Abstract: A two-dimensional thin-walled capsule of a flexible
semi-permeable membrane is adhered onto a rigid planar substrate
under adhesive forces (derived from a potential function) in the
presence of osmosis across the membrane. The capsule is immersed
in a hypotonic and diluted binary solution of a non-electrolyte
solute. The Stokes flow problem is solved by the immersed interface
method (IIM) with equal viscosities for the enclosed and
surrounding fluid of the capsule. The numerical results obtained are
verified against two simplified theoretical solutions and the
agreements are good. The osmotic inflation of the adhered capsule is
studied as a function of the solute concentration field, hydraulic
conductivity, and the initial capsule shape. Our findings indicate that
the contact length shrinks in dimension as capsule inflates in the
hypotonic medium, and the equilibrium contact length does not
depend on the hydraulic conductivity of the membrane and the
initial shape of the capsule.