Mathematical model of the inflation of a spherical layer of a non-Newtonian fluid in conditions of weightlessness

The paper proposes a mathematical model of the inflation of a liquid spherical layer to a specified size through the injection of gas into a gaseous cavity. Attention is given to a spherically symmetric layer of liquid with viscoelastic properties, e.g., a polymer or oligomer. The problem considered is how to organize in time the gas delivery into the gas bubble in such a way that the spherical layer is inflated to a specified size while the layer remains liquid. The modeling is based on the equations of continuum mechanics and thermodynamics.