Wall slip for complex liquids - Phenomenon and its causes

Temperature-dependent yield stress and wall slip behaviour of thermoresponsive Pluronic F127 hydrogels

This study explores the temperature-dependent dynamic yield stress of a triblock thermoresponsive polymer, Pluronic F127, with chemical structure (PEO)100(PPO)65(PEO)100, during the sol-gel transition. The yield stress can be defined as static, dynamic, or elastic, depending on the experimental protocol. We examine the dynamic yield stress estimation for this study, which usually entails utilizing non-Newtonian models like the Herschel-Bulkley (HB) or Bingham models to extrapolate the flow curve (shear rate against shear stress). Initially, we determine the yield stress using the HB model. However, apparent wall slip makes it difficult to calculate yield stress using conventional methods, which could lead to underestimates. To validate the existence of apparent wall slip in our trials, we carry out meticulous experiments in a range of rheometric geometries. To determine the true yield stress corrected for slip, we first use the traditional Mooney method, which requires labor-intensive steps and large sample sizes over various gaps in the parallel plate (PP) design. To overcome these drawbacks, we use a different strategy. We modify the Windhab model equation by adding slip boundary conditions to the HB equation, which allowed us to calculate the slip yield stress in addition to the true yield stress. In contrast to other typical thermoresponsive polymers like poly(N-isopropyl acrylamide) (PNIPAM), our findings demonstrate that PF127's yield stress obeys the Boltzmann equation and increases with temperature.

Interplay between wall slip and shear banding in a thixotropic yield stress fluid

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Modeling of Shear Flows over Superhydrophobic Surfaces: From Newtonian to Non-Newtonian Fluids

The design and use of superhydrophobic surfaces have gained special attentions due to their superior performances and advantages in many flow systems, e.g., in achieving specific goals including drag reduction and flow/droplet handling and manipulation. In this work, we conduct a brief review of shear flows over superhydrophobic surfaces, covering the classic and recent studies/trends for both Newtonian and non-Newtonian fluids. The aim is to mainly review the relevant mathematical and numerical modeling approaches developed during the past 20 years. Considering the wide ranges of applications of superhydrophobic surfaces in Newtonian fluid flows, we attempt to show how the developed studies for the Newtonian shear flows over superhydrophobic surfaces have been evolved, through highlighting the major breakthroughs. Despite the fact that, in many practical applications, flows over superhydrophobic surfaces may show complex non-Newtonian rheology, interactions between the non-Newtonian rheology and superhydrophobicity have not yet been well understood. Therefore, in this Review, we also highlight emerging recent studies addressing the shear flows of shear-thinning and yield stress fluids in superhydrophobic channels. We focus on reviewing the models developed to handle the intricate interaction between the formed liquid/air interface on superhydrophobic surfaces and the overlying flow. Such an intricate interaction will be more complex when the overlying flow shows nonlinear non-Newtonian rheology. We conclude that, although our understanding on the Newtonian shear flows over superhydrophobic surfaces has been well expanded via analyzing various aspects of such flows, the non-Newtonian counterpart is in its early stages. This could be associated with either the early applications mainly concerning Newtonian fluids or new complexities added to an already complex problem by the nonlinear non-Newtonian rheology. Finally, we discuss the possible directions for development of models that can address complex non-Newtonian shear flows over superhydrophobic surfaces.

Rheology of Highly Filled Polymer Compositions-Limits of Filling, Structure, and Transport Phenomena

The current state of the rheology of various polymeric and other materials containing a high concentration of spherical solid filler is considered. The physics of the critical points on the concentration scale are discussed in detail. These points determine the features of the rheological behavior of the highly filled materials corresponding to transitions from a liquid to a yielding medium, elastic-plastic state, and finally to an elastic solid-like state of suspensions. Theoretical and experimental data are summarized, showing the limits of the most dense packing of solid particles, which is of key importance for applications and obtaining high-quality products. The results of model and fine structural studies of physical phenomena that occur when approaching the point of filling the volume, including the occurrence of instabilities, are considered. The occurrence of heterogeneity in the form of individual clusters is also described. These heterogeneous objects begin to move as a whole that leads to the appearance of discontinuities in the suspension volume or wall slip. Understanding these phenomena is a key for particle technology and multiphase processing.

The Role of Structure in Polymer Rheology: Review

The review is devoted to the analysis of the current state of understanding relationships among the deformation-induced structure transformations, observed rheological properties, and the occurrence of non-linear effects for polymer liquids (melts, solutions, and composites). Three levels of non-linearity are the base for consideration. The first one concerns changes in the relaxation spectra of viscoelastic liquids, which are responsible for weak non-linear phenomena. The second one refers to the strong non-linearity corresponding to such changes in the structure of a medium that leads to the emergence of a new relaxation state of a matter. Finally, the third one describes the deformation-induced changes in the phase state and/or the occurring of bifurcations and instability in flow and reflects the thermodynamic non-linear behavior. From a structure point of view, a common cause of the non-linear effects is the orientation of macromolecules and changes in intermolecular interaction, while a dominant factor in describing fluid dynamics of polymer liquids is their elasticity. The modern understanding of thixotropic effects, yielding viscoplastic materials, deformation-induced phase transition, and the experimental observations, demonstrating direct correlations between the structure and rheology of polymer liquids, are the main objects for discussion. All these topics are reviewed and discussed mainly on the basis of the latest five-year publications.

Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

One approach to achieve a homogeneous mixture in microfluidic systems in the quickest time and shortest possible length is to employ electroosmotic flow characteristics with heterogeneous surface properties. Mixing using electroosmotic flow inside microchannels with homogeneous walls is done primarily under the influence of molecular diffusion, which is not strong enough to mix the fluids thoroughly. However, surface chemistry technology can help create desired patterns on microchannel walls to generate significant rotational currents and improve mixing efficiency remarkably. This study analyzes the function of a heterogeneous zeta-potential patch located on a microchannel wall in creating mixing inside a microchannel affected by electroosmotic flow and determines the optimal length to achieve the desired mixing rate. The approximate Helmholtz–Smoluchowski model is suggested to reduce computational costs and simplify the solving process. The results show that the heterogeneity length and location of the zeta-potential patch affect the final mixing proficiency. It was also observed that the slip coefficient on the wall has a more significant effect than the Reynolds number change on improving the mixing efficiency of electroosmotic micromixers, benefiting the heterogeneous distribution of zeta-potential. In addition, using a channel with a heterogeneous zeta-potential patch covered by a slip surface did not lead to an adequate mixing in low Reynolds numbers. Therefore, a homogeneous channel without any heterogeneity would be a priority in such a range of Reynolds numbers. However, increasing the Reynolds number and the presence of a slip coefficient on the heterogeneous channel wall enhances the mixing efficiency relative to the homogeneous one. It should be noted, though, that increasing the slip coefficient will make the mixing efficiency decrease sharply in any situation, especially in high Reynolds numbers.

Nanoscale slip length prediction with machine learning tools

This work incorporates machine learning (ML) techniques, such as multivariate regression, the multi-layer perceptron, and random forest to predict the slip length at the nanoscale. Data points are collected both from our simulation data and data from the literature, and comprise Molecular Dynamics simulations of simple monoatomic, polar, and molecular liquids. Training and test points cover a wide range of input parameters which have been found to affect the slip length value, concerning dynamical and geometrical characteristics of the model, along with simulation parameters that constitute the simulation conditions. The aim of this work is to suggest an accurate and efficient procedure capable of reproducing physical properties, such as the slip length, acting parallel to simulation methods. Non-linear models, based on neural networks and decision trees, have been found to achieve better performance compared to linear regression methods. After the model is trained on representative simulation data, it is capable of accurately predicting the slip length values in regions between or in close proximity to the input data range, at the nanoscale. Results also reveal that, as channel dimensions increase, the slip length turns into a size-independent material property, affected mainly by wall roughness and wettability.

Carbomer microgels as model yield-stress fluids

The review presents current research results for Carbopol-based microgels as yield-stress materials, covering three aspects: chemical, physical and rheological. Such a joint three-aspect study has no analog in the literature. The chemical aspects of Carbopol polymers are presented in terms of a cross-linking polymerization of acrylic acid, their molecular structure, microgel formulation, polyacid dissociation and neutralization, osmotic pressure and associated immense microgel swelling. The physical characterization is focused on models of the shear-induced solid-to-liquid transition of microgels, which are formed of mesoscopic particles typical for soft matter materials. Models that describe interparticle effects are presented to explain the energy states of microgel particles at the mesoscale of scrutiny. Typical representatives of the models utilize attributes of jamming dispersions, micromechanical and polyelectrolyte reactions. Selected relationships that result from the models, such as scaling rules and nondimensional flow characteristics are also presented. The rheological part presents the discussion of problems of yield stress in 2D and 3D deformations, appearance and magnitude of the wall slip. The theory and characteristics of Carbopol microgel deformation in rotational rheometers are presented with graphs for the steady-state measurements, stress-controlled oscillation and two types of transient shear deformation. The review is concluded with suggestions for future research.

Ultrasound Super-Resolution Flow Measurement of Suspensions in Narrow Channels

Zinc-air flow batteries provide a scalable and cost-efficient energy storage solution. However, the achieved power density depends on the local flow conditions of the zinc particle suspension in the electrochemical cell. Numerical modeling is challenging due to the complex multiphase fluid and the interaction of flow and electrochemistry. Hence, performing experiments is crucial to investigate the influence of the flow conditions on the electrical performance, which requires flow instrumentation for the opaque suspension. To resolve the flow field across the 2.6-mm-wide flow channel of the investigated zinc-air flow battery (ZAB), a spatial resolution below 100 [Formula: see text] has to be typically achieved. Using ultrasound techniques, the achieved spatial resolution is limited by the trade-off between ultrasound frequency and imaging depth. This trade-off is even more critical for suspensions due to the scattering of the ultrasound, which increases strongly with frequency. We propose super-resolution particle tracking velocimetry (SRPTV) to overcome this limitation by achieving the required spatial resolution at a low ultrasound frequency. SRPTV is based on the super-resolution technique ultrasound localization microscopy, which is adapted to strongly scattering suspensions by using a dual-frequency-phased array and applying a coherence weighting beamformer to suppress speckles, which result from the scattering at the zinc particles of the suspension. The spatial resolution and the velocity uncertainty are characterized through calibration measurement and numerical simulation. A spatial resolution of 66 [Formula: see text] at an excitation wavelength of 330 [Formula: see text] was achieved, which is sufficient for performing flow investigation in an operational ZAB. The measured flow profile reveals shear-thinning properties and wall slip and therefore differs significantly from a parabolic flow profile of a Newtonian fluid. The presented technique offers potential for performing flow investigations of suspensions in small geometries with a spatial resolution beyond the diffraction limit.

Electrochemically Induced Mesomorphism Switching in a Chlorpromazine Hydrochloride Lyotropic Liquid Crystal

The discovery of electrochemical switching of the L_α phase of chlorpromazine hydrochloride in water is reported. The phase is characterized using polarizing microscopy, X-ray scattering, rheological measurements, and microelectrode voltammetry. Fast, heterogeneous oxidation of the lyotropic liquid crystal is shown to cause a phase change resulting from the disordering of the structural order in a stepwise process. The underlying molecular dynamics is considered to be a cooperative effect of both increasing electrostatic interactions and an unfolding of the monomers from "butterfly"-shaped in the reduced form to planar in the oxidized form.

Evaporation kinetics of continuous water and dispersed oil droplets

Drying of volatile oil droplets immersed in a continuous water phase was observed and analysed. Drying sample solutions were sandwiched between two glass plates and the water and oil phases were observed by confocal microscopy. In the initial stage of drying, evaporation of water was dominant and drying of the oil droplets was negligible. However, the rate of water evaporation decreased when the oil droplets were compressed. Comparison of experimental data with a diffusion model of water vapour showed that the decline in drying rates occurred earlier in the experiment than in the theoretical prediction. This implies that compression and narrowing of water paths caused the decline in the rate of water evaporation. After most water had evaporated, evaporation of the oil droplets occurred. The oil droplets did not shrink isotropically and the air-liquid interface invaded into the drying oil droplets. Cross-sectional observation by z-scanning revealed direct exposure of the oil droplets and they were pinned by the residual water phase. The water network between the oil droplets collapsed after the oil droplets had evaporated. The correlation between changes in structures and drying kinetics in both liquid phases was discussed.

Viscosity of API/fatty acid suspensions: Pitfalls during analysis

This article describes how to obtain reliable data during rheological analysis of active pharmaceutical ingredient/fatty acid suspensions. These materials are specifically used for prilling, an innovative pharmaceutical technique for the production of a multiparticulate dosage form. Nevertheless, presented guidelines are applicable for a wide range of pharmaceutical suspensions. Reliable rheological results can only be obtained when being aware of artefacts, such as a non-continuous medium, sedimentation, apparent wall slip and protrusion flow. To comply with the continuum hypothesis at high phase volumes (≥25% w/w), the required gap-to-particle-size ratio may be larger than the generally accepted 10:1 ratio. Reproducible flow curves that are not disturbed by sedimentation during sample analysis can be obtained faster by varying the shear rate stepwise from high to low values. While apparent wall slip (at low shear rates) can be prevented via serrated instead of smooth plates, protrusion flow (at high shear rates) during measurements with serrated plates results in non-reliable data. Therefore, in general, high viscous suspensions with yield stress can be analysed with serrated plates, while low viscous suspensions without yield stress should be analysed with geometries having smooth surfaces. By following these guidelines, accurate rheological properties of pharmaceutical suspensions can be obtained.

Deformation Properties of Concentrated Metal-in-Polymer Suspensions under Superimposed Compression and Shear

Concentrated metal-in-polymer suspensions (55 vol.% and 60 vol.%) of aluminum powder dispersed in low molecular weight polyethylene glycol) demonstrate elastoplastic properties under compression and shear. The rheological behavior of concentrated suspensions was studied in a rotational rheometer with uniaxial compression (squeezing), as well as shearing superimposed on compression. At a high metal concentration, the elasticity of the material strongly increases under strain, compared with the plasticity. The elastic compression modulus increases with the growth of normal stress. Changes in the shear modulus depend on both normal and shear stresses. At a low compression force, the shear modulus is only slightly dependent on the shear stress. However, high compression stress leads to a decrease in the shear modulus by several orders with the growth of the shear stress. The decrease in the modulus seems to be rather unusual for compacted matter. This phenomenon could be explained by the rearrangement of the specific organization of the suspension under compression, leading to the creation of inhomogeneous structures and their displacement at flow, accompanied by wall slip. The obtained set of rheological characteristics of highly loaded metal-in-polymer suspensions is the basis for understanding the behavior of such systems in the powder injection molding process.

Influence of Polymer Concentration and Nozzle Material on Centrifugal Fiber Spinning

Centrifugal fiber spinning has recently emerged as a highly promising alternative technique for the production of nonwoven, ultrafine fiber mats. Due to its high production rate, it could provide a more technologically relevant fiber spinning technique than electrospinning. In this contribution, we examine the influence of polymer concentration and nozzle material on the centrifugal spinning process and the fiber morphology. We find that increasing the polymer concentration transforms the process from a beaded-fiber regime to a continuous-fiber regime. Furthermore, we find that not only fiber diameter is strongly concentration-dependent, but also the nozzle material plays a significant role, especially in the continuous-fiber regime. This was evaluated by the use of a polytetrafluoroethylene (PTFE) and an aluminum nozzle. We discuss the influence of polymer concentration on fiber morphology and show that the choice of nozzle material has a significant influence on the fiber diameter.

The Behavior of Melts with Vanishing Viscosity in the Cone-and-Plate Rheometer

A semi-analytic solution for material flow in the cone-and-plate rheometer is presented. It is assumed that the viscosity is solely a function of the second invariant of the strain rate tensor. A distinguishing feature of the constitutive equations used is that the viscosity is vanishing as the shear strain rate approaches infinity. This feature of the constitutive equations affects the qualitative behavior of the solution. Asymptotic analysis is carried out near the surface of the cone to reveal these features. It is shown that the regime of sliding must occur and the shear strain rate approaches infinity under certain conditions. It is also shown that the asymptotic behavior of the viscosity as the shear strain rate approaches infinity controls these qualitative features of the theoretical solution. Some of these features are feasible for experimental verification. An interpretation of the theoretical solution found is proposed.

Flow Structure and Mixing Efficiency of Viscous Fluids in Microchannel with a Striped Superhydrophobic Wall

The peculiarities of a Newtonian fluid flow structure in microchannels with a striped superhydrophobic lower wall texture are studied by means of numerical modeling. In the Cassie-Baxter state, an oblique orientation of such a texture induces helicoidal streamlines with micro spirals. Such a flow structure favors the enhancement of fluid mixing efficiency, which can be quantified using the total root-mean-square deviation of streamlines from the microchannel axis. This characteristic was shown to be a nonmonotonic function of the striped texture tilt angle and to depend strongly on microchannel thickness. The mechanisms of micro and macro helicoidal flow structure formation are investigated, and the mixing quality of miscible fluids is estimated for various Peclet numbers and texture tilt angles. It was found that the striped superhydrophobic wall leads to a notable enhancement in the microchannel mixing efficiency at sufficiently large Peclet numbers.

Viscoplastic Couette Flow in the Presence of Wall Slip with Non-Zero Slip Yield Stress

The steady-state Couette flow of a yield-stress material obeying the Bingham-plastic constitutive equation is analyzed assuming that slip occurs when the wall shear stress exceeds a threshold value, the slip (or sliding) yield stress. The case of Navier slip (zero slip yield stress) is studied first in order to facilitate the analysis and the discussion of the results. The different flow regimes that arise depending on the relative values of the yield stress and the slip yield stress are identified and the various critical angular velocities defining those regimes are determined. Analytical solutions for all the regimes are presented and the implications for this important rheometric flow are discussed.

Large slippage and depletion layer at the polyelectrolyte/solid interface

The slippage of polymer solutions on solid surfaces is often attributed to a depletion layer whose origin, thickness, and interaction with the flow are poorly understood. Using a Dynamic Surface Force Apparatus we report a structural and nanorheological study of the interface between hydrolyzed poly-acrylamide solutions and platinum surfaces. Polyelectrolyte chains adsorb on the surfaces in a thin charged layer, acting as a nonattractive wall for the bulk solution. We investigate the flow of the visco-elastic solution on the adsorbed layer from the nanometer to 10 micrometers, bridging microscopic to macroscopic properties. At distances larger than 200 nanometers, the flow is well described by an apparent slip boundary condition. At smaller distance the apparent slip is found to decrease with the gap. In contrast to the apparent slip model, we show that a 2-fluids model taking into account the finite thickness of depletion layers at the non-attractive wall describes accurately the dynamic forces over 4 spatial decades of confinement. Depletion layers are found to be an equilibrium property of the interface, independent on the flow and on the confinement. Their thickness is phenomenologically described by ξ + 2l_D with ξ the correlation length of the semi-dilute solutions and l_D the Debye length. We interpret this result in terms of screened repulsion between the charged adsorbed layer and the bulk polyions.

A Preliminary Computational Investigation Into the Flow of PEG in Rat Myocardial Tissue for Regenerative Therapy

Myocardial infarction (MI), a type of cardiovascular disease, affects a significant proportion of people around the world. Traditionally, non-communicable chronic diseases were largely associated with aging populations in higher income countries. It is now evident that low- to middle-income countries are also affected and in these settings, younger individuals are at high risk. Currently, interventions for MI prolong the time to heart failure. Regenerative medicine and stem cell therapy have the potential to mitigate the effects of MI and to significantly improve the quality of life for patients. The main drawback with these therapies is that many of the injected cells are lost due to the vigorous motion of the heart. Great effort has been directed toward the development of scaffolds which can be injected alongside stem cells, in an attempt to improve retention and cell engraftment. In some cases, the scaffold alone has been seen to improve heart function. This study focuses on a synthetic polyethylene glycol (PEG) based hydrogel which is injected into the heart to improve left ventricular function following MI. Many studies in literature characterize PEG as a Newtonian fluid within a specified shear rate range, on the macroscale. The aim of the study is to characterize the flow of a 20 kDa PEG on the microscale, where the behavior is likely to deviate from macroscale flow patterns. Micro particle image velocimetry (μPIV) is used to observe flow behavior in microchannels, representing the gaps in myocardial tissue. The fluid exhibits non-Newtonian, shear-thinning behavior at this scale. Idealized two-dimensional computational fluid dynamics (CFD) models of PEG flow in microchannels are then developed and validated using the μPIV study. The validated computational model is applied to a realistic, microscopy-derived myocardial tissue model. From the realistic tissue reconstruction, it is evident that the myocardial flow region plays an important role in the distribution of PEG, and therefore, in the retention of material.

Moses effect: physics and applications

Deformation of the surface of a diamagnetic liquid by a magnetic field is called the "Moses Effect". Magnetic fields of ca 0.5 T give rise to near surface dips with a depth of dozens of microns. The physics and applications of direct and inverse Moses effects are reviewed, including trapping and self-assembly of particles. Experimental techniques enabling visualization of the effects are surveyed. The impact of a magnetic field on micro- and macroscopic properties of liquids is addressed. The influence of surface tension on the shape of the near-surface dip formed in a diamagnetic liquid by magnetic field is reported. Floating of diamagnetic bodies driven by the Moses effect is treated. The "magnetic memory of water" in relation to the Moses Effect is discussed. The dynamics of self-healing of near-surface dips due to the Moses Effect is considered.

Vortical Fountain Flows in Plasticating Screws

Variances in polymers processed by single-screw extrusion are investigated. While vortical flows are well known in the fluids community and fountain flows are well known to be caused by the frozen layers in injection molding, our empirical evidence and process modeling suggests the presence of vortical fountain flows in the melt channels of plasticating screws adjacent to a slower-moving solids bed. The empirical evidence includes screw freezing experiments with cross-sections of processed high-impact polystyrene (HIPS) blended with varying colorants. Non-isothermal, non-Newtonian process simulations indicate that the underlying causality is increased flow conductance in the melt pool caused by higher temperatures and shear rates in the recirculating melt pool. The results indicate the development of persistent, coiled sheet morphologies in both general purpose and barrier screw designs. The behavior differs significantly from prior melting and plastication models with the net effect of broader residence time distributions. The process models guide potential strategies for the remediation of the processing variances as well as potential opportunities to achieve improved dispersion as well as complex micro and nanostructures in polymer processing.