Multiscale Laminar Flows with Turbulentlike Properties

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multiscale stagnation point topology. This topology is shown to control the evolution of pair separation ($\Delta$) statistics by imposing a turbulentlike locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case $\overline{{\Delta }^2}\sim t^{\gamma }$ is a good approximation with $\gamma$ close to 3. Spatially multiscale laminar flows with turbulentlike spectral and stirring properties are a new concept with potential applications in efficient and microfluidic mixing.

Figure 1

(a) Schematic of rig; (b) Schematic of multiscale flow based on an 8 in 8 topology, (c) Electromagnetic forcing distribution computed for our spatial distribution of multisized magnets ($I=1\mathrm{A}$, $B=1\mathrm{T}$; $f_y$ in $\mathrm{N}/{\mathrm{m}}^3$; $x$ and $y$ in mm).

Figure 2

(a) PIV velocity field ($\mathbf{u}/{\mathbf{u}}_{\mathrm{rms}}$, $1/64$ arrows), ${\mathrm{Re}}_{2\mathrm{D}}=600$, squares refer to hyperbolic stagnation points, disks to elliptic stagnation points; (b) scatter plot of hyperbolic stagnation point strain rates, $\lambda L_E/u_{\mathrm{rms}}$, and sizes, $L_S/L_E$.

Figure 3

Left: Dimensionless mean stagnation point strain rates versus ${\mathrm{Re}}_{2\mathrm{D}}$. Right: Areas of direct influence of stagnation points related to $M_{160}$ and $M_{40}$ for various ${\mathrm{Re}}_{2\mathrm{D}}$.

Figure 4

Two-particle dispersion, ${\mathrm{Re}}_{2\mathrm{D}}=7400$, (a) $\overline{{\Delta }^2}/L_E^2$ (b) $\frac{L_E}{u_{\mathrm{rms}}}\frac{\partial \overline{{\Delta }^m}}{\partial t}$.

Figure 5

(a) Richardson-like exponent, $\gamma$, ($\overline{{\Delta }^2}\sim t^{\gamma }$) and ratio $L_E/u_{\mathrm{rms}}$ to $H^2/\nu$ as function of ${\mathrm{Re}}_{2\mathrm{D}}$; (b) two-particle dispersion, $\overline{{\Delta }^2}/L_E^2$, various ${\mathrm{Re}}_{2\mathrm{D}}$.