Stable alignment of a flexible sheet-like particle in shear flow: effect of surface slip and edges.*

Very thin sheet-like particles presenting hydrodynamic surface slip (e.g., graphene colloids and other 2D nanomaterials) can attain a constant orientation in a shear flow when the slip length exceeds a length scale comparable to the particle thickness. To study the effect of bending deformations on this phenomenon, we develop a 2D fluid-structure interaction model, based on coupling the Euler-Bernoulli beam equation with a Boundary Integral method, of a flexible plate rotating in a simple shear flow. We find that: i) a stable alignment is observed even for relatively flexible particles - non-dimensional bending rigidity$\sigma_{B} /(\mu \dot{{\gamma }}a^{3})<<1$, where $\sigma_{B} $is the bending rigidity, $a$is the major semi-axis, $\dot{{\gamma }}$is the shear rate, and$\mu $is the fluid viscosity; ii) the effect of the edges on the shape of the plate is important, for values of the aspect ratio $a/b$ at least as large as 100. In our parameter range, the mild effect of flexibility on orientation is primarily due to the markedly reduced axial compressive stresses that a flow-oriented sheet presenting slip experiences, compared to a no-slip sheet. Our results are particularly relevant in view of recent research on graphene suspensions.