlet velocities studied in this work. Both geometric domains have similar dimension of length and width but different configuration of microchannel. The mixing starts when the fluids with different concentrations denoted as blue and red enter the discharge slit. A clear separation of the

where *c* is the concentration of the species (SI unit: mol/m<sup>3</sup>

In this model, *R* = 0, because there is no reaction occurred. The species is introduced at different concentration from the range of 0–1 mol/m<sup>3</sup> where one species is at a concentration of 1 mol/m<sup>3</sup> on one of the input boundaries, while the other is at zero concentration. At the output boundary, the substance flows through

As mentioned earlier, there are two physics interface models that were solved in this work which are laminar flow (LF) and transport of diluted species (TDS). The LF interface model considers the fluid flow of the system with inlet velocity ranging from 1 to 10,000 μm/s chosen as input parameter. The LF interface model is solved independently. However, the TDS interface model is solved by obtaining a data of velocity field from the solution of the LF interface model. This is the reason why both physics interface models are used together. **Figures 5** and **6** show the velocity profile from the top view (XY view) of the geometric configuration comprised of corrugated and straight microchannel, respectively. The color gradient shows the maximum velocity of the microchannel at the middle of the channel which can be

s)); and *v* is velocity vector (SI unit: m/s).

**3.3 Velocity and concentration profile visualization**

/s); *R* is a reaction rate expression for the species (SI unit:

coefficient (SI unit: m<sup>2</sup>

the boundary by convection [21].

*Computational Fluid Dynamics Simulations*

mol/(m<sup>3</sup>

**Figure 5.**

**110**

*Velocity profile of corrugated microchannel from XY-axis view.*

); *D* is the diffusion

As compared to concentration profiles, the mixing intensity profile gave information of mixing quality with respect to discharge slit position. The discharge slit position can represent the mixing length. These mean that complete mixing occurred at different mixing length. The mixing profile shows the difference of mixing intensity profile among the microchannel configurations. The corrugated microchannel has gradually increased the profile of mixing intensity from the entrance toward the end of the discharge slit. This might be due to the corrugated shape of the microchannel which serves to form multi-lamination of fluid that gives even distribution of concentration which then results in a smooth mixing intensity profile. This might prove that the concept of multi-lamination of fluid as the

*Computational Fluid Dynamics of Mixing Performance in Microchannel*

This chapter discussed a study of mixing simulation in microchannel. An analysis is carried out to investigate the effect of the changes of inlet velocity toward mixing intensity over the two different microchannel configurations. The simulation results show the visualization of velocity and concentration profiles along the microchannel. A laminar parabolic flow of velocity profile is observed for two microchannel configurations simulated. The concentration profile gave visualization on the mixing process that occurred in the microchannel. Evaluation of the mixing intensity value represents the mixing performance of the geometry structure. It also gave information on the mixing length requirement to achieve complete mixing. The microchannel needs longer discharge slit to achieve complete mixing if high inlet velocity is used. The result showed that inlet velocity has significant effects on the mixing performance which is represented by the mixing intensity in this study. The higher the inlet velocity, the lower the mixing quality. Careful observation on the mixing intensity profiles among geometry configurations shows

different trends of mixing intensity between the corrugated and straight

c concentration (mol/dm<sup>3</sup>

D diffusion coefficient (m<sup>2</sup>

Dh hydraulic diameter (m) F volume force vector (N/m<sup>3</sup>

*T* absolute temperature (K)

μ dynamic viscosity (Pa.s)

p pressure (Pa) L length (m) w width (m) h height (m) R reaction (mol/(m<sup>3</sup>

*v* velocity (m/s)

I would like to thank everybody who was important to the successful realization

)

s))

/s)

)

purpose of microreactor is designed in such way.

*DOI: http://dx.doi.org/10.5772/intechopen.89928*

**4. Conclusions**

microchannels.

of this chapter.

**113**

**Acknowledgements**

**Appendices and nomenclature**

#### **Figure 8.**

*Concentration profile of straight microchannel for various inlet velocity.*

concentration is observed at the entrance, but this diminishes toward the end of the discharge slit for inlet velocity equal to 100 μm/s. Thus the mixing process is completed. For inlet velocity lower than 100 μm/s, the mixing completely occurred instantaneously as the fluids enter the discharge slit. For inlet velocity higher than 100 μm/s, the mixing is not complete as distinct color can be seen from the entrance until the end of discharge slit.

In short, complete mixing occurred at low inlet velocity, and the mixing is incomplete at higher inlet velocity of 100 μm/s for both configurations of microchannel.

### **3.4 Mixing intensity evaluation**

As mentioned in previous section, the Danckwerts segregation intensity or the so-called mixing intensity is defined with the mean square deviation of the concentration profile of the component *i* in a cross section of the discharge slit. The segregation intensity can be transformed to a value between 0 (completely segregated) and 1 (completely mixed) [22].

In this work, to determine the mixing quality with respect to discharge slit length, the value of mixing intensity is evaluated at every 100 μm of discharge slit position starting from 300 μm where the fluid starts to mix until 4300 μm which is the end of discharge slit. The mixing intensity value against the discharge slit position for both corrugated and straight microchannels at inlet velocity of 10,000 μm/s is plotted in **Figure 9**. The mixing intensity of corrugated microchannel is higher than the mixing intensity of straight microchannel.

**Figure 9.** *Comparison of mixing intensity between geometric configuration at inlet velocity of 10,000 μm/s.*

#### *Computational Fluid Dynamics of Mixing Performance in Microchannel DOI: http://dx.doi.org/10.5772/intechopen.89928*

As compared to concentration profiles, the mixing intensity profile gave information of mixing quality with respect to discharge slit position. The discharge slit position can represent the mixing length. These mean that complete mixing occurred at different mixing length. The mixing profile shows the difference of mixing intensity profile among the microchannel configurations. The corrugated microchannel has gradually increased the profile of mixing intensity from the entrance toward the end of the discharge slit. This might be due to the corrugated shape of the microchannel which serves to form multi-lamination of fluid that gives even distribution of concentration which then results in a smooth mixing intensity profile. This might prove that the concept of multi-lamination of fluid as the purpose of microreactor is designed in such way.
