On finite element modelling of surface tension phenomena.

The objective of this work is to develop a computational framework for modelling the motion of liquid phase between moving particles associated with the processing of complex multiphase materials. The liquid phase may be present at various levels of saturation and necessarily includes numerous and irregular free surfaces. In this kind of situation the surface tension is dominant and governs the interparticle motion that plays a fundamental role during material processing. This work focuses on surface tension modelling using the finite element method. Two issues related to the modelling of surface tension are addressed in this thesis, the first one is the development of a finite element procedure capable of modelling accurately the motion of the free surface boundaries between the gas and liquid phases. The second issue is finite element modelling of surface tension at such boundaries. The finite element formulation is based on the use of the incremental flow formulation of the Lagrangian form of the initial boundary value problem governing the free surface flow. The incompressibility constraint associated with the Newtonian fluid employed in this work is imposed using the penalty method. With regard to the surface tension model, the constitutive model commonly known as the Laplace-Young equation is employed. In the Lagrangian framework the surface tension formulation emerges naturally through the weak form of the Laplace-Young equation and the use of the surface divergence theorem reduces the continuity requirement across the element boundary from to C[1] to C[0]. The performance of the finite element model of surface tension is validated by means of numerical examples for both equilibrium and dynamic cases. The finite element results are compared against both analytical solutions and experimental results

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