  It is commonly expected that a friction force on the bubble wall in a
first-order phase transition can only arise from a departure from thermal
equilibrium in the plasma. Recently however, it was argued that an effective
friction, scaling as $\gamma_w^2$ (with $\gamma_w$ being the Lorentz factor for
the bubble wall velocity), persists in local equilibrium. This was derived
assuming constant plasma temperature and velocity throughout the wall. On the
other hand, it is known that, at the leading order in derivatives, the plasma
in local equilibrium only contributes a correction to the zero-temperature
potential in the equation of motion of the background scalar field. For a
constant plasma temperature, the equation of motion is then completely
analogous to the vacuum case, the only change being a modified potential, and
thus no friction should appear. We resolve these apparent contradictions in the
calculations and their interpretation and show that the recently proposed
effective friction in local equilibrium originates from inhomogeneous
temperature distributions, such that the $\gamma_w^2$-scaling of the effective
force is violated. Further, we propose a new matching condition for the
hydrodynamic quantities in the plasma valid in local equilibrium and tied to
local entropy conservation. With this added constraint, bubble velocities in
local equilibrium can be determined once the parameters in the equation of
state are fixed, where we use the bag equation in order to illustrate this
point. We find that there is a critical value of the transition strength
$\alpha_{\rm crit}$ such that bubble walls run away for $\alpha>\alpha_{\rm
crit}$.
