Mixing performance of T, Y, and oriented Y-micromixers with spatially arranged outlet channel: evaluation with Villermaux/Dushman test reaction

Abstract

This study aims to investigate the micromixing performance of three basic types of spatial shaped micromixers. New configurations of T, Y, and oriented Y-spatial mixers were designed with change in the angles of the confluence and the outlet channel to achieve the efficient micromixing. These micromixers offer advantages that are not attainable with the typical types of these mixers. Experimental tests were carried out in the laminar flow regime and the mixing efficiency was evaluated using Villermaux/Dushman test reaction. The geometries of the channels were cylindrical with the length of 30 mm and the diameter of 800 μm. The experimental results show that the angle of outlet channel has a significant effect on the pressure drop and segregation index. Generally, the results reveal that at various feed flow rates the spatial shape of channels can lead to considerable improvement in micromixing performance. In all T, Y, and oriented Y-mixers, significant enhancement by increasing the confluence angle was also seen because the fluid elements were stretched and folded in the two inlet fluid interfaces. Furthermore, the micromixing time for the more efficient geometry of three shapes of microchannels was determined based on the incorporation model, which it was in the range of 0.001–0.1 s.

Appendix: Kinetic of the Villermaux–Dushman reaction

The kinetics of the iodide-iodate chemical test reaction for characterizing micromixing efficiency was presented in literature. In summary, the reaction rate equations are as follows (Rahimi et al. 2014):

$$ r_{1} = k_{1} [H^{ + } ][H_{2} BO_{3}^{ - } ] $$

(20)

While k ₁  = 10¹¹ L mol⁻¹ s⁻¹

$$ r_{2} = k_{2} [H^{ + } ]^{2} [I^{ - } ]^{2} [IO_{3}^{ - } ] $$

(21)

k₂ is measured relative to ionic strength (I) of solution (Parvizian et al. 2012):

$$ \log_{10} k_{2} = 9.28105 - 3.664\sqrt I \quad \text{for }I \le 0.166\,\text{M} $$

(22)

$$ \log_{10} k_{2} = 8.383 - 1.5112\sqrt I + 0.237I\quad \text{for }I \ge 0.166\,\text{M} $$

(23)

I is defined as a function of all ion concentrations (c) in the solution and their charge number (z) (Falk and Commenge 2010):

$$ I = \frac{1}{2}\sum\limits_{i = 1}^{n} {c_{i} z_{i}^{2} } $$

(24)

In the present work, the calculated value of I is 1.01393. The maximum absolute uncertainty of I is 0.0012. Therefore, the value of k₂ according to Eq. (24) is equal to 1.26 × 10⁷ mol L⁻¹ s⁻¹ (Falk and Commenge 2010; Rahimi et al. 2014).

$$ r_{3} = r_{3}^{ + } - r_{3}^{ - } = k_{3}^{ + } [I^{ - } ][I_{2} ] - k_{3}^{ - } [I_{3}^{ - } ] $$

(25)

at 25 °C:

$$ k_{3}^{ + } = 5.9 \times 10^{9} \,\text{L}\,\text{mol}^{ - 1} \cdot \text{s}^{ - 1} $$

$$ k_{3}^{ - } = 7.5 \times 10^{6} \,\text{s}^{ - 1} $$

The mole number of I₂ can be calculated in terms of mass balance of iodine atoms and chemical equilibrium of reaction. The mass balance of reaction (3) expresses as follows (Jiao et al. 2010):

$$ [I_{2} ] = \frac{{[I_{3}^{ - } ]}}{{K_{B} [I^{ - } ]}} $$

(26)

The equilibrium constant K_B is a factor that is related to temperature, which follows the equation as (Kolbl et al. 2008; Jiao et al. 2010; Zhendong et al. 2012):

$$ \log_{10} K_{B} = \frac{555}{T} + 7.355 - 2.575\log_{10} T $$

(27)

In this work, all the experiments were conducted at 25 °C, and then the value of K_B was constant at 702 L/mol.