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1

Structural changes of viscoelastic solutions of zwitterionic and anionic surfactant mixtures under the influence of simple salt

Różańska Sylwia, Warmbier Ewelina, Wagner Patrycja, Różański Jacek

Chemical and Process Engineering : New Frontiers

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2023

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Vol. 44, nr 2

art. no. e10

EN

The paper presents the effects of sodium chloride on the rheological properties of aqueous solutions of cocamidopropyl betaine (CAPB) and sodium dodecylbenzene sulfonate (SDBS) mixtures. Studies were carried out in the CAPB/SDBS molar ratio range of 0.95 to 3.5, at sodium chloride concentrations varying from 0.03 M to 0.75 M. Continuous and oscillatory flow measurements showed that the impact of sodium chloride concentration on shear viscosity and relaxation time was closely linked to the CAPB/SDBS molar ratio. The maximum shear viscosity and the longest Maxwell relaxation time were obtained at the CAPB/SDBS molar ratio of 2. Based on CryoTEM images, it was determined that the shear viscosity and relaxation time peaks identified at a certain concentration of sodium chloride could be attributed to the transition of the entangled wormlike micellar network into branched wormlike micelles. Changes in the micellar microstructure accompanying modifications of the CAPB/SDBS molar ratio and sodium chloride concentration were accounted for on the basis of the packing parameter.

2

A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model

Li J., Huang H., Wang M.

Acta Geophysica

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2017

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Vol. 65, no. 1

55--64

EN

In this paper, the micro-cracks in the brittle rocks are assumed to be penny shaped and evenly distributed; the damage and dilatancy of the brittle rocks is attributed to the growth and expansion of numerous micro-cracks under the local tensile stress. A single crack’s behaviour under the local tensile stress is generalized to all cracks based on the distributed damage mechanics. The relationship between the local tensile stress and the external loading is derived based on the Maxwell model. The damage factor corresponding to the external loading is represented using thep–alpha (p–α) model. A dilatancy equation that can build up a link between the external loading and the rock dilatancy is established. A test of dilatancy of a brittle rock under triaxial compression is conducted; the comparison between experimental results and our theoretical results shows good consistency.

3

Rheological scaling properties of starch solutionsin dimethylsulfoxide

Ptaszek P., Ptaszek A., Łukasiewicz M., Grzesik M.

Chemical and Process Engineering

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2012

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Vol. 33, nr 3

323-333

EN

The possibility of scaling viscoelastic properties of starch solutions in relation to biopolymer concentration was presented in this study. An application of this empirical method enabled to widen the observation horizon of viscoelastic properties. It was also determined that the scope of its applicability is limited by amylose content in the solution. In high amylose solutions, for which up to 40% (w/w) concentration was the highest one obtained, calibration caused the formation of master curve in the widest frequency range. Determined values of scaling coefficients aC changed exponentially in starch concentration function in the solution. For waxy starch solutions of maximum concentration equal to 20% (w/w), scaling did not significantly widen the observation window. Based on master curves constructed in such way, continuous relaxation spectra H([lambda]) were determined using Tikhonov regularisation method. Their structure indicates advantageous of viscous elements in the process of viscoelastic phenomena formation.

4

Viscoelastic Characterization of Different Solid Rocket Propellants Using the Maxwell Spring-Dashpot Model

Shekhar H., Kankane D. K.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 3

189-199

EN

A single spring and a single dashpot in series was utilized to simulate the stress-strain curve for different classes of solid rocket propellants, namely extruded double base propellants (EDBP) and composite propellants (CP), in the uniaxial tensile mode in a constant rate of travel machine. The propellant behaves as a viscoelastic material and invariably exhibits stress relaxation, which cannot be simulated by elastic mechanical property parameters. In order to generate a complete stress-strain curve of a solid rocket propellant under tensile testing, different classes of solid rocket propellants were evaluated and the stress-strain curve generated was modelled using the single spring-single dashpot Maxwell fluid model. Using two constants, called the spring constant (K) and the damping factor (D), it was possible to generate a complete stress-strain curve. Mathematical formulation gives the stress (σ) - strain (ε) relation as….[wzór]. Additionally the physical nature of the spring constant resembles that of the elastic constant and the damping coefficient gives the contribution of the viscous part of the load bearing capacity of solid rocket propellants. The development of a general mathematical formulation, the calculation of constants for different classes of propellants and insight into the viscoelastic nature of propellants are the main themes of this article. For all classes of propellants, two ratios are defined. The first is a dimensionless parameter 'H', which is the ratio of the spring constant to the initial elastic modulus. The second is the ratio of the damping coefficient to the spring constant depicted by parameter 'S'. The spring constant is higher than the initial elastic modulus and the value of 'H' is always higher than 1. For brittle propellants (extruded double base propellants, EDBPs, with a high elastic modulus), the spring constant is numerically very close to the spring constant (H is around 1.75). As the ductility (percentage elongation) of the solid rocket propellants increases (from cartridge loaded composite propellants, CLCPs, to case-bonded composite propellants, CBCPs), the value of parameter 'H' also increases (H ~ 10 for CP). For EDBPs the parameter 'S' is smaller (~ 1.24), but for CLCPs and CBCPs, it is high (S ~ 5 to 8). Both of these ratios are basic properties of the polymeric matrix. The first ratio depicts the departure of the actual stress-strain curve from linearity, while the second ratio is another way of expressing the relaxation time. A higher 'H' indicates a softer and more ductile propellant, while a higher 'S' indicates a shorter relaxation time for the propellant. A lower 'S' indicates that the propellant recovers faster on removal of strain.

5

Visco-hypoelastic model of photo-polymerization process for small changes of temperature

Gambin W.

Archives of Mechanics

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2010

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Vol. 62, nr 5

379-403

EN

The aim of the paper is to propose a model for estimation of the shrinkage stress in photo-cured dental restorations. Up to now, the elastic and viscoelastic models of photo-curing process use an incremental approach with a large number of time steps, with a fixed Young’s modulus and viscosity within each of the time increments. The elastic approach with a stepped increasing Young’s modulus gives the stress values too high. On the other hand, the incremental viscoelastic approach requires long-lasting computations. In the present paper, a consistent model of the photo-curing process for the case of small temperature changes is proposed. The proposition bases on the Maxwell model, in which the Young’s modulus and the viscosity are continuous functions of time. The assumptions of the model follow from the dental practice, as well as from a physical nature of the process and from the rules of continuum mechanics. A performed incremental analysis of the process enables to formulate an integral model of the process, with an explicit rule for the shrinkage stress for 1D and 3D cases. The model has been tested for the material data of dental composite Clearfil F2. Results of the calculations coincide with the values of stresses measured in thin layers of Clearfil F2.

6

Return voltage measurements Diagnostic interpretations based on the dielectric time constants

Patsch R., Kamenka D., Menzel J.

Materials Science Poland

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2009

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Vol. 27, No. 4/2

1157--1169

EN

Return voltage measurements of paper-oil insulations such as medium voltage cables have proven to be a reliable method to determine the actual state of degradation and/or the humidity of the insulation. As a first step, the interpretation of the measurements can be done based on the p-factor. This parameter is sensitive to the dielectric properties and especially the humidity of the solid part of the insulation, whereby aged or humid cables show a higher p-factor. The calculation of the dielectric time constants ?1 and ?2 of the two insulating materials oil and cellulose is unique for the return voltage method and hence exceeds the information extractable from other diagnostic methods.

7

Rectilinear viscoelastic flows in ducts

Beaulne M., Mitsoulis E.

Computer Methods in Materials Science

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2008

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Vol. 8, No. 3

121-129

EN

Axial flows in generalized ducts are studied for viscoelastic materials including a linear low-density polyethylene (LLDPE) melt. Viscoelasticity is described by an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times, which fits well experimental data for the shear and elongational viscosities and the normal stresses as measured in shear flow. The K-BKZ model can be reduced to the Newtonian and Maxwell models with appropriate choice of the parameters. A new technique is developed where the Finger and Cauchy-Green tensors are simplified for axial flows, since particle tracking is only required in the flow z-direction (not required in the x-y coordinate plane). Numerical solutions are presented in two-dimensional cross-sectional geometries, namely square, concave square, and eccentric annulus, for different flow rate and pressure drop changes. For the Maxwell model, the dimensionless pressure drop is independent of the Weissenberg number and a function only of the geometry. For the K-BKZ model representing the LLDPE melt, the dimensionless pressure drop is reduced with increasing flow rate, hence Weissenberg number. The present results are offered as benchmark solutions for the imposition of entry velocity and stress profiles in three-dimensional ducts, when secondary flows are not present.

PL

W pracy opisano badania osiowego przepływu przez kanał dla lepkoplastycznego materiałów, w tym dla liniowego polietylenu o niskiej gęstości. Lepkoplastyczność jest opisana przez całkowe równanie konstytutywne typu K-BKZ ze spektrum czasów relaksacji, które dopasowano do wyników badań doświadczalnych dla lepkości na ścinanie i wydłużenie i dla normalnych naprężeń zmierzonych w przepływie ze ścinaniem. Model K-BKZ może zostać zredukowany do modelu Newtona i Maxwella poprzez odpowiedni dobór współczynników. W ramach projektu opracowano nową technikę, w której tensory Fingera i Cauchy'ego-Greena są uproszczone do przepływów osiowych, ponieważ śledzenie ruchu cząstki jest wymagana tylko w jednym kierunku z (nie ma potrzeby śledzenia ruch w płaszczyźnie x, y). W pracy przedstawiono rozwiązanie numeryczne dla dwuwymiarowych obszarów na przekroju po-przecznym. Rozważono przekroje kwadratowy, wklęsły kwadratowy i ekscentryczny dla różnych prędkości przepływu i różnych spadków ciśnienia. Dla modelu Maxwella bezwymiarowy spadek ciśnienia jest niezależny od liczby Weissenberga i jest funkcją tylko kształtu obszaru. Dla modelu K-BKZ reprezentu-jącego liniowy polietylen o niskiej gęstości, spadek bezwymiarowego ciśnienia zmniejsza się ze wzrostem prędkości przepływu, a zatem także ze wzrostem liczby Weissenberga. Przedstawione w pracy wyniki są proponowane jako "benchmark" dla nakładania wejściowej prędkości i profilu naprężeń w trójwymiarowych kanałach, kiedy wtórny przepływ nie występuje.

8

Return voltage measurements - diagnostic interpretations on the basis of the dielectric time constants.

Patsch R., Kamenka D., Menzel J.

Prace Naukowe Instytutu Podstaw Elektrotechniki i Elektrotechnologii Politechniki Wrocławskiej. Konferencje

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2007

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Vol. 46, nr 19

58-64

EN

Return Voltage Measurements of paper-oil insulations such as medium voltage cables have proven to be a reliable method to determine the actual state of degradation and/or the humidity of the insulation. As a first step the interpretation of the measurements can be done on the basis of the p-factor. This parameter is sensitive on the dielectric properties and especially the humidity of the solid part of the insulation, whereby aged or humid cables show a higher p-factor. The calculation of the dielectric time constants t1 and t2 of the two insulating materials oil and cellulose is unique for the Return Voltage Method and hence exceeds the information extractable from other diagnostic methods.

9

Niektóre błędy wyznaczania parametrów modelu reologicznego na podstawie testu relaksacji naprężeń na przykładzie bulwy ziemniaka

Stropek Z., Gołacki K.

Inżynieria Rolnicza

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2005

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R. 9, nr 4

291--297

PL

Artykuł prezentuje procedury oszacowania niektórych błędów wyznaczania parametrów modelu Maxwella opisującego zachowanie się walcowych próbek w teście relaksacji naprężeń na przykładzie tkanki ziemniaka odmiany Irga. Wyznaczono błędy zarówno toru pomiarowego jak i wynikające z niedokładności wykonania próbek. Uwzględniono także zmienny w funkcji siły reakcji próbki błąd systematyczny przy wyliczaniu współczynników sprężystości i lepkości dynamicznej modelu.

EN

This paper presents the estimation procedures of Maxwell’s model parameters describing the behaviour of potato samples during stress relaxation test. Into consideration were taken errors resulting from an inaccuracy of sample preparation, as well as the used measurement device (defined, limited precision). Moreover systematic error depending on sample reaction force, at calculation of elastic and viscosity coefficients was taken into account.

10

Determination of material coefficients for the thermomechanical model of drying

Banaszek J., Kowalski S., Musielak G.

Studia Geotechnica et Mechanica

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2004

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Vol. 26, nr 1-2

15-24

PL

Wilgotne materiały kapilarno-porowate zmieniają swe właściwości fizyczne podczas procesu suszenia. Pracę poświęcono badaniu zmian współczynników materiałowych występujących w termomechanicznym modelu suszenia w funkcji stanu zawilżenia. Zanalizowano współczynniki lepkosprężystego modelu Maxwella, w którym występują dwa współczynniki sprężystości, tj. moduł Younga E i moduł ścinania G, oraz odpowiadające im dwa współczynniki lepkosprężystości E i n. Badania przeprowadzono na glince kaolinowej, korzystając z uniwersalnej maszyny wytrzymałościowej.

EN

Wet capillary-porous materials change their physical properties during drying. The aim of this paper was to examine the material coefficients in the thermomechanical model of drying as a function of moisture content. The coefficients appearing in the viscoelastic Maxwell model are analyzed. They are as follows: Young's modulus E, shear modulus G, and equivalent to them viscoelastic coefficients E and n. The studies were carried out on the kaolin clay using universal strength-measuring instrument.

11

Włókna mieszankowe typu polipropylen-kauczuk butadienowo-akrylonitrylowy - otrzmywanie i właściwości

Linek M., Tarniowy A.

Kompozyty

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2001

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R. 1, nr 2

163-166

PL

W pracy przedstawiono wyniki badań nad modyfikacją włókien polipropylenowych przez wprowadzenie do polipropyle nu dodatku kauczuku butadienowo-akrylonitrylowego w postaci proszku. Dokonano oceny wybranych właściwości mecha nicznych otrzymanych włókien mieszankowych. Na podstawie doświadczalnych krzywych relaksacji naprężeń wyznaczono parametry uogólnionego modelu Maswella, dobrze opisującego cechy reologiczne tworzywa mieszanki i pokazano wpływ dodatku kauczuku na ich zmiany.

EN

The application of rubber powders is the promising way to simplification of manufacture of composites containing elastomers. This work presents the results of modification of polypropylene fibers by the addition of the powdered butadiene--acrylonitrile rubber. Powdered rubber was obtained by precipitation method. The preparation details as well as the morphology of modified fibers have been shown. The influence of the rubber additive on generalised Maxwell model parameters (Figs. 4-6), calculated based on relaxation tests and results of strength tests (Tab. 1) for polymer blend fibers have been presented.