The difference between γ _S and γ _E, using Eq. (13). (a) External force F _ext at interfacial region shows linear dependence with sphere velocity v. The open circles indicate five different values of v. The red dashed line denotes the best fitting with a slope 1.45 × 10 − 8 kg · s − 1 , which is very close to the Stokes drag coefficient 1.41 × 10 − 8 kg · s − 1 ( = 6 π η a , 3% lower than the slope). The external force becomes zero when v is exactly at the electrophoretic velocity. The external electric field strength was maintained at E ∞ = 500 V /m. (b) Viscous force F _visc at interfacial region with sphere velocity v = μ E E ∞ . The external electric field strength is varied from 100 V/m to 500 V/m in 100 V/m steps. The red dashed line indicates fitting with slope 2.9 × 10 − 8 kg · s − 1 ( = 2.1 × 6 π η a ). All simulations were performed with surface charge density σ = − 7 × 10 3 e / μ m 2 , radius a = 0.75 μ m , and ionic strength 0.01 mM (λ _D=100 nm).