PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 16

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Heuristic derivation of Brinkman's seepage equation
Wojnar R.
Technical Sciences / University of Warmia and Mazury in Olsztyn
|
2017
|
nr 20(4)
359--374
EN
Brinkman’s law is describing the seepage of viscous fluid through a porous medium and is more acurate than the classical Darcy’s law. Namely, Brinkman’s law permits to conform the flow through a porous medium to the free Stokes’ flow. However, Brinkman’s law, similarly as Schro¨dinger’s equation was only devined. Fluid in its motion through a porous solid is interacting at every point with the walls of pores, but the interactions of the fluid particles inside pores are different than the interactions at the walls, and are described by Stokes’ equation. Here, we arrive at Brinkman’s law from Stokes’ flow equation making use of successive iterations, in type of Born’s approximation method, and using Darcy’s law as a zero-th approximation.
2
Content available remote Macroscopic thermal properties of quasi-linear cellular medium on example of the liver tissue
Gambin B., Kruglenko E., Gałka A. A., Wojnar R.
Computer Assisted Methods in Engineering and Science
|
2015
|
Vol. 22, no. 4
329--346
EN
There are two main topics of this research: (i) one topic considers overall properties of a nonlinear cellular composite, treated as a model of the liver tissue, and (ii) the other topic concerns the propagation of heat in the nonlinear medium described by the homogenised coefficient of thermal conductivity. For (i) we give a method and find the effective thermal conductivity for the model of the liver tissue, and for the point (ii) we present numerical and analytical treatment of the problem, and indicate the principal difference of heat propagation in linear and nonlinear media. In linear media, as it is well known, the range of the heat field is infinite for all times t > 0, and in nonlinear media it is finite. Pennes’ equation, which should characterize the heat propagation in the living tissue, is in general a quasi-nonlinear partial differential equation, and consists of three terms, one of which describes Fourier’s heat diffusion with conductivity being a function of temperature T. This term is just a point of our analysis. We show that a nonlinear character of the medium (heat conductivity dependent on the temperature) changes in qualitative manner the nature of heat transfer. It is proved that for the heat source concentrated initially (t = 0) at the space point, the range of heated region (for t > 0) is finite. The proof is analytical, and illustrated by a numerical experiment.
3
Content available Laminar flow past the bottom with obstacles – a suspension approximation
Wojnar R., Bielski W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
|
Vol. 63, nr 3
685--695
EN
From Albert Einstein’s study (1905) it is known that suspension introduced to a fluid modifies its viscosity. We propose to describe the influence of obstacles on the Stokesian flow as a such modification. Hence, we treat the fluid flow through small obstacles as a flow with suspension. The flow is developing past the plane bottom under the gravity force. The spatial distribution of suspension concentration is treated as given, and is regarded as an approximation of different obstacles which modify the fluid flow and change its viscosity. The different densities of suspension are considered, beginning of small suspension concentration until 40%. The influence of suspension concentration on fluid viscosity is analyzed, and Brinkman’s formula as fitting best to experimental data is applied.
4
Content available Flow of Stokesian fluid through a cellular medium and thermal effects
Wojnar R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 2
321--329
EN
The thermal effects of a stationary Stokesian flow through an elastic micro-porous medium are compared with the entropy produced by Darcy’s flow. A micro-cellular elastic medium is considered as an approximation of the elastic porous medium. It is shown that after asymptotic two-scale analysis these two approaches, one analytical, starting from Stoke’s equation and the second phenomenological, starting from Darcy’s law give the same result. The incompressible and linearly compressible fluids are considered, and it is shown that in micro-porous systems the seepage of both types of fluids is described by the same equations.
5
Content available Boussinesq equation for flow in an aquifer with time dependent porosity
Wojnar R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2010
|
Vol. 58, nr 1
165-170
EN
A problem of the Boussinesq type for flow of incompressible fluid through a medium with the porosity being a given function of time is studied. At first, from the continuity equation the Dupuit relation for the fluid velocity in the considered medium is found. Next the Boussinesq equation is derived for the medium. This equation, if written for quantity H = h/ and not for the hydraulic head h, has a form of the classical Boussinesq equation, with the coefficient not constant but dependent on time, however. An example of the solution of the modified Boussinesq equation is also given.
6
Content available remote Electrokinetics in random piezoelectric porous media
Telega J.J., Wojnar R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2007
|
Vol. 55, nr 1
125-128
EN
Macroscopic coefficients together with a Darcy law are obtained for porous piezoelectric medium wit h random, not necessarily ergodic, distribution of pores in which a two-ionic electrolyte flows. Peculiarities of stochastic porosity are indicated.
7
On the Smoluchowski flow in zeta-potential
Wojnar J., Wojnar R.
Journal of Technical Physics
|
2006
|
Vol. 47, no 1
39-46
EN
Two-scale expansion of functions describing stationary incompressible flow in electric field is used at first to recover the Smoluchowski formula for electrolyte incompressible flow, conditioned by zeta-potential of electric double layer (EDL) and to observe that the pressure is not constant along the depth of the EDL. Next, the analogous formula for non-incompressible electrolytes is derived.
8
Content available Structural control in tissue development
Wojnar R
Journal of Theoretical and Applied Mechanics
|
2005
|
Vol. 43 nr 4
805--812
EN
Occurrence of defects begins a process of destruction of a crystal, its existence is, however, necessary for the crystal growth. In an analogous manner as in propagation of defects during crystallization, the growing of a tissue stress leads to buckling and undulation down to order of the cell diameter. It is shown that the structural control in a tissue development is accomplished by wave-like rearrangement of 5-7 dislocations. The oriented cell divisions as 5-7 climbing can be explained analogously.
PL
Pojawienie się defektów w krysztale zapoczątkowuje jego zniszczenie, jednak ich istnienie i ruch jest konieczne także podczas wzrostu. W podobny sposób, w jaki powstaje ruch defektów w czasie krystalizacji, napięcia wzrostu tkanki wywołują wyboczenie i falowanie struktury na różnych poziomach aż do poziomu komórki. Pokazujemy, że sterowanie rozwojem tkanki biologicznej zachodzi poprzez falopodobną zmianę układu dyslokacji typu 5-7. Podobnie jako pojawianie się układów komórek typu 5- i 7-kątów można wyjaśnić podział zorientowanych komórek.
9
Content available Piezoelectric effects in biological tissues
Telega J. J., Wojnar R
Journal of Theoretical and Applied Mechanics
|
2002
|
Vol. 40 nr 3
723-759
EN
The aim of this paper is to analyze different contibutions and differents points of view concerning the meaning of the piezoelectric effect in the bone. It is now obvious that this effect is overhelming in dry bone. In wet bone more important are streaming potentials.
PL
Analizujemy różne prace i różne punkty widzenia dotyczące zjawiska piezoelektrycznego w kości i jego znaczenia dla biologii tej tkanki. Zjawisko to obserwowane wyraźnie w kości suchej, odgrywa według ostatnich badań mniejszą niż sądzono początkowo rolę w procesach adaptacyjnych kości żywej. Tym niemniej własności piezoelektryczne są istotne dla różnych procesów biologicznych.
10
Content available Modelling electric and elastic properties of cartilage
Gałka A., Telega J. J., Wojnar R.
Engineering Transactions
|
2001
|
Vol.49, iss.2/3
283-313
EN
The aim of the paper is to propose a novel approach to modelling the macroscopic electromechanical behaviour of cartilage within the framework of linear response. The cartilage is treated as multiphase material with four constituents: anions, cations, viscous fluid and piezoelectric skeleton. The macroscopic equations were derived by using homogenization methods. Only stationary flow was studied. The elastic macroscopic moduli were determined by assuming, after Broom [60], the honeycomb microstructure of the cartilage. Mathematical developments are preceded by a review of structure and properties of a cartilage.
11
Content available remote Nonstationary two-phase flow through elastic porous medium
Bielski W., Telega J. J., Wojnar R.
Archives of Mechanics
|
2001
|
Vol. 53, nr 4-5
333-366
EN
The aim of this contribution is to derive macroscopic equations governing the dynamic flow of two immiscible viscous fluids through an elastic microperiodic porous medium. To this end homogenization methods were employed. The procedure used can be justified by the method of two-scale convergence. Passage to the stationary case and illustrative example were also provided.
12
Content available Thermodynamics of solids with a state equation
Wojnar R.
Journal of Theoretical and Applied Mechanics
|
1999
|
nr 4
809-827
EN
The thermodynamic relations describing equilibrium of a multi--phase thermoelastic solid are obtained in a way similar to that used in the multiphase fluid theory. The phase transitions of the first order are defined and equilibrium equations of the Capeyron--Clausius type are derived. Also, the phase transistions of the second order are introduced and equilibrium equations of the Ehrenfest type are obtained. A general theory is illustrated by examples.
PL
Analizujemy związki termodynamiczne opisujące równowagę ciała termosprężystego złożonego z wielu faz. Czynimy to w sposób podobny do stosowanego w teorii płynów wielofazowych. Po określeniu przejść fazowych drugiegi i trzeciego rodzaju wyprowadzamy związki typu Clapeyrona--Clausiusza i Ehrenfesta. Ogólną teorię uzupełniamy przykładami.
13
Content available remote Macroscopic equations for nonstationary flow of Stokesian fluid through porous elastic medium
Bielski W., Telega J., Wojnar R.
Archives of Mechanics
|
1999
|
Vol. 51, nr 3-4
243-274
EN
The aim of this contribution is to apply homogenization methods in order to describe the nonstationary flow of a viscous fluid through a microperiodic porous elastic medium. By using the method of two-scale asymptotic: expansions, the macroscopic phenomenological equations describing such a two-phase structure are derived and the formulae for the effective mechanical coefficients are given. The asymptotic approach is justified by the two-scale convergence. It is shown that Darcy's law is nonlocal in time.
14
Content available remote Distortion equation of motion in linear incompatible elastodynamics
Wojnar R.
Archives of Mechanics
|
1999
|
Vol. 51, nr 1
3-13
EN
The paper deals with an initial-boundary value problem of linear incompatible elastodynamics, based on Kosevich' theory of continuonsly distributed defects due to prescribed plastic fields, [1, 2, 3]. In analogy to a stress formulation of linear incompatible elastodynamics with continuously distributed defects, [4], a distortion formulation is proposed. In such a formulation the tensorial inlitial-boundary value problem for an unknown asymmetric tensor field is to be solved. A solution to the problem generates the associated stress and rotation fields.
15
On fluctuations in thermoelasticity of composites
Wojnar R.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika
|
1998
|
Z. 66
277-283
16
Content available Flow of conductive fluids through poroelastic media with piezoelectric properties
Telega J.J., Wojnar R.
Journal of Theoretical and Applied Mechanics
|
1998
|
nr 3
775-794
EN
The aim of this contribution is to elaborate a general framework for modelling flows of electrolytes through porous piezoelectric media. Organic materials like animal and human bones provide an example of materials to which our results apply, though in wet bones the piezoelectric effect is smaller than the electrokinetic one. Those materials may be treated as piezoelectric porous materials through which a condictive fluid flows. The present work is confined to a regular distribution of poroes. On the interfaces between the piezoelectric skeleton and conductive fluid natural jump conditions are imposed. By using the method of two-scale asymptotic expansions, the macroscopic phenomenological equations describing electrokinetics of such a two-phase structure are derived and the formulae for the effective mechanical and nonmechanical coefficients are given.
PL
W pracy podajemy ogólny opis przepływu elektrolitu przez porowaty ośrodek piezoelektryczny. Otrzymane wyniki mogą być wykorzystane do materiałów organicznych; kości zwierząt i ludzi stanowią przykład takich materiałów, choć w kościach żywych efekt piezoelektryczny jest mniejszy od elektrokinetycznego. W niniejszej pracy ograniczamy się do regularnego (okresowego) rozkładu porów. Na powierzchniach między fazami zakładamy naturalne warunki styku. Korzystamy z metody dwuskalowych rozwinięć asymptotycznych i wyprowadzamy makroskopowe równanie fenomenologiczne dla elektrokinetyki takiego układu dwufazowego. Podajemy też wzory matematyczne na współczynniki skuteczne (zhomogenizowane), zarówno mechaniczne jak i niemechaniczne.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.