It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter
$\lambda$
is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle
$(1/2)\cos ^{-1}((1-k)/(1+k))$
to the flow direction where
$0 \le k \le 1$
is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of
$1/\lambda$
and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle
$k < 1$
provided
$\lambda \ge \lambda _{crit}(k)$
where
$\lambda _{crit}(k)$
is a critical Navier-slip length parameter determined here. As the case
$k \to 1$
of a circular cross-section is approached, it is found that
$\lambda _{crit}(k) \to \infty$
, so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.
Study of Effective Edge Safety Factor Using Analytical Solution of Grad-Shafranov Equation for Circular Cross Section Tokamak