Translating surfactant-coated bubble
= Translating surfactant-coated bubble
{title2=$\lambda=\gamma_1C_0a/[3\mu(ka^2+2D_s)]$}
A spherical inviscid bubble moving slowly through a viscous liquid has a dipolar <surfactant> perturbation. The associated <Marangoni stress> reduces the tangential velocity from its clean-bubble value towards zero. In the linear regime, with $\mathbf u_s=A(I-\mathbf n\mathbf n)\mathbf U$, the consistent <Newtonian fluid stress tensor> gives $A=-1/[2(1+2\lambda)]$.