(a) Comparison between the friction coefficients Γ ( 1 ) calculated from D ′ s ( n ) and the friction coefficients Γ ∥ , ⊥ ( 2 ) of the three samples S1 (black pentagon), S2 (red dot), and S3 (purple star) on a log–log plot. The solid dots correspond to Γ ∥ ( 2 ) , and the open dots correspond to Γ ⊥ ( 2 ) . The cyan line is the guide for the eye, where the slope of the line is 1.0. In the inset, a comparison is shown between the friction coefficients Γ ∥ ( 2 ) and Γ ⊥ ( 2 ) on a log–log plot. The cyan line is the guide for the eye, where the slope of the line is 1.0. (b) The friction coefficient Γ ⊥ ( 2 ) obtained from R ⊥ = λ s follows a power-law relationship with the friction coefficient Γ ( 1 ) for the three samples. The cyan lines represent fits of the form Γ ⊥ ( 2 ) ∼ ( Γ ( 1 ) ) 2 / 3 . (c) Relationship between the characteristic lengths R ∥ and R ⊥ scaled by the particle radius a for the three samples on a log–log plot. The green line is the fit to R ∥ / a = ( R ⊥ / a ) 3 / 2 .