Experimental findings have well established that membranes of biological origin may exhibit stable wrinkles at low flow rates and stable pointed edges or even sharp tips at high enough flow rates. In addition, red cells affected by hereditary spherocytosis (which reduces the membrane's bending resistance) have been found to show stable pointed ends. Recent computational studies, based on low-order interfacial discretization of bi-cubic B-splines, have established the onset of interfacial buckling at low or high enough flow rates for membranes obeying the Skalak constitutive law. However those computations were unable to determine stable wrinkles and tips in disagreement with the experimental observations.

In this talk we present our computational investigation of the dynamics of stable wrinkles and tips on Skalak membranes by utilizing our high-order spectral boundary element method for cell interfacial dynamics. Our algorithm is shown to be particularly suited to determine accurately and efficiently even the most complicated membrane shapes. The physical origin of stable wrinkle and tip formation is also presented.