Chaotic Micromixer Based on 3D Horseshoe Transformation

Abstract

To improve the efficiency of mixing under laminar flow with a low Reynolds number (Re), a novel three-dimensional Horseshoe Transformation (3D HT) was proposed as the basis for the design of a micromixer. Compared with the classical HT, the Lyapunov exponent of the 3D HT, which was calculated based on a symbolic dynamic system, proved the chaotic enhancement. Based on the 3D HT, a micromixer with a mixing length of 12 mm containing six mixing units was obtained by sequentially applying “squeeze”, “stretch”, “twice fold”, “inverse transformation”, and “intersection” operations. Numerical simulation and Peclet Number (Pe) calculations indicated that when the squeeze amplitude 0 < α < 1/2, 0 < β < 1/2, the stretch amplitude γ > 4, and Re ≥ 1, the mass transfer in the mixer was dominated by convective diffusion induced by chaotic flow. When Re = 10, at the outlet of the mixing chamber, the simulated mixing index was 96.4%, which was far less than the value at Re = 0.1 (σ = 0.041). Microscope images of the mixing chamber and the curve trend of pH buffer solutions obtained from a mixing experiment were both consistent with the results of the simulation. When Re = 10, the average mixing index of the pH buffer solutions was 91.75%, which proved the excellent mixing efficiency of the mixer based on the 3D HT.

A Numerical Study of Sub-Millisecond Integrated Mix-and-Inject Microfluidic Devices for Sample Delivery at Synchrotron and XFELs

“…The mixing efficiency was measured at each of the 12 probe points (shown in Figure 3a shows the simulated velocity magnitude distribution within the serpentine micromixer. The serpentine geometry causes the maximum fluid velocity to vary, moving from the centre of the microchannel towards the edges along the x-direction [43]. This is a key characteristic required to induce chaotic flow in low Reynolds number microfluidic systems, where it is essential to have transverse components of liquid flow that stretch and fold volumes of fluid over the cross-section of the microfluidic channel.…”

The Influence of the Unit Junction on the Performance of a Repetitive Structure Micromixer

“…On the basis of Baker transformation that is isomorphic to Bernoulli transformation, Wang et al designed a micromixer that successfully induced chaotic flow through repeated compression, stretching, cutting and stacking operations [ 20 ]. In the previous work by our group, a micromixer was designed on the basis of plane horseshoe transformation [ 21 ] and three-dimensional horseshoe transformation [ 22 ], which also successfully induced chaotic flow by multiple “squeeze–stretch” and “bend–fold” operations.…”

Horseshoe lamination mixer (HLM) sets new standards in the production of monodisperse lipid nanoparticles

“…Recently, a concept of a microfluidic mixer based on the Smale horseshoe transformation, 50 where the cutting is replaced by folding, was introduced, but wall contacts of both phases still occur in the described geometry. 53 We recently reported on a coaxial lamination mixer (CLM) with channel geometries preventing material-wall interactions while ensuring efficient and fast mixing. 54 This unique micromixer, fabricated using two-photon polymerization (2PP), includes inlet filters, a nozzle for coaxial injection, and a series of coaxial lamination elements that increase the interfacial area and reduce the layer thickness of the organic phase.…”

“…Recently, a concept of a microfluidic mixer based on the Smale horseshoe transformation, 50 where the cutting is replaced by folding, was introduced, but wall contacts of both phases still occur in the described geometry. 53…”