In this paper is proposed an analytical technique which can be used to obtain the forced response of a cantilevered tube conveying fluid. Considering the pipe subjected to an arbitrary harmonic force either distributed or concentrated, an analytical solution is found using Green’s function method. The solution obtained of the closed form satisfies the differential equations in a classical sense. The presented method giving the exact solutions is more precise than the classical eigenfunction expansion or Galerkin’s method with no need to the eigenfunctions or eigenvalues.

In this paper, a numerical modeling of the impact, spreading, and eventually rebound of a viscoelastic droplet is reported. The numerical model is based on the volume of fluid (VOF) method coupled with the FENE-CR constitutive equations, and accounts for both the surface tension and the substrate wettability. The FENE-CR constitutive equations are used to model the polymer solution, while taking advantage of its rheological characterization. The comparison is performed between droplets of Newtonian solvent and a monodisperse polymer solution. The droplet impact on both hydrophilic and superhydrophobic substrate is analyzed through a detailed analysis of the spreading diameter evolution. It is found that while the droplet kinematic phase seems independent of the substrate and fluids properties, the recoiling phase is highly related to all of them. In addition, the model infers a critical polymer concentration above which the droplet rebound from a superhydrophobic substrate is suppressed. The simulation is of particular interest to ink-jet processing, and demonstrates the capability of the model to handle complex non-Newtonian droplet dynamics.

Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by direct simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive meshing technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a good master curve is derived when normalizing the mobility for both the carbonate and the sandstone.