Microfluidic Mixing via Acoustically Driven Chaotic Advection

Mixing presents a notoriously difficult problem in small amounts of fluids. Herein, surface acoustic waves provide a convenient technique to generate time-dependent flow patterns. These flow patterns can be optimized in such a way that advected particles are mixed most efficiently in the fluid within a short time compared to the time pure diffusion would take. Investigations are presented for the mixing efficiency of a flat cylinder that is driven by two surface acoustic waves. The experimental results favorably agree with model calculations of the flow patterns and the advective transport.

Figure 1

The SAW mixer chip. (a) Two TIDTs exciting SAWs in $x$ and $y$ directions. An envelope controller runs predefined programs modulating the amplitude of the SAW arbitrarily. The fluid is confined in a catenoidal geometry between the substrate and a glass cover slide. When operating in dual-jet mode, TIDT I works at constant power (solid line), and the power of TIDT II is modulated (dashed line). (b) A 3D view of the SAW mixer chip.

Figure 2

Top view of the mixing status of dual-jet experiments after $t=105.6\mathrm{s}$. TIDT I operates at constant power, while the power of TIDT II is constant in (a), and modulated at frequencies $\nu =0.042$, 0.083, 0.17, 0.34, and 0.68 Hz for panels (b), (c), (d), (e), and (f), respectively. Only for panel (d) at $\nu =0.17\mathrm{Hz}$, a homogeneous bead distribution is observed (images inverted for printing, scale bar $300\mu \mathrm{m}$).

Figure 3

Quantitative measure of the mixing efficiency $c_V^{-1}$. For the dual-jet mode, $c_V^{-1}$ is evaluated in the experiment (⋄ $t=136.0\mathrm{s}$; ▵ $t=105.6\mathrm{s}$) together with the theoretical result (solid line $t=136.0\mathrm{s}$, dashed line $t=105.6\mathrm{s}$) as described in the text. In each case the theoretical curve was scaled to have the same maximal value as the experimental one. The experimental data were taken at two different times after starting the experiment. Optimum mixing is achieved for a modulation frequency of $\nu =0.17\mathrm{Hz}$ for this particular geometry. This optimum frequency is well reproduced in our theoretical description.