Inflation dynamics of fluid annular menisci inside a mold cavity—I. Deformation driven by small gas pressures

On the gas-penetration in straight tubes completely filled with a viscoelastic fluid

“…For the boundary integral term on the free surface, we use Ruschak's [27] idea in order to avoid the appearance of second derivatives in the normal force balance. According to it, the mean curvature multiplied by the normal vector of the free surface is split into two parts: one that describes the change of the tangential vector along the free surface and another one where the normal vector is multiplied by the inverse of the second principal radius of curvature of the surface; see also Poslinski and Tsamopoulos [28]. In order to impose fully developed flow at the tube exit we use the open boundary condition of Papanastasiou et al [29], which is based on the simple evaluation of the integral Γ [n · (−PI + τ)]φ i dΓ along that boundary.…”

Numerical simulation of bubble growth in Newtonian and viscoelastic filaments undergoing stretching

“…The numerical scheme determines simultaneously the velocity and pressure fields, the geometry of the bubble-liquid and liquid-air interfaces and the gas pressure inside the bubble [37][38][39]. For a viscoelastic medium, the stress components should also be determined at each time step, together with the rest of the unknowns.…”

A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations

“…These, when mapped to the physical domain, were found to better conform to its large deformations. The mixed Galerkin finite element method was used following the work by Poslinski et al [17,18] for viscous free-surface problems. With the term ÔmixedÕ we imply using higher order polynomials to interpolate the velocity field than the pressure in order to comply with the Babuska-Brezzi condition [31].…”

“…The mean curvature has to be specially treated as it involves products of the free surface position with its second derivative. Using the methodology proposed by Ruschak [32] and applied by Poslinski and Tsamopoulos [17], the mean curvature on the free surface is split into two parts. The first term is the derivative of the tangent vector, t, of the free surface with respect to its arc length (s), while the second part is composed of the normal vector multiplied by the inverse of the second principal radius,…”

“…The evolving physical domain is mapped onto a simple and time-independent computational one in which the moving boundary coincides with one of the coordinate surfaces and in which it is trivial to generate the mesh. It is fairly easy to perform this boundaryconforming mapping using simple algebraic relations [10,17,18]. However, this technique is restricted to relatively simple initial shapes and small deformations and requires that the mapping function is singlevalued.…”