  A thermodynamically consistent phase-field model is introduced for simulating
multicellular deformation, and aggregation under flow conditions. In
particular, a Lennard-Jones type potential is proposed under the phase-field
framework for cell-cell, cell-wall interactions. A second-order accurate in
both space and time $C^0$ finite element method is proposed to solve the model
governing equations. Various numerical tests confirm the convergence, energy
stability, and nonlinear mechanical properties of cells of the proposed scheme.
Vesicles with different adhesion are also used to explain the pathological risk
for patients with sickle cell disease.
