Illustration of a dumbbell in shear flow. ϑ is the angle between the bond vector R and its projection onto the flow-gradient plane, and φ is the angle between the projection and the flow direction.
MPC particle hydrodynamic radii as function the collision time (squares). The solid line is the theoretical expectation based on Eqs. (25)–(27) .
Equilibrium relaxation times τ0 divided by the mean square extension l 2 of the dumbbells as function of the collision time. The data points refer to the bond lengths l/a = 3 (red), 5 (green), 7 (dark blue), and 10 (light blue). The dashed lines are guides for the eye only. The theoretical relaxation times obtained from Eq. (10) (not shown) are hardly distinguishable from the simulation data for l/a = 10.
Comparison of the factor (solid lines) and the ratio l 2/(6Dτ0) (squares; dashed lines are guides for the eye only) which measures the effect of intra-dumbbell hydrodynamic interactions. The data points refer to the bond lengths l/a = 3 (red), 5 (green), 7 (dark blue), and 10 (light blue).
Dumbbell-monomer density distributions in the shear-gradient plane for the Weissenberg numbers Wi = 0.27 (top left), 0.8 (top right), 2.7 (bottom left), and 8 (bottom right) and the dumbbell length l/a = 3. The distributions are normalized such that integration over the xy-plane yields unity.
Mean square bond lengths along the flow (upper curve) and gradient direction (lower curve) as function of the Weissenberg number. Symbols correspond to simulation results and solid lines are obtained from the theoretical expressions (29) and (30) . The inset shows , the sum of all three components. The same color code is used as in Fig. 4 .
Simulation results for the distribution functions of the angle ϑ (top) and φ (bottom) for Wi = 1.5 (red), 2.9 (green), 5.8 (dark blue), 15 (purple), and 29 (light blue). The black lines indicate the equilibrium distribution functions without shear. Note that P(φ) is normalized such that The theoretical distribution functions are indistinguishable from the simulation results.
Nonequilibrium relaxation times τ as a function of the Weissenberg number Wi and the dumbbell lengths l/a = 3 (red), 5 (green), 7 (dark blue), and 10 (light blue). The black line represents the theoretical result (10) . Both, the simulation results and the theoretical relaxation time are normalized by the respective zero-shear relaxation time. (Inset) Ratio between the relaxation times extracted from the simulations ( ) and the theoretical value (τ/τ0) as function of the Weissenberg number.
(Top) First and (bottom) second normal stress coefficient as function of the Weissenberg number Wi and various dumbbell lengths. (Top) The solid line is obtained from the theoretical expression (42) . (Bottom) The solid line indicates the power-law |Ψ2| ∼ Wi−2/3. For the color code see Fig. 4 .
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