  The Sakiadis boundary layer induced by a moving wall in a semi-infinite fluid
domain is a fundamental laminar flow field relevant to high speed coating
processes. This work provides an analytical solution to the boundary layer
problem for Ostwald-de Waele power law fluids via a power series expansion, and
extends the approach taken for Newtonian fluids [Naghshineh et al., "On the use
of asymptotically motivated gauge functions to obtain convergent series
solutions to nonlinear ODEs", IMA J. of Appl. Math., (2023)] in which variable
substitutions (which naturally determine the gauge function in the power
series) are chosen to be consistent with the large distance behavior away from
the wall. Contrary to prior literature, the asymptotic behavior dictates that a
solution only exists in the range of power law exponents, $\alpha$, lying in
the range $0.5 < \alpha \leq 1$. An analytical solution is obtained in the
range of approximately $0.74 \leq \alpha < 1$, using a convergent power series
with an asymptotically motivated gauge function. For power laws corresponding
to $0.5 < \alpha<0.74$, the gauge function becomes ill-defined over the full
domain, and an approximate analytical solution is obtained using the method of
asymptotic approximants [Barlow et al., "On the summation of divergent,
truncated, and underspecified power series via asymptotic approximants", Q. J.
Mech. Appl. Math., (2017)]. The approximant requires knowledge of two physical
constants, which we compute a priori using a numerical shooting method on a
finite domain. The utility of the power series solution is that it can be
solved on the entire semi-infinite domain and--in contrast to a numerical
solution--does not require a finite domain length approximation and subsequent
domain length refinement.
