*Article* **Numerical and Experimental Study of Cross-Sectional Effects on the Mixing Performance of the Spiral Microfluidics**

**Omid Rouhi 1,2,†, Sajad Razavi Bazaz 1,† , Hamid Niazmand <sup>2</sup> , Fateme Mirakhorli <sup>1</sup> , Sima Mas-hafi 3,4 , Hoseyn A. Amiri 3,4 , Morteza Miansari 3,4 and Majid Ebrahimi Warkiani 1,5,\***


**Abstract:** Mixing at the microscale is of great importance for various applications ranging from biological and chemical synthesis to drug delivery. Among the numerous types of micromixers that have been developed, planar passive spiral micromixers have gained considerable interest due to their ease of fabrication and integration into complex miniaturized systems. However, less attention has been paid to non-planar spiral micromixers with various cross-sections and the effects of these cross-sections on the total performance of the micromixer. Here, mixing performance in a spiral micromixer with different channel cross-sections is evaluated experimentally and numerically in the *Re* range of 0.001 to 50. The accuracy of the 3D-finite element model was first verified at different flow rates by tracking the mixing index across the loops, which were directly proportional to the spiral radius and were hence also proportional to the Dean flow. It is shown that higher flow rates induce stronger vortices compared to lower flow rates; thus, fewer loops are required for efficient mixing. The numerical study revealed that a large-angle outward trapezoidal cross-section provides the highest mixing performance, reaching efficiencies of up to 95%. Moreover, the velocity/vorticity along the channel length was analyzed and discussed to evaluate channel mixing performance. A relatively low pressure drop (<130 kPa) makes these passive spiral micromixers ideal candidates for various lab-on-chip applications.

**Keywords:** 3D printing; spiral micromixers; dean flow; trapezoidal cross-section; mixing index; convection and diffusion
