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Dispersion Curves of Love Waves in Elastic Waveguides Loaded with a Newtonian Liquid Layer of Finite Thickness

Kiełczyński Piotr, Szalewski Marek, Balcerzak Andrzej, Wieja Krzysztof

Archives of Acoustics

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2020

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Vol. 45, No. 1

19--27

EN

In this paper, the authors analyse the propagation of surface Love waves in an elastic layered waveguide (elastic guiding layer deposited on an elastic substrate) covered on its surface with a Newtonian liquid layer of finite thickness. By solving the equations of motion in the constituent regions (elastic substrate, elastic surface layer and Newtonian liquid) and imposing the appropriate boundary conditions, the authors established an analytical form of the complex dispersion equation for Love surface waves. Further, decomposition of the complex dispersion equation into its real and imaginary part, enabled for evaluation of the phase velocity and attenuation dispersion curves of the Love wave. Subsequently, the influence of the finite thickness of a Newtonian liquid on the dispersion curves was evaluated. Theoretical (numerical) analysis shows that when the thickness of the Newtonian liquid layer exceeds approximately four penetration depths 4δ of the wave in a Newtonian liquid, then this Newtonian liquid layer can be regarded as a semi-infinite half-space. The results obtained in this paper can be important in the design and optimization of ultrasonic Love wave sensors such as: biosensors, chemosensors and viscosity sensors. Love wave viscosity sensors can be used to assess the viscosity of various liquids, e.g. liquid polymers.

2

Foam drainage on thick porous substrate

Armstrong T., Smith H., Arjmandi-Tash O., Cook J., Trybala A., Starov V.

Physicochemical Problems of Mineral Processing

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2018

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Vol. 54, iss. 1

193--202

EN

The use of foam-based applications as a method of drug delivery represents a recent and promising area of research. The interaction of foam and porous substrates have been recently theoretically described using a mathematical model, which combines the equation of foam drainage with that of imbibition of liquid into the porous substrate. Below the drainage of foam placed on chalk experimentally investigated to verify the theory prediction. The surfactants sodium dodecyl sulfate (SDS) and Triton X-100 were used to form a foam. The initial liquid volume fractions of the foam were found to be ranging in between 14.12 and 16.46%. The porosity and permeability of the chalk substrate were experimentally obtained at 59.1% and 3.122·10-11 m2 respectively. The height of foam deposited onto the thick porous substrate (chalk) was 2.5 cm and 6 cm. The imbibition into the chalk, the height of foam, and the bubble size within the foam were monitored. The latter enabled the kinetics of the drainage/imbibition to be determined and compared with the predictions according to the theoretical model. The rate of decrease in foam height was initially high and decreased over time as predicted by the theoretical model. All the foam displayed an initial rapid imbibition through the porous substrate, which is again in the agreement with the theory predictions. It was found that solutions with lower surfactant concentrations could penetrate deeper into the chalk. The imbibition front was observed to be uniform: evenly distributed liquid throughout the cross-section of the porous substrate.

3

A new analytical procedure for solving the non-linear differential equation arising in the stretching sheet problem

Siddheshwar P. G., Mahabaleswar U. S., Andersson H. I.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

955--964

EN

The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

4

Współczynniki wypływu cieczy przez otwory o nieregularnych kształtach

Dziubiński M., Przelazły Ł.

Inżynieria i Aparatura Chemiczna

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2009

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Nr 4

31-33

PL

W niniejszym artykule przedstawiono wyniki badań dotyczące grawitacyjnego wypływu cieczy ze zbiorników przez otwory o nieregularnych kształtach. Uzyskany szeroki zakres danych eksperymentalnych opisano oryginalnymi równaniami korelacyjnymi i przedstawiono w postaci zależności φ=f(Re).

EN

Experimental investigations of Iiquid discharge from vessels through irregularly shaped orifices arę presented in the paper. A wide rangę of experimental data were correlated by original correlation equations and presented in figures according to the dependence φ=f(Re).

5

Wpływ wielkości i kształtów otworów na wartość współczynnika wypływu mieszanin dwufazowych ciecz - gaz ze zbiornika

Dziubiński M., Przelazły Ł.

Inżynieria i Aparatura Chemiczna

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2009

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Nr 6

57-59

PL

W niniejszym artykule przedstawiono wyniki badań dotyczące wypływu mieszanin dwufazowych ciecz — gaz ze zbiornika przez otwory o nieregularnych kształtach. Uzyskany szeroki zakres danych eksperymentalnych opisano oryginalnymi równaniami korelacyjnymi i przedstawiono w postaci zależności φ = f(Re).

EN

Experimental investigation results of two-phase gas - liquid mixture discharge through irregularly shape orifices from a vessel are presented in the paper. A wide range of experimental data were correlated using original correlation equations and presented in a form of dependence φ = f(Re).

6

A collocation method utilizing curvilinear coordinates and Bézier surfaces for analysis of a flow of Newtonian liquids

Zapomel J

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2006

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z. 31

161-164

EN

A new collocation method for analysis of a flow of Newtonian liquids based on application of curvilinear coordinates has been developed. The procedure arrives at division of the investigated region into quadrilateral domains and at approximation of the geometrie, pressure, and velocity parameters by Bezier surfaces in each domain. These approximations are substituted into the Navier-Stokes equations and into the equation of continuity and the unknowns are the control points, the parametres defining the Bézier surfaces. Their calculation strats from satisfying the Navier-Stokes equations and the equation of continuity at a specified number of collocation points whose positions in the domains are defined by curvilinear coordinates. This results into a set of overestimated linear algebraic equations and their solution must satisfy the boundary conditions and the conditions of continuity at borders of the adjacent domains. Advantage of this approach is that no new discretization is needed if the shape of the investigated region is changed.

7

Wypływy cieczy newtonowskich i nienewtonowskich ze zbiornika przez otwory o nieregularnych kształtach

Dziubiński M., Przelazły Ł.

Inżynieria i Aparatura Chemiczna

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2006

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Nr 4s

38-39

EN

Experimental investigations of liquid discharge through orifices arising during breakdown of a vessel have been presented. A wide range of experimental data has been correlated using a simple correlation and presented in the figures as a dependence f = f(Re).

8

Wypływ cieczy nienewtonowskich ze zbiorników

Dziubiński M., Marcinkowski A.

Inżynieria Chemiczna i Procesowa

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2001

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T. 22, z. 3B

397--402

PL

Praca dotyczy wypływu cieczy newtonowskich i nienewtonowskich ze zbiorników. W wyniku przeprowadzonych badań stwierdzono, że mechanizm wypływu cieczy nienewtonowskich ze zbiorników nie różni się znacznie od mechanizmu wypływu cieczy newtonowskich. Zaproponowano proste równanie korelacyjne opisujące w szerokim zakresie wartość współczynnika wypływu w funkcji liczby Reynoldsa dla wypływu cieczy newtonowskich i nienewtonowskich ze zbiornika.

EN

This paper deals with the discharge of Newtonian and non-Newtonian liquids from vessels. A great similarity between behaviour of Newtonian and non-Newtonian liquids during discharging from vessels was shown. A simple correlation equation for discharge coefficient for the wide range of Reynolds number was proposed.

9

Wytwarzanie zawiesiny cząstek ciała stałego w lepkiej cieczy w mieszalniku zaopatrzonym w niestandardowe przegrody

Karcz J., Więch D.

Zeszyty Naukowe. Inżynieria Chemiczna i Procesowa / Politechnika Łódzka

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2000

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Z. 27

131-138

PL

Przeprowadzono doświadczalne badania warunków wytwarzania zawiesiny cząstek ciała stałego w cieczy niutonowskiej o znacznie większej lepkości niż woda w mieszalniku wyposażonym w niestandardowe, krótkie przegrody i mieszadło turbinowe tarczowe. Na podstawie tych badań określono krytyczne częstości obrotów mieszadła dla każdej z testowanych konfiguracji przegród w mieszalniku.

EN

Experimental studies of the suspending of the particles in a viscous Newtonian liquid were carried out in the agitated vessel of diameter D = 0.3 m equipped with Rushton disc turbine and nonstandard baffles of length L (where L + p = H). On the basis of the measurements, critical impeller speeds nkr were determined for each configurations of the baffles tested. The results of the studies show that critical impeller speeds decrease with the increase of the geometrical parameter p/H and slightly only depend on the liquid viscosity within the range of the low mean concentration of the particles in the liquid.