arXiv subjects

Kostas D. Housiadas

Publications and source records attributed to Kostas D. Housiadas.

4 recordsLinked to original sources

arXiv2026

Wall slip effects on the fiber orientation of a short-fiber suspension in hyperbolic channel flow

We investigate the effect of wall fluid slip on the orientation of non-Brownian, short, rigid, and high aspect ratio cylindrical fibers suspended in a Newtonian fluid in flow through a symmetric hyperbolic planar channel. The fiber orientation is described using a second-order tensor formulation that accounts for fiber-fiber interactions and employs a hybrid closure to approximate the fourth-order orientation tensor, while neglecting the extra-stress contribution of the fibers to the total stress tensor. Building on our previous work on the no-slip case (Housiadas, Beris and Advani, J. Rheol., 2025), the analytical Newtonian velocity field that has been obtained via the extended lubrication theory is utilized (Sialmas and Housiadas, Eur. J. Mech. B Fluids, 2024). Corresponding to this velocity field, the magnitude of the rate-of-deformation decreases as the slip coefficient increases. The resulting equations for the orientation tensor are solved numerically using a fully implicit finite difference method.The results show that the fiber orientation gradually evolves from its initial pure-shear state at the inlet toward a more aligned configuration as the channel exit is approached.The region of higher fiber alignment, that is most pronounced at the midplane where the flow is purely extensional, extends further toward the walls as the slip increases.

physics.flu-dyn↗

arXiv2025

An exact solution of the lubrication equations for the Oldroyd-B model in a hyperbolic channel

An exact similarity solution of the lubrication equations for the steady flow of a viscoelastic Oldroyd-B fluid in a contracting and symmetric hyperbolic channel is derived. The solution is valid for small values of the Deborah number, De (the ratio of the polymer's longest relaxation time to a characteristic residence time of the fluid in the channel), all values of the polymer viscosity ratio, η (the ratio of polymer viscosity to the total viscosity of the fluid), as well as to typical values of the contraction ratio, Λ (the ratio of the channel height at the inlet to the channel height at the outlet). The solution, the significance of which for the hyperbolic geometry is analogous to the classic Poiseuille solution in a straight channel, precisely satisfies the exact analytical solution of the Oldroyd-B model along the walls, but does not satisfy any initial conditions for the polymer extra-stresses at the inlet of the hyperbolic section of the channel. The exact solution is given in terms of the streamfunction which is used in the momentum balance to derive a non-linear ordinary differential equation with an unknown function which corresponds to a modified fluid velocity. The final equation is solved numerically using a fully spectral method with a Galerkin-type approach to calculate the unknown function and the pressure gradient. The exact solution for the polymer extra-stresses allows for deriving a variety of expressions for the average pressure-drop in the channel. The most accurate expression is that resulting from the mechanical energy of the flow. Its range of validity is determined in terms of De, Λ and η, and confirmed by numerical pseudospectral simulations of the lubrication equations. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De and/or η is predicted.

physics.flu-dyn↗

arXiv2024

Annular Newtonian Poiseuille flow with pressure-dependent wall slip

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier's slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.

physics.flu-dyn↗

arXiv2023

Pressure-driven viscoelastic flow in axisymmetric geometries with application to the hyperbolic pipe

We investigate theoretically the steady incompressible viscoelastic flow in a rigid axisymmetric tube (cylindrical pipe) with varying cross-section. We use the Oldroyd-B viscoelastic constitutive equation to model the fluid viscoelasticity. First, we derive new exact results expressed in the form of general formulas: for the average pressure-drop through the pipe as a function of the wall shear rate and the viscoelastic axial normal extra-stress, for the viscoelastic extra-stress tensor at the axis of symmetry and the Trouton ratio of the fluid as function of the fluid velocity at the axis, and for the viscoelastic extra-stress tensor along the wall in terms of the tangential shear rate at the wall. We then proceed by exploiting the classic lubrication approximation, valid for small values of the square of the aspect ratio of the pipe, to simplify the original governing equations. The final equations are solved analytically using a regular perturbation scheme in terms of the Deborah number, De, up to eight order in De. For the specific case of a hyperbolic pipe, we reveal that the pressure-drop and the Trouton ratio (when reduced by their corresponding Newtonian values) can be recast in terms of a modified Deborah number, Dem, and the polymer viscosity ratio, η, only. Furthermore, we enhance the convergence and accuracy of the eight-order solutions by deriving transformed analytical formulas using Padé diagonal approximants. The results show the decrease of the pressure drop and the enhancement of the Trouton ratio with increasing Dem and/or increasing η. Comparison of the transformed solutions with numerical simulations of the lubrication equations using pseudospectral methods shows excellent agreement between the results revealing the robustness, validity and efficiency of the theoretical methods and techniques developed in this work.

physics.flu-dyn↗