Polymeric Fluids Research Articles

Numerical study on thermal performance of Sisko fluid with hybrid nano-structures

Sisko fluid rheological correlations accurately determine relationships between stress and strain for polymer fluids. The simultaneous use of rheological stress-strain relations for Sisko fluid and thermophysical properties for pure fluid, nano-structures, and nano-Sisko fluid is a challenge towards numerical simulations. The present investigation has addressed this challenge and successfully implemented the finite element method (FEM) to complex mathematical models. It is a proven fact that FEM for steady problems is stable, convergent, and consistent. Therefore, stable, accurate, and convergent solutions are computed as present problems are steady and well-posed. The parametric investigation is carried out and validated of results is done. The outcomes in form of graphical and numerical outputs are displayed. A significant increase in shear stress and heat flux due to suspension of nano-structures is noticed. However, this increase in shear stress and heat flux because of hybrid nanostructures is greater than the shear stress and heat flux associated with mono nano-Siskofluid. The dissipation of heat due to the friction among the particles of fluid is responsible for increasing the thermal boundary layer thickness. Thus boundary layer thickness for the case of hybrid nanofluid is wider than that associated with mono-nanofluid. The diffusion of species in hybrid nanofluid is slower than the diffusion of species in pure and mono-nanofluid. Magnetic field causes drag on the surface. Therefore, the strength of the surface must afford the drag in order to avoid the failure of the system. Viscous dissipation contributes to enhancing the temperature of fluid particles. Heat generation affects thermal performance adversely, therefore nonheat generation fluid performance as better coolant. The optimized raise in thermal conductivity of Sisko fluid due to the inclusion of hybrid nano-particles is noticed. Therefore dispersion of hybrid nanoparticles is recommended.

Thermocapillary effects on viscoelastic drops suspended in axisymmetric pressure driven flows

Dynamics and deformation of a viscoelastic drop in another immiscible viscoelastic medium in the presence of externally imposed pressure and temperature gradients are analyzed asymptotically in the present work. Both of the phases obey the linear Phan–Thien–Tanner constitutive model, capable of accounting for shear thinning behavior in polymeric fluids. The first two asymptotic corrections to the leading order Newtonian behavior are reported here, in the limit of small Deborah and Capillary numbers, which, respectively, characterize the extent of viscoelasticity and interfacial deformation. We establish that the viscoelastic properties of the inner phase strongly influence the migration velocity and the interfacial deformation of the drop. Our analysis reveals the possibility of realizing a maximum migration velocity for an intermediate viscosity of the interior phase, provided it has stronger viscoelastic characteristics than the suspending medium. We further compute the critical thermal gradient required to completely arrest the drop's motion and demonstrate that the same depends on the Deborah number as well as the viscosity of the inner phase. The viscoelastic stresses also dictate the deformation as the drop's shape changes from prolate to oblate when those stresses become significant. Our results may find potential applications in areas such as polymer processing and handling of biologically relevant media in medical diagnostics.

Coalescence of polymeric sessile drops on a partially wettable substrate

Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from the inertial to viscoelastic regime at concentration ratio c/c*∼1. Our findings unveil that the temporal evolution of the growing bridge height follows a power law behavior tb, such that the coefficient b continuously decreases from 2/3 in the inertial regime (c/c*<1) to an asymptotic value of 1/2 in the viscoelastic regime (c/c*>1). To account for fluid elasticity and characteristic timescale in the viscoelastic regime, a modified thin film equation under lubrication approximation has been proposed using the linear Phan–Thien–Tanner constitutive equation. The temporal evolution of the droplet has been evaluated by solving the modified one-dimensional thin film equation using a marching explicit scheme. The initial droplet shapes are obtained by resorting to energy minimization. Good agreement between numerical and experimental results is obtained.

Empirical and Theoretical Analysis of Particle Diffusion in Mucus

Mucus is a complex fluid that coats multiple organs in animals. Various physicochemical properties can alter the diffusion of microscopic particles in mucus, impacting drug delivery, virus infection, and disease development. The simultaneous effect of these physicochemical properties in particle diffusion, however, remains elusive. Here, we analyzed 106 published experiments to identify the most dominant factors controlling particle diffusion in mucus. The effective diffusion—defined using a one-second sampling time window across experiments—spanned seven orders of magnitude, from 10–5to 102 μm2/s. Univariate and multivariate statistical analyses identified the anomalous exponent (the logarithmic slope of the mean-squared displacement) as the strongest predictor of effective diffusion, revealing an exponential relationship that explained 89%of the variance. A theoretical scaling analysis revealed that a stronger correlation of the anomalous exponent over the generalized diffusion constant occurs for sampling times two orders of magnitude larger than the characteristic molecular (or local) displacement time. This result predicts that at these timescales, the molecular properties controlling the anomalous exponent, like particle–mucus unbinding times or the particle to mesh size ratio, would be the most relevant physicochemical factors involved in passive microrheology of particles in mucus. Our findings contrast with the fact that only one-third of the studies measured the anomalous exponent, and most experiments did not report the associated molecular properties predicted to dominate the motion of particles in mucus. The theoretical foundation of our work can be extrapolated to other systems, providing a guide to identify dominant molecular mechanisms regulating the mobility of particles in mucus and other polymeric fluids.

Exact Controllability of a Faedo–Galërkin Scheme for the Dynamics of Polymer Fluids

Exact Controllability of a Faedo–Galërkin Scheme for the Dynamics of Polymer Fluids

Magneto Casson-Carreau Fluid Flow through a Circular Porous Cylinder with Partial Slip

In the current study, a comparative analysis of two-dimensional heat transfer by the free convective flow of non-Newtonian Casson and Carreau fluid in electro-conductive polymer on the outside surface of a horizontal circular cylinder under slip and radial magnetic field effects is regarded. The Casson and Carreau fluid model formulation were first developed for the problem of the boundary layer of the horizontal circular cylinder and by using non-similarity transformations, the combined governing partial differential equations are translated into ordinary differential equations. The differential equations obtained are resolved by the Keller Box Method (KBM). The impact of the key parameters, the rate of heat transfer and skin friction is evaluated through graphs and tables. The result reveals that an increase in magnetic number decreases the velocity field of both Casson and Carreau fluid also Casson fluid is higher values when compared to Carreau fluid in variation of magnetic number.

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin–Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a “drop vibration rheometer”, suggesting future experiments using either ultrasonic levitation or a microgravity environment.

Shear-banding fluid(s) under time-dependent shear flows. Part II: A test of the Moorcroft–Fielding criteria

Complex systems often exhibit shear banding—the coexistence of two different states characterized by their internal structuring and local shear rates. For some of them, the heterogeneous flow corresponds to the final steady-state response, while for others, shear banding can only be transient, the banding structure healing back to a homogeneous flow in the ultimate steady state after long-lived periods. In order to explain the diversity of observations, Moorcroft and Fielding have established general criteria for the onset of banding in time-dependent flows of complex systems, ranging from polymeric fluids to soft glassy materials [Moorcroft et al., Phys. Rev. Lett. 110, 086001 (2013)]. The proposed criteria are based on the time evolution of the bulk rheological response function of the system to a given time-dependent flow protocol and are associated with a specific signature in the mechanical response. In this contribution, we test the validity of these criteria in the case of two common time-dependent flow protocols: a step stress and a shear startup. Two types of fluids are examined. On the one hand, a wormlike micelles system exhibiting steady shear banding is studied experimentally, using rheometry coupled with direct visualizations and particle image velocimetry. On the other hand, we analyze previous literature on yield stress fluids exhibiting transient shear banding. Under conditions of a constant imposed stress, for both types of fluids, the onset of banding arises in a time window compatible with the Moorcroft–Fielding criterion. However, the mechanical signature, i.e., the shape of the bulk mechanical signal as a function of time, is not the one expected within some of the specific models with which the general Moorcroft–Fielding criteria were tested numerically. Under shear startup, both types of fluids behave differently. The criterion holds for yield stress fluids, the onset of banding arising just after the stress overshoot, as expected. On the contrary, for wormlike micelles, the window of instability is delayed, even if the overshoot clearly plays a crucial role in the nucleation of shear-induced structures. Regardless of the flow protocol or the system, wall slip seems to go hand in hand with banding indicating that it is a key ingredient to take into account.

Numerical simulation of a stabilizing Poiseuille-type polymer fluid flow in the channel with elliptical cross-section

This work is devoted to the numerical analysis of stabilization of the incompressible viscoelastic polymer fluid flow in the channel with elliptical cross-section. To describe the flow, mesoscopic rheological relations are used, and resolving non-stationary equations are derived. For solving them a special pseudo-spectral method is developed and implemented. As time increases, under certain conditions on the parameters of flow the solution to the non-stationary problem stabilizes and converges to the one of three branches of the solution to the corresponding stationary problem. It is shown that the variation of the parameters describing polymer microstructure leads to the switch of stabilized solution between these branches. The work provides the results of simulation of the flow stabilization and the analysis of the threshold values of parameters at which the switching occurs.

Evaluation of Antifungal Activity of Various Plant Latex against Selected Fungal Strains

Abstract: Latex is a natural plant polymer and milky white fluid distributed throughout the plant body like leaves, stems, roots and fruits of all flowering plants and consists of proteins, alkaloids, starches, sugars, oils, tannins, resins and gums that coagulate on-air exposure. It is secreted by specialized plant cells called Laticifers. Plants exude latex in response to physical damage. The present study was carried out to assess the potential antifungal activity of latex of five different plants namely Plumeria rubra, Plumeria alba, Aloe vera, Calotropis procera and Calotropis gigantea against three different pathogenic strains of fungi. All five latexes were found to show good to moderated activity against all the three fungal strains, namely Trichoderma viride, Aspergillus flavus and Aspergillus niger. The latex of each plant was tested in two volumes (i.e. 10µl & 20µl), and it was found that the antifungal activity was volume-dependent, and a significant difference was also observed in the case of different fungal strains. The antifungal activity of plant latexes was evaluated by Agar well diffusion method; results revealed that among all the five latexes, the fresh latex of Plumeria rubra (Vol: 10µl &20µl) showed excellent antifungal activity against Aspergillus niger and Aspergillus flavus, whereas fresh latex of Aloe vera (Vol: 10µl & 20µl) showed excellent antifungal activity against Trichoderma viride. The results of the current research imply that the antifungal activity of latex varies with the species of plants and the fungal strains used. The results therefore demonstrated that, the used five latexes effectively inhibited the growth of three tested fungi. Hence, these plant latexes are natural, ecofriendly and can be used as good candidates for the treatment of various fungal diseases. In further words, they can be used for therapy of antifungal-resistant fungi. Keywords: Antifungal activity, Proteins, Alkaloids, Tannins, Resins, Laticifers, Plumeria rubra, Plumeria alba, Aloe vera, Calotropis procera, Calotropis gigantea, Aspergillus flavus, Aspergillus niger, Trichoderma viride, Latex, Agar well diffusion.

Different Formulations to Solve the Giesekus Model for Flow between Two Parallel Plates

This work presents different formulations to obtain the solution for the Giesekus constitutive model for a flow between two parallel plates. The first one is the formulation based on work by Schleiniger, G; Weinacht, R.J., [Journal of Non-Newtonian Fluid Mechanics, 40, 79–102 (1991)]. The second formulation is based on the concept of changing the independent variable to obtain the solution of the fluid flow components in terms of this variable. This change allows the flow components to be obtained analytically, with the exception of the velocity profile, which is obtained using a high-order numerical integration method. The last formulation is based on the numerical simulation of the governing equations using high-order approximations. The results show that each formulation presented has advantages and disadvantages, and it was investigated different viscoelastic fluid flows by varying the dimensionless parameters, considering purely polymeric fluid flow, closer to purely polymeric fluid flow, solvent contribution on the mixture of fluid, and high Weissenberg numbers.

Application of Wavelet Feature Extraction and Artificial Neural Networks for Improving the Performance of Gas-Liquid Two-Phase Flow Meters Used in Oil and Petrochemical Industries.

Measuring fluid characteristics is of high importance in various industries such as the polymer, petroleum, and petrochemical industries, etc. Flow regime classification and void fraction measurement are essential for predicting the performance of many systems. The efficiency of multiphase flow meters strongly depends on the flow parameters. In this study, MCNP (Monte Carlo N-Particle) code was employed to simulate annular, stratified, and homogeneous regimes. In this approach, two detectors (NaI) were utilized to detect the emitted photons from a cesium-137 source. The registered signals of both detectors were decomposed using a discrete wavelet transform (DWT). Following this, the low-frequency (approximation) and high-frequency (detail) components of the signals were calculated. Finally, various features of the approximation signals were extracted, using the average value, kurtosis, standard deviation (STD), and root mean square (RMS). The extracted features were thoroughly analyzed to find those features which could classify the flow regimes and be utilized as the inputs to a network for improving the efficiency of flow meters. Two different networks were implemented for flow regime classification and void fraction prediction. In the current study, using the wavelet transform and feature extraction approach, the considered flow regimes were classified correctly, and the void fraction percentages were calculated with a mean relative error (MRE) of 0.4%. Although the system presented in this study is proposed for measuring the characteristics of petroleum fluids, it can be easily used for other types of fluids such as polymeric fluids.

Machine Learning for the Flow Prediction of Fluids with Memory Effects on the Stress

We have recently developed a machine learning method capable of inferring the constitutive equation for the stress of a fluid with memory (e.g., polymeric fluid) from microscopic simulations. For this, we used a Gaussian Process regression scheme to learn the constitutive relation, given as the time-derivative of the stress, as a function of the local stress and velocity strain tensors. Crucially, no assumptions are made regarding the functional form of this relation. We have applied our method to the Hookean dumbbell model, for which the exact analytical constitutive relation (Maxwell equation) is known, in order to validate the approach. Our results are in excellent agreement with the analytical solution, showing that we are able to capture the history dependence of the flow, as well as the elastic effects in the fluid. Compared to full multi-scale simulations, in which the micro and macro degrees of freedom are directly coupled, our method provides a similar degree of accuracy, at a small fraction of the cost. In addition, the method can be easily generalized to more complex and realistic polymer models. (As part of this article, we include a Japanese summary of our main results, published in [7], CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).)

Numerical Simulation and Linearized Theory of Vortex Waves in a Viscoelastic, Polymeric Fluid

In a high viscosity, polymeric fluid initially at rest, the release of elastic energy produces vorticity in the form of coherent motions (vortex rings). Such behavior may enhance mixing in the low Reynolds number flows encountered in microfluidic applications. In this work, we develop a theory for such flows by linearizing the governing equations of motion. The linear theory predicts that when elastic energy is released in a symmetric manner, a wave of vorticity is produced with two distinct periods of wave motion: (1) a period of wave expansion and growth extending over a transition time scale, followed by (2) a period of wave translation and viscous decay. The vortex wave speeds are predicted to be proportional to the square root of the initial fluid tension, and the fluid tension itself scales as the viscosity. Besides verifying the predictions of the linearized theory, numerical solutions of the equations of motion for the velocity field, obtained using a pseudo-spectral method, show that the flow is composed of right- and left-traveling columnar vortex pairs, called vortex waves for short. Wave speeds obtained from the numerical simulations are within 1.5% of those from the linear theory when the assumption of linearity holds. Vortex waves are found to decay on a time scale of the order of the vortex size divided by the solution viscosity, in reasonable agreement with the analytical solution of the linearized model for damped vortex waves. When the viscoelastic fluid is governed by a nonlinear spring model, as represented by the Peterlin function, wave speeds are found to be larger than the predictions of the linear theory for small polymer extension lengths.

Shear-Thinning in Oligomer Melts-Molecular Origins and Applications.

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving–Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Generalized Newtonian fluid constitutive equation for polymer liquids considering chain stretch and monomeric friction reduction for very fast flows modeling

In this work, the recently proposed frame-invariant Generalized Newtonian Fluid (GNF) constitutive equation [M. Zatloukal, “Frame-invariant formulation of novel generalized Newtonian fluid constitutive equation for polymer melts,” Phys. Fluids 32(9), 091705 (2020)] has been modified to provide uniaxial extensional viscosity at a high strain rate limit corresponding to molecular expression for a fully extended Fraenkel chain reported in Ianniruberto et al. [“Melts of linear polymers in fast flows,” Macromolecules 53(13), 5023–5033 (2020)]. It uses basic rheological and molecular parameters together with the ratio of monomeric friction coefficients for equilibrium and fully aligned chains. The modified GNF model was successfully tested by using steady-state uniaxial extensional viscosity data for well-characterized entangled polymer melts and solutions [namely, linear isotactic polypropylenes, poly(n-butyl acrylate), polyisoprenes, and polystyrenes] covering a wide range of strain rates, including those, at which the chain stretch occurs. Only two fitting parameters were sufficient to describe all uniaxial extensional viscosity data, one related to the Rouse stretch time and the other controlling the extensional thinning and thickening behavior at medium and high strain rates. The model was compared to five different advanced viscoelastic constitutive equations, which are based on Doi–Edwards theory and include chain stretch along with a number of important additions. The ability of the proposed GNF model to represent steady uniaxial extensional viscosities under fast flow conditions for entangled polymer fluids has been shown to be superior to the predictions of selected advanced viscoelastic constitutive equations. It is believed that the modified GNF model can be used in the stable modeling of non-Newtonian polymer liquids, especially in very fast steady-state flows where chain stretch begins to occur.

Lyapunov instability of the stationary flows of a polymeric fluid in an infinite plane channel with constant flow rate

In this study, we consider a rheological Pokrovski–Vinogradov model of the flows of solutions and melts of an incompressible viscoelastic polymeric medium for a flow in an infinite plane channel with perforated walls. We prove the linear Lyapunov instability of the base solution with a constant flow rate in a perturbation class, which is periodic with respect to the variable and changing along the channel wall.

Modeling orthogonal superposition rheometry to probe nonequilibrium dynamics of entangled polymers

Understanding changes to microstructural dynamics under nonlinear deformations is critical for designing flow processes of entangled polymeric fluids, motivating the development of experimental methods to probe strain- and rate- dependent modifications to relaxation mechanisms. Although orthogonal superposition rheometry (OSR) holds promise as such a probe, the ability to interpret the superposition moduli accessible by OSR in the context of entangled polymer dynamics remains an open question. To fill this gap, we report model OSR predictions using detailed microstructural models for both monodisperse and polydisperse entangled polymers, i.e., the Rolie-Poly and the Rolie-Double-Poly models, respectively, which account for reptation, chain retraction, and convective constraint release. By combining numerical calculations with a perturbation analysis, we demonstrate that for polymers that can be described by a single-mode model, the OSR superposition moduli at different shear rates and frequencies can generally be collapsed onto a single master curve, with rate-dependent shift factors that depend on the nonlinear rate-dependent modification of polymer conformation and relaxation rates without changing the dominant relaxation mechanisms. We systematically study how the OSR moduli are sensitive to the shape and dispersity of the molecular weight distribution. We discuss the generality of our results for a broad class of constitutive models and suggest an analogy to Laun’s rule to relate OSR moduli to the first normal stress difference. Our results provide a foundation to guide the design and interpretation of future experiments and demonstrate that orthogonal superposition rheometry often probes features in nonlinear dynamics more directly than conventional rheometry techniques.

Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

Nanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

Lyapunov instability of the stationary flows of polymeric fluid with constant flow rate

AbstractWe study a rheological Pokrovski‐Vinogradov model for the flows of solutions and melts of incompressible viscoelastic polymeric medium in case of a flow in an infinite plane channel with perforated walls. We prove the linear Lyapunov instability of the base solution with the constant flow rate in a perturbation class, periodic with respect to the variable, changing along the channel wall.