Singular-point characterization in microscopic flows

We suggest an approach to microrheology based on optical traps capable of measuring fluid fluxes around singular points of fluid flows. We experimentally demonstrate this technique, applying it to the characterization of controlled flows produced by a set of birefringent spheres spinning due to the transfer of light angular momentum. Unlike the previous techniques, this method is able to distinguish between a singular point in a complex flow and the absence of flow at all; furthermore it permits us to characterize the stability of the singular point.

Figure 1

(Color online) (a) Image of a trapped probe near a single spinning sphere. The bar is $1\mu \text{m}$. (b) 2D probability density function (PDF) when the spinning sphere is at rest. (c)–(f) Experimental probability density functions and reconstructed total force field. Insets: reconstructed hydrodynamic force field near $x=0$ and $y=0$. The reconstruction is accurate only over the region visited by the Brownian particle. The sphere is spinning (c)–(d) counterclockwise and (e)–(f) clockwise.

Figure 2

(Color online) (a) Force field and (b) autocorrelation (red dashed line) and cross-correlation (blue solid line) functions when only the optical force is acting on a $0.5\mu \text{m}$ radius probe in absence of drag force field.

Figure 3

(Color online) (a) Image of a trapped probe between a couple of spinning spheres. The bar is $1\mu \text{m}$. (b) 2D probability density function (PDF) when the spinning spheres are at rest. (c)–(f) Experimental probability density functions and reconstructed total force field. Insets: reconstructed hydrodynamic force field near $x=0$ and $y=0$. The reconstruction is accurate only over the region visited by the Brownian particle. The spheres are spinning (c),(d) counterclockwise and (e),(f) clockwise.

Figure 4

(Color online) (a) Image of a trapped probe between four spinning spheres. The bar is $3\mu \text{m}$. (b) 2D probability density function when the spinning sphere is at rest. (c)–(f) Total force fields—insets: drag force field contribution—and autocorrelation (red dashed line) and cross-correlation (blue solid line) functions when the sphere is spinning (c),(d) counterclockwise and (e),(f) clockwise. For each of the plots (b), (d), and (e) ten data sets acquired during 15 s with sampling rate 2000 Hz were analyzed and averaged.