Shear-induced domain deformation in a tilted lipid monolayer: from circle to ellipse and kinked stripe

The shear-induced domain deformation in a lipid monolayer comprised of tilted molecules is studied as a mechanical balance between surface pressure, line tension, electrostatic energy due to the dipole-dipole interaction, hexatic-elastic stress, and viscous stress. It is found that a simple shear can deform a circular domain into an elliptic shape with the long axis inclined 45 degrees from the shear direction. The "ellipse" is elongated in the long axis as shear rate increases, and evolves to a straight or kinked stripe, which was observed as a "shear band" by Fuller's group [Science 274, 233 (1996)] and "avalanche-like fronts" by Schwaltz's group [Langmuir 17, 3017 (2001)], at a threshold shear rate. The propagation of stripe-shaped domains is discussed in the context of electrostatic energy. The dependence of the threshold shear rate on surface pressure is predicted in good agreement with observation and can be used to estimate surface viscosity. The shear-induced domain deformation is maintained by the effect of the lattice elastic stress when shear ceases.