Effective picture of bubble expansion

Recently the thermal friction on an expanding bubble from cosmic first-order phase transition has been calculated to all orders of interactions between wall and plasma, leading a $\gamma^2$-scaling instead previously estimated $\gamma^1$-scaling for exerted fast-moving with Lorentz factor $\gamma$. We propose first time effective equation motion (EOM) in presence arbitrary $\gamma$-scaling compute efficiency collisions, which, case friction, is found be larger than recently updated estimation when walls collide after starting approach constant terminal velocity, slightly signal gravitational waves background collisions due its quadratic dependence collision factor, although itself already suppressed contribution compared that friction. also suggest phenomenological parameterization out-of-equilibrium term Boltzmann could reproduce $(\gamma^2-1)$-scaling EOM wall, which merits further study future numerical simulations expansion collisions.