  The quantitative extraction of quark-gluon plasma (QGP) properties from
heavy-ion data, such as its specific shear viscosity $\eta /s$, typically
requires comparison to viscous hydrodynamic or "hybrid" hydrodynamics+transport
simulations. In either case, one has to convert the fluid to hadrons, yet
without additional theory input the conversion is ambiguous for dissipative
fluids. Here, shear viscous phase-space corrections calculated using linearized
transport theory are applied in Cooper-Frye freezeout to quantify the effects
on anisotropic flow coefficients $v_n(p_T)$ at both RHIC and LHC energies.
Expanding upon our previous flow harmonics studies [1,2], we calculate pion and
proton $v_2(p_T)$, $v_4(p_T)$, and $v_6(p_T)$. Unlike in Ref. [1], we
incorporate a hadron gas that is chemically frozen below a temperature of 175
MeV, and use hypersurfaces from realistic viscous hydrodynamic simulations.
With additive quark model cross sections and relative phase-space corrections
with $p^{3/2}$ momentum dependence, rather than the quadratic Grad form, we
find at moderately high transverse momentum noticeably higher $v_4(p_T)$ and
$v_6(p_T)$ for protons than for pions. In addition, the value of $\eta /s$
deduced from elliptic flow data differs by nearly 50\% from the value extracted
using the naive "democratic Grad" form of freeze-out distributions. To
facilitate the use of the self-consistent viscous corrections calculated here
in hydrodynamic and hybrid calculations, we also present convenient
parameterizations of the corrections for the various hadron species (cf. Table
I).
