S. A. Patlazhan

Simulation of small-strain deformations of semi-crystalline polymer: Coupling of structural transformations with stress-strain response

The small strain (below yielding) tensile loading-unloading tests were carried out on the low-density polyethylene (LDPE) and polypropylene (PP) at low strain rate and room temperature. The experiments unambiguously indicate to a remarkable decrease in residual strains in comparison with those predicted by conventional viscoelastic models. These deviations cannot be explained without taking into account structural transformations of semi-crystalline polymers. As long as small deformations cannot result in significant change in content and texture of crystalline and amorphous components, it was assumed that such transformations should include disintegration of connectivity in crystallite clusters. This structural rearrangement is supposed to be caused by the strain-induced decrystallization of narrow (and thus highly stressed) “bridges” connecting domains of conjugated crystallites or inside crystallites. A simple 1D modelling of the deformation processes supports this expectation. The disconnection in polymer morphology is simulated by small portions of amorphous ligaments appearing between neighbouring crystallites in the course of deformation. In spite of simplicity of the model a precise fitting of the stress-strain diagram is obtained along with small variations in structural and material characteristics (crystallinity degree, effective rigidity and plastic ability) of the concerned polymers.

Rheological properties of polyethylene/metaboric acid thermoplastic blends

The rheological properties of molten low-density polyethylene/metaboric acid blends were studied. It was found that the blend behavior can be rather different, depending on volume fraction of the inorganic component. Specifically, at some concentration of metaboric acid, the dynamic moduli and the Newtonian viscosity of the blends demonstrate a jump-like change. The concentration threshold depends on temperature and equals to 21.9 and 14.1 vol %, at 150 and 180 ∘C, respectively. In the concentration range below the threshold, the gain in the content of inorganic component results in an enhancement of the blend dynamic moduli and viscosity, without changing the general character of the rheological behavior of composition in the region of linear response. On the other hand, at higher concentrations of metaboric acid, the yield stress is observed, and the elastic modulus in the linear region of mechanical behavior becomes virtually independent of frequency. It was suggested that the rheological behavior of blends is related to a spontaneous change in their structure as well as planar molecular structure of the inorganic component.

Stress-strain behavior of high-density polyethylene below the yield point: Effect of unloading rate

The stress-strain behavior of HDPE under uniaxial tensile drawing below the yield point is discussed. Special attention is placed on studying the tensile loading-unloading diagrams at different unloading rates. Experimental data are analyzed in terms of a set of two-phase basic structural mechanical elements, which take into account the plastic flow and structural rearrangements of both hard and soft components. Parameters of these elements are calculated by optimal fitting of theoretical curves to an arbitrary experimental tensile loading-unloading curve measured at a constant strain rate. This approach allows description of a decrease in the residual strain with decreasing unloading rate at fixed model parameters. The physical nature of the observed deformational effects is considered.

Wall slip for complex liquids – Phenomenon and its causes

In this review, we tried to qualify different types and mechanisms of wall slip phenomenon, paying particular attention to the most recent publications and issues. The review covers all type of fluids - homogeneous low molecular weight liquids, polymer solution, multi-component dispersed media, and polymer melts. We focused on two basic concepts - fluid-solid wall interaction and shear-induced fluid-to-solid transitions - which are the dominant mechanisms of wall slip. In the first part of the review, the theoretical and numerical studies of correlation of wetting properties and wall slip of low molecular weight liquids and polymeric fluids are reviewed along with some basic experimental results. The influence of nanobubbles and microcavities on the effectiveness of wall slip is illuminated with regard to the bubble dynamics, as well as their stability at smooth and rough interfaces, including superhydrophobic surfaces. Flow of multi-component matter (microgel pastes, concentrated suspensions of solid particles, compressed emulsions, and colloidal systems) is accompanied by wall slip in two cases. The first one is typical of viscoplastic media which can exist in two different physical states, as solid-like below the yield point and liquid-like at the applied stresses exceeding this threshold. Slip takes place at low stresses. The second case is related to the transition from fluid to solid states at high deformation rates or large deformations caused by the strain-induced glass transition of concentrated dispersions. In the latter case, the wall effects consist of apparent slip due to the formation of a low viscous thin layer of fluid at the wall. The liquid-to-solid transition is also a dominant mechanism in wall slip of polymer melts because liquid polymers are elastic fluids which can be in two relaxation states depending on the strain rate. The realization of these mechanisms is determined by polymer melt interaction with the solid wall.

Features of the melt flow of polyethylene and boron oxide oligomer blends

The features of melt flow of LDPE and boron oxide oligomer blends during extrusion mixing are investigated. It is established that the extruder-wall pressure and the torque of the screw decrease monotonically with an increase in the boron oxide oligomer content up to 25 vol %. Exceeding this concentration threshold leads to a several-fold stepwise fall in of the mentioned characteristics. This result is explained within the concepts about spontaneous restructuring of the blend accompanied by an increase of the specific surface of phases and by slipping at the interface of the blend components that is caused by the planar structure of the boron oxide oligomer molecules.

Segregation of a two-phase mixture of incompatible viscous fluids in laminar flow

Investigation of segregation of multiphase fluid sys� tems is of significant scientific and practical interest. In practical terms, the obtained knowledge is in demand in the chemical and oil industries, for which data on the kinetics of the spatial redistribution of the dispersed phase are of considerable applied impor� tance. For example, a change in the specific surface area of emulsions due to coalescence of drops can lead to noticeable variations in chemical reaction rates, including the emulsion polymerization kinetics. This should be taken into account in designing industrial dispersers and mixers. At the same time, in production and transportation of petroleum products containing a certain amount of water, phase separation processes can give rise to discontinuous water domains or con� tinuous water streams along the lower generatrix of pipelines [1, 2]. The presence of dissolved gases, e.g., CO2 and/or H2S, leads to accelerated development of pitting or groove corrosion [3–6], which is fraught with service life reduction and even breakdown of pipelines. In oil pipelines, water dispersions deposit in a flow of a medium. The combination of these processes can change the segregation kinetics of components of the medium in comparison to the deposition kinetics at rest. In particular, this can be caused by variations in the drop collision frequency and drop shape, which, in turn, influence the coalescence conditions and, hence, the deposition velocity. Numerous studies were made of sedimentation of liquid and solid dispersions in flows of air and gases, river streams, ocean currents, and also oil transportation [7–10]. However, this chal� lenge continues to be in the limelight. Specifically, this is highly topical for representative sampling during

Deformation Behavior of a Composite Drop in a Simple Shear Flow

The hydrodynamics of disperse liquid mediaattracts increased attention, first of all, owing to theirnumerous applications in various industries (chemical, medical, pharmaceutical, processing of polymers,etc.). The theoretical analysis of such systems is basedon studying the dynamic behavior of an isolated dropin a flow for determining the strain, orientation, andstability of the drop in various flow modes. To date, anextensive body of experimental data on the mechanisms of deformation and breakup of homogeneousdrops has been accumulated [1–6]. However, thehydrodynamic behavior of composite drops containing one or several internal inclusions (cores) remainslittle studied. At the same time, such objects have adiversity of applications: from increasing the impactresistance of mixed polymer composites to targeteddrug delivery [5, 6]. Therefore, the comprehensiveinvestigation of composite drops is of fundamental andpractical interest.Studying the hydrodynamic behavior of such dropsis complicated by a number of difficulties related to thenecessity of taking into account a large number ofparameters and also the dynamic changes in theshapes of both inner and outer interfaces. In the simplest case, a composite drop consists of a single coreand a shell, which are immersed in a dispersion liquid(Fig. 1). In this case, features of the deformation andshaping of the drop are determined by the relative values of the surface tensions at the interfaces betweenthe components of the medium, their viscosities, andalso the core size as compared to the shell size.It was previously shown that, in a shear flow, a corewith low viscosity and low surface tension takes theshape of an extended dumbbell rotating in the direction of the flow [7]. In this work, we studied the hydrodynamic behavior of a twodimensional compositedrop in which the viscosity of the core is much higherthan that of the shell and also the core–shell interfacial tension significantly increases the surface tensionat the interface between the shell and the dispersionliquid. In such a formulation, the main contribution tothe total strain and orientation of the composite dropIs made by the transformation of the shape of the shell.The deformation and dynamic structuring of this typeare also characteristic of swollen microgels immersedin a thermodynamically incompatible liquid [8–10].Comparison of the hydrodynamic behaviors of composite and homogeneous drops enabled one to understand the effect of flow perturbations caused by thepresence of the viscous core on the deformationbehavior of the composite drop.

Peculiarities of shear flow in microchannels with superhydrophobic wall

203 Liquid flow in microscopic channels with hydro philic or hydrophobic walls is characterized by signifi cant hydrodynamic resistance. It can be reduced by using superhydrophobic coatings, which became known, first of all, for their record large contact angles [1]. This effect is due to small scale roughness of supe rhydrophobic surfaces, owing to which the liquid rests on the tops of surface asperities without entering troughs between them (Cassie–Baxter state). The absence of contacts with the solid walls in troughs also influences the liquid flow. At the interface with regions filled with gas bubbles, the shear components of the stress tensor are close to zero and virtually correspond to the conditions on a free surface. As a result, on the gas bubbles, the liquid flows freely (slips), whereas on the solid asperities the flow velocity is zero (stick boundary condition). The alternation of the slip and no slip regions reduces losses in comparison with the flow on a smooth surface and, as a consequence, gives rise to effective slip, which is characterized by effective slip length b*. This parameter is the extrapolated dis tance from the wall to an imaginary point at which the velocity is zero [2–4] (Fig. 1). The slip intensity increases with increasing surface fraction of gas bubble zones, because of which the effective slip length b* can reach several tens of microns [5, 6].

Mechanism of stability of the shear flow of a two-layer system of viscous liquids

171 The evolution of the morphology of multicompo� nent liquid media in the course of mechanical treat� ment is related, first of all, to the development of hydrodynamic instability at the interface. In the initial stage of the shear flow, this is caused by an exponential increase in the amplitude A(t) = A0e kΔct of capillary waves over a wide range of wavenumbers k. At positive values of the rate of change in the perturbation ampli� tude , the flow is unstable, while at negative values of this rate, it is stable. It was shown (1) that the Cou� ette and Poiseuille shear flows can be destabilized by applying weak longwave perturbations to the inter� face of a twolayer system of incompressible Newto� nian liquids at certain values of the viscosity ratio m and the thickness ratio n of the layers and at arbitrarily low Reynolds numbers. This qualitatively distin� guishes the instability of this type from the transition to turbulent flow. It was demonstrated (2, 3) that the change in the amplitude of short and long waves is caused by a phase shift of the velocity perturbation wave induced by inertial liquid transfer. At the same time, the mechanism of instability of shear flow at arbitrary wavelengths remained unclear. Solving this question requires involving numerical methods of analysis of the equations of momentum transfer of media with nonuniform viscosity distributions. In this work, for the first time, we performed a direct numerical modeling of the simple shear flow instability development of a twolayer system of New� tonian liquids over a wide range of wavelengths. We determined the conditions for the transition between the asymptotic solutions corresponding to longand Δ c shortwave perturbations. We also showed that the inertial shift of vortices of flow rate perturbations is proportional to the growth rate of the interface pertur� bation amplitude.

Effect of wall slip on the shear flow of a polymer in a channel with a wavy bottom

The effect of stick and wall slip boundary conditions on the specific features of the shear flow of viscous polymers in a confined two-dimensional channel with a wavy bottom is studied. The distribution of flow-rate disturbances across the transverse cross section of the channel is calculated by the numerical simulation of the Navier-Stokes equation for an incompressible fluid at arbitrary amplitudes and an arbitrary wave number of the wall. The wall slip is modeled by the introduction of a thin layer of a low-viscosity fluid at the bottom face. Slippage leads to a marked enhancement of flow rate disturbances including inertial advection. The results agree with the known analytical solutions for the low-amplitude wall wave.