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Analytical solutions for a general mixed boundary value problem associated with motions of fluids with linear dependence of viscosity on the pressure

Vieru D., Fetecau C., Bridges C.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

181--197

EN

An unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finie Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

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Basic flows of generalized second grade fluids based on a Sisko model

Walicka A.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

1019--1033

EN

The present investigation is concerned with basic flows of generalized second grade fluids based on a Sisko fluid. After formulation of the general equations of motion three simple flows of viscoplastic fluids of a Sisko type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow in a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation the Sisko model one was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.

3

Characteristics of falling liquid films of surfactants and polymers solutions

Broniarz-Press L., Dulska D.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no spec

77-83

EN

In the present work the results of the studies on the effect of surface active-agents and polymers on a mean film thickness have been presented. The experimental studies on mean thickness of a film of water and aqueous solutions of hexadecyltrimethylammonium bromide HTAB and polyacrylamide flowing down the hydrophobic organic glass plate, have been carried outIt was stated that the reduction of the film thickness is observed when the shear induced structures of a polymer and surfactant are present in a solution. The best results were obtained for aqueous solutions of HTAB with addition of sodium salicylate.

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Numeryczne modelowanie przepływu nieściśliwego płynu lepkiego metodą rzutowania i dekompozycji operatora różniczkowego

Kudela H., Lewtak R.

Inżynieria Chemiczna i Procesowa

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2004

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T. 25, z. 4

2207-2213

PL

Przedstawiono metodę numerycznego rozwiązywania niestacjonarnych równań ruchu płynu lepkiego w przestrzeni trójwymiarowej. Oryginalną cechą proponowanej metody numerycznej jest połączenie w jednym algorytmie numerycznym dwóch metod: metody rzutowania (dekompozycji) wektora prędkości i (dekompozycji operatora różniczkowego wzdłuż kierunków przestrzennych. Uzyskany w ten sposób algorytm numeryczny umożliwia zastosowanie w obliczeniach szybkiej metody bezpośredniej rozwiązywania macierzy trójprzekątniowej.

EN

The paper presents a numerical method for modelling of an unsteady incompressible flow of viscous fluid in a three-dimensional domain. The characteristic feature of the numerical method is nice coupling of the projection method and the operator splitting method into one numerical algorithm. The numerical method was found as a very attractive way of solving equations of the fluid motion since a fast direct method for solving a three-diagonal matrix was used in the computation.