Interfacial Flow around Brownian Colloids

Understanding the flow created by particle motion at interfaces is a critical step toward understanding hydrodynamic interactions and colloidal self organization. We have developed correlated displacement velocimetry to measure flow fields around interfacially trapped Brownian particles. These flow fields can be decomposed into interfacial hydrodynamic multipoles, including force monopole and dipole flows. These structures provide key insights essential to understanding the interface’s mechanical response. Importantly, the flow structure shows that the interface is incompressible for scant surfactant near the ideal gaseous state and contains information about interfacial properties and hydrodynamic coupling with the bulk fluid. The same dataset can be used to predict the response of the interface to applied, complex forces, enabling virtual experiments that produce higher order interfacial multipoles.

Figure 1

(a) Particles at the air-water interface are moving randomly as shown in (b) for $\tau =0.04\mathrm{s}$. Vectors are scaled up by a factor of ${10}^3$; inset shows a coordinate system located on the original position of particle $s$ with the $Y$ axis aligned with particle displacement. (c) Displacement at the interface induced by the motion of colloids captured by the correlated displacement velocimetry. Streamlines indicate the local direction of the displacement, and the color scheme indicates its magnitude. The scale bar is $20\mu \mathrm{m}$. (d) Spatial decay of interfacial Stokeslet; symbols show measured velocity by CDV, and lines are the best fit to $u_y{|}_{x=0}={\mathrm{\Phi }}_{\parallel }f$ and $u_y{|}_{y=0}={\mathrm{\Phi }}_{\perp }f$. Displacement field for an interfacial Stokeslet flow at (e) an ideal compressible interface and (f) an incompressible interface.

Figure 2

(a) Distribution of the drag coefficient; symbols are measured value with line showing the best fit to the model. (b) Drag coefficient of particles at different neighborhood of the interface. Color and size of each circle indicate its drag coefficient. The sample trajectories with large and small mobility are shown with blue and orange lines, respectively.

Figure 3

(a) and (c) Displacement, $\mathit{U}$, generated by virtual force dipoles exerted at interface by relative motion of particles pairs moving parallel (a) and normal (c) to their interparticle distance for $\tau =0.04\mathrm{s}$. (b) and (d) Analytical force dipole flows obtained from the best fit to Eq. (9). Streamlines indicate the local direction of the displacement, and the color contours indicate velocity magnitude. (e)–(f) Spatial decay of the flow field, $\mathit{u}$, along $x$ and $y$ axis. Symbols are the measured velocity, dashed lines are the best fit to force dipole flows, and dot-dashed lines are the best fit to the flow due to a pair of Stokeslets centered at $y=\pm 10\mu \mathrm{m}$.