Table 4.

Summary of asymptotic limits, when available, of the resistance coefficient |F|/4πηR|U| for the translation of a cylindrical disk.

	deep subphase (H ≫ R)	shallow subphase (H ≪ R)
clean interface	$\frac{4}{3\pi }$	$\frac{2}{5}\frac{R}{H}$
Incompressible, inviscid monolayer Ma ≫ 1 and Bq = 0	$\frac{2}{\pi }$	$\frac{1}{2}\frac{R}{H}$
Incompressible, viscous monolayer Ma ≫ 1 and Bq → ∞	$\frac{Bq}{\text{log}(2Bq)-{\gamma }_E}$	$\frac{Bq}{\text{log}(2\sqrt{BqH/R})-{\gamma }_E}$
Compressible, inviscid monolayer Ma → 1 and Bq → 0	$\frac{4}{3\pi }$	$\frac{2}{5}\frac{R}{H}$
Compressible, viscous monolayer Ma → 1, Bq → ∞, and κs ≪ ηs	-	$\frac{Bq/2}{\text{log}(\sqrt{2BqH/R})-{\gamma }_E}$
Compressible, viscous monolayer Ma → 0, Bq → ∞, and κs ≫ ηs	-	$\frac{Bq}{\text{log}(2\sqrt{BqH/R})-{\gamma }_E}$