Model of blood flow along the arterial bed, taking into account the bioactivity of the vessel wall

The modification of a two-dimensional model of incompressible viscous fluid motion along a deformed thick-walled tube from viscoelastic bioactive material is proposed in connection to the modeling of blood flow along the arterial bed is proposed. The motion of a viscous incompressible fluid is described by a system of equations including the Navier-Stokes equations and the continuity equation. The behavior of the tube wall material is described by a 5-element rheological model with one active element. The solution of the problem is solved setting boundary conditions on the interface of the two media, the outer surface of the tube is considered as non-moving. At the end of the tube, a zero-dimensional Frank model with regulation is considered, as a model of the microcirculatory bed. The dispersion equation for the propagation of wave velocity is obtained for the case of active properties of tube, the amplitudes of fluid velocities, wall displacements, and fluid and tube pressures. Numerical computations have been carried out for the model parameters corresponded to the normal and pathological arterial wall.

Stokes Flow between Two Cylinders

The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been evaluated. Some numerical values for the force have been presented in a table and compared with corresponding known values where both inner and outer cylinders are rigid. DOI: http://dx.doi.org/10.3329/jbas.v36i1.10928 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 1, 123-135, 2012

The Analysis of Wave Form for 3-D Wave Tank

The 3-D numerical model of wave tank is developed considering the effects of wave generating and absorbing based on viscous fluid motion differential equations (N-S equation) and the volume of fluid (VOF) method by the use of FLUENT solver. The simulation is also made by the analysis of the existing methods of wave simulation. The wave form of the 3-D wave tank is analyzed with the result of diverse diversification at different wave location and their relationship. The flow path of each particle of the wave during the propagation is also been analyzed, which provides guidance for the wave form analysis.

Rheological Properties of Emulsions Immersed in Electric Fields

The results of fully three-dimensional direct numerical simulations of the effects of electric fields on emulsions of drops will be displayed. The examination of the rheological properties of these systems is performed by imposing a simple-shear flow between two plates where the drops are immersed. An electric potential difference is applied perpendicular to the plates. The resulting electric field leads to two effects: a polarization of the drops and a viscous fluid motion on the interface between the drops and the suspending fluid. The direction and intensity of the viscous fluid motion depends on the electrical properties of the fluids. Drops more conductive than the suspending fluid exhibit a viscous fluid motion from the equator to the poles, whereas drops less conductive than the suspending fluid exhibit a viscous fluid motion from the poles to the equator. The numerical simulations show that the response of the emulsions is governed by the competition between the electric attraction and the fluid shear. The former leads to the aggregation of the drops in chains parallel to the electric field, while the latter tries to break-up the aggregated chains. The results are presented as a function of the Mason number and the electric capillary number, Mn and Ce. These non-dimensional numbers quantify the strength of the electric forces versus the fluid shear and the capillary forces, respectively. The significance of the electrical field on the viscosity and the normal stress differences will be discussed: At low Mason numbers, Mn<0.1, the application of the electric field results in the aggregation of the drops. This aggregation leads to an increase in the effective viscosity of the system and to an increase in the stresses, which result in higher normal stress differences than in hydrodynamic emulsions. At high Mason numbers, Mn>1.0, the fluid shear breaks up the aggregated structures and the properties are similar to hydrodynamic emulsions. At 0.1<Mn<1.0 the properties of the emulsions exhibit an intermediate behavior.