Elastohydrodynamic Lift at a Soft Wall

We study experimentally the motion of nondeformable microbeads in a linear shear flow close to a wall bearing a thin and soft polymer layer. Combining microfluidics and 3D optical tracking, we demonstrate that the steady-state bead-to-surface distance increases with the flow strength. Moreover, such lift is shown to result from flow-induced deformations of the layer, in quantitative agreement with theoretical predictions from elastohydrodynamics. This study thus provides the first experimental evidence of “soft lubrication” at play at small scale, in a system relevant, for example, to the physics of blood microcirculation.

Figure 1

(a) Flow chamber with bottom surface functionalized with a HA brush via biotin-streptavidin binding. (b) Bead traveling in a shear flow of velocity gradient $\dot{\gamma }$. Dual color RICM is used to monitor its distance $h$ from the substrate and its translation velocity $V$.

Figure 2

(a) Left: interference patterns at ${\lambda }_1=532\mathrm{nm}$ (scale bar $5\mu \mathrm{m}$). Right: radial intensity profile (black dots) extracted from image, azimuthally averaged (magenta line), and fitted with an optical model (cyan line) to determine $h_{\mathrm{meas}}$, from which we compute $h=h_{\mathrm{meas}}-h_{\mathrm{off}}$, with $h_{\mathrm{off}}$ the offset due to the contribution of the gold and streptavidin layers (measured independently, see Supplemental Material [25]). (b) Same as (a) at ${\lambda }_2=635\mathrm{nm}$. (c) Time series for $h$ (green: ${\lambda }_1$, magenta: ${\lambda }_2$) and $V$ (blue), for a bead flowing close to the HA brush.

Figure 3

(a) $V(\dot{\gamma })$ measured on control surface (solid triangle), HA840-h (solid square), HA840-l (solid diamond), and HA58 (solid circle) brushes. The solid line is the GCB prediction for nondeformable surfaces separated by 20 nm. (b) Experimentally measured $h(\dot{\gamma })$ [symbols as in panel (a)]. Solid line indicates the constant value of $z=20\mathrm{nm}$ used in GCB theory. Error bars accounting for standard error and uncertainty on $h$ and $V$ are about the size of the symbols.

Figure 4

(a) $h(\dot{\gamma })-H_0$ data on HA brushes (symbols as in Fig. 3, vertical scale according to arrows) and theoretical predictions for $\delta (\dot{\gamma })$ with $M=5\mathrm{Pa}$ (dashed line), 57 Pa (solid line), and 15 000 Pa (dotted line). The shaded area around the theoretical curves is defined by the predictions obtained when $\xi$ is varied from lower to upper bound for each brush. Inset: sketch showing the location of the no-slip plane at $\xi$ below the brush surface. (b) Theoretical ($V_{\mathrm{th}}$) vs experimental ($V_{\exp }$) velocities [symbols as in panel (a)]. The solid line corresponds to $V_{\mathrm{th}}=V_{\exp }$ and the dashed line to $V_{\mathrm{th}}=1.2V_{\exp }$. Variations of $V_{\mathrm{th}}$ due to changes in $\xi$ and error bars on $V_{\exp }$ are about the symbol size. Inset: measured (symbols) and predicted (lines) deviation from linearity, $\mathrm{\Delta }V=V(\dot{\gamma })-S\dot{\gamma }$, with $S$ the slope in the limit of small shear rates. (c) Best fit values (solid square), measured reference (solid circle), and predictions (solid line) for $M$ as a function of $\xi$. Error bars correspond to the uncertainty on $\xi$.