Rheofluidics: frequency-dependent rheology of single drops

Abstract

We present Rheofluidics, a microfluidic technique that measures the frequency-dependent rheology of individual micron-scale objects. We apply oscillatory hydrodynamic stresses by flowing them through channels with modulated constrictions, and measure their deformation. Unlike bulk rheology, which measures collective properties, Rheofluidics provides heretofore unattainable measurements of individual particles. We apply Rheofluidics to discover frequency-dependent surface tension of surfactants, very high-frequency viscoelasticity of microgels and unexpected frequency-dependent bending modulus of vesicles.

Figures (4)

• Figure 1: Channel design (a) Microscopy image of a channel section obtained for $L_0=100~\mu$m, $\tilde{\sigma}L_0^2=0.23$ and $\tilde{\omega}L_0^2=0.46$. Black arrows: flow speed. Color scale: extensional rate. (b) FEM simulation results. (c) extensional stress from PIV (black crosses), FEM along the channel axis and 25 $\mu$m away (orange and yellow dashed lines) and droplet speed (gray triangles). Blue line: prescribed sinusoidal stress in time. (d) Gray triangles, left axis: extensional stress for $\omega=1000$ rad/s. Red circles, right axis: droplet deformation. Insets: snapshots of droplets ar maximum and minimum deformation. Scale bar is 10 $\mu$m. (e) Black lines, left axis: chirp Rheofluidic channel shape. Blue symbols, right axis: frequency for different channel sections.
• Figure 2: Dynamic surface tension (a) Symbols: time-dependent deformation profiles measured for $\omega=100$, 350 and 1500 rad/s (left to right). Lines: sinusoidal fits. (b) Symbols: surface tension for oil droplets stabilized by SDS (gray squares), and Tween80 (red circles). Error bars: data dispersion over many droplets. Red line: exponential fit.
• Figure 3: Hydrogel viscoelasticity (a) Gray diamonds: Lissajous figure for $\omega=10^3$ rad/s. Black line: fitted $\sigma(\gamma)$. (b) Squares: storage (blue) and loss (red) moduli measured by Rheofluidics. Solid lines are linear fits, with $G_0=140$ Pa and $\tau=0.8$ ms. Open circles: linear viscoelastic moduli measured by shear rheology in bulk hydrogels at $\omega=10$ rad/s. (c) Open circles: $G^\prime$, $G^{\prime\prime}$ for a bulk hydrogel measured by shear rheology; Full symbols: same data as panel b
• Figure 4: Lipid vesicles (a) image of a POPC vesicle. (b) blue line, right axis: extensional stress profile. Symbols, right axis: vesicle deformation. Black solid line: nonlinear model fitted to the data. Dashed line: model without strain stiffening, highlighting deviations from the sinusoidal deformation profile. (c) Lissajous figure constructed with data in panel a. (d) Bending stiffness measured at $\omega=100$rad/s for different vesicle compositions (e) Frequency-dependent bending stiffness (gray symbols, left axis) and membrane tension (red symbols, right axis) for POPC. Error bars represent data dispersion. Dashed lines are a guide to the eye.