Illustration of the experimental setup. The colloid (green) surrounded by coils of DNA (blue) is held in an optical trap (red). Due to short ranged repulsion, the DNA’s center of mass can approach the colloid only up to the green dashed circle.
(a) Microscope image of a single colloid ( radius) in the optical trap; (b) fit of the intensity distribution for the image shown in (a) using the Levenberg–Marquardt algorithm.
Drag force on colloids of radii (boxes), (circles), and (diamonds) in (solid symbols) and (half-filled symbols), as well as in pure water (open symbols), as a function of the pulling speed . Also shown are linear fits to the data from which one can extract a density dependent viscosity via the Stokes formula Eq. (3). However, as shown in Fig. 4, these viscosities are inconsistent as they depend on the colloid radius.
Viscosity as a function of DNA concentration extracted from linear fits to the data shown in Fig. 3 using the Stokes formula Eq. (3) compared to the viscosities measured in a viscosimeter (see Table I). From the viscosimeter data, one obtains an intrinsic viscosity of the DNA of .
The measured drag force on a colloid of radius normalized to the velocity as a function of the DNA concentration (open symbols). For the clarity of the presentation only a subset of the experimental data is shown. The data collapse demonstrates that is proportional to ; however, the dependence on is nonlinear. The drag is also significantly larger than expected from the increased viscosity as measured in a viscosimeter . In pure water we obtain (dashed horizontal line). Also shown are simulation results for polymers with modified mobility (as explained in the text, solid symbols). A fit for concentrations between 0 and (solid line) highlights the nonlinearity of the force and the linearity of the viscosity in the density.
Drag force on a colloid of radius measured in pure water and in a DNA solution as a function of the velocity . The DNA concentration in (a) is and in (b) it is . The data are compared to the Stokes friction in pure water (solid line) and in the DNA solution (dotted line) calculated from the measured viscosity, as well as to plus the contribution from the DNA jammed in front of the colloid for (dashed line) and for (dashed-dotted line). Also shown is a fit to BD simulation results between and .
Flow field (arrows) around a moving colloid (solid circle) with radius in the frame of reference comoving with the colloid. Particles (e.g., DNA, open circle) with radius can approach the colloid only up to a distance (dashed circle). The flow field has a component normal to this circle, which leads to an accumulation of particles in front and a depletion of particles in the back of the colloid.
Numerically calculated drag force for the radii used in the experiment as a function of the Peclet number (symbols) and the affine fits to the data for .
A cut through a part of the simulated system . Polymers are shown as small circles and the colloid as a large circle with a ring. The arrow indicates the direction of motion of the colloid. Even though the density map and the density profiles shown in Fig. 10 clearly show an accumulation of polymers in front of the colloid and a depletion region behind it, this cannot be seen from a single snapshot of the system.
[(a) and (b)] Polymer density around the colloid averaged over 2000 snapshots of the system at concentrations of and , respectively. The dimensions of the snapshots are , averaged over a thick slice. Lighter colors denote higher polymer densities. (c) Normalized average polymer density on a line through the colloid center in the direction of motion for concentrations of and and velocity . The vertical lines indicate the size of the colloid . Polymers accumulate in front of the colloid and the concentration in the back is reduced due to the finite Peclet number of the polymers. While this depletion region is more pronounced at a low polymer concentration [part (a)], the accumulation of polymers is stronger at higher concentrations [part (b)].
Effective viscosity [calculated with Eq. (3) from drag force measured in the simulations] vs drag velocity for different polymer concentrations. For velocities larger than about , the effective viscosity is independent of the velocity even for high polymer concentrations. For low velocities, the drag force increases. The horizontal line indicates the viscosity of the solvent water.
Viscosity as a function of DNA concentration extracted from linear fits to the data shown in Fig. 3 using the Stokes formula Eq. (3) compared to the viscosities measured in a viscosimeter. From the viscosimeter data, one obtains an intrinsic viscosity of the DNA of . See also Fig. 4.
Effective colloid radius extracted from the linear fits to the data in Fig. 3.
Fitting coefficients for the extrapolation of the force to large velocities (Peclet numbers) for the three colloid sizes used in the experiments. The radius of gyration is assumed to be .
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