Table 1 Crossover shear rates \({\dot{\gamma }}_{\times }\) and Weissenberg numbers Wi× from tumbling to inflation phase.

From: Hydrodynamic inflation of ring polymers under shear

Topology

N

\({\dot{\gamma }}_{\times }\ \ [{({k}_{{\rm{B}}}T)}^{0.5}{m}^{-0.5}{a}^{-1}]\)

Wi×

01

100

1.4 × 10−2

1.19 × 102

01

150

1.0 × 10−2

1.57 × 102

01

200

7.2 × 10−3

1.86 × 102

31

100

1.3 × 10−2

0.66 × 102

31

200

5.2 × 10−3

0.82 × 102

41

200

3.8 × 10−3

0.52 × 102

51

200

4.5 × 10−3

0.59 × 102

52

200

6.2 × 10−3

0.62 × 102

61

200

6.6 × 10−3

0.88 × 102

62

200

7.2 × 10−3

0.86 × 102

63

200

6.4 × 10−3

0.74 × 102

71

200

7.7 × 10−3

1.05 × 102

81

200

7.9 × 10−3

0.90 × 102

  1. The crossover values \({\dot{\gamma }}_{\times }\) and Wi× for the transition from the tumbling to the inflation phase of ring polymers with topology denoted in the left column and degree of polymerisation N in the second-to-left. Note that for the cases of N = 100 (01- and 31-rings), a fully developed inflation phase does not emerge and \({\dot{\gamma }}_{\times }\) denotes the crossover value between the two power-law regimes in Fig. 2b.
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