Viscous Potential Research Articles

Visco-Hyperelastic Constitutive Modeling for High-Damping Rubber Materials During Combined Quasi-Static Compression–Cyclic Shear Deformation Process

High-damping rubber materials utilized in high-damping rubber isolation bearings are frequently subjected to multiple deformations during the occurrence of earthquakes. Typically, large combined compression–shear deformations of the material could potentially cause compressive shear damage to rubber bearings. During this process, visco-hyperelastic properties of rubber materials will greatly change, which would significantly impact the seismic performance of rubber bearings. Thus, to give out a deep insight into their variations, it is necessary and urgent to develop a high-performance numerical method to investigate this process. This paper proposed a visco-hyperelastic constitutive modeling approach for high-damping rubber materials based on the experimental assessment of combined quasi-static compression–cyclic shear deformation process. Within the thermodynamic framework, the Clausius–Duhem inequality associated with the intrinsic dissipation of the material was firstly derived in accordance with the Lagrangian formulism. Then, stress–strain relations were obtained upon considering the occurrence of entropy production due to viscous dissipation. In the model, Stumpf–Marczak strain energy density function, which satisfies the Baker–Ericksen (B–E) inequality, was harnessed to describe the hyperelasticity of the material. By introducing higher orders of strain and strain rates and taking their couplings into account, a generalized viscous dissipation potential was proposed to capture nonlinear strain and strain rate-sensitivity effects of the material. To identify constitutive parameters, the deformation gradient was particularized for the combined quasi-static compression–cyclic shear deformation process. And, an inverse identification procedure was carried out at different levels of compression stress. The prediction results revealed that the proposed model exhibits remarkable prediction ability and adaptivity for different rubber materials during this process. Several new insights were highlighted on the variations of visco-hyperelastic characteristics of high-damping rubber materials with respect to the compression stress. The accuracy of the model was further validated by design parameters including initial shear modulus, secant shear modulus and equivalent viscous damping factor. This work could provide a fundamental guideline for the optimization and reliability analysis of high-damping rubber isolation bearings used in the field of seismic engineering.

Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

Modeling steady state rate- and temperature-dependent strain hardening behavior of glassy polymers

In this paper, we use molecular dynamics (MD) simulations to investigate the origin of strain hardening in glassy polymers, with a particular focus on the influences of strain rate and temperature. We demonstrate that strain hardening in uniaxial tension arises from bond stretching and is relaxed by bond rotation, characterized by the evolution of dihedral angles. Based on this rotational relaxation, strain rate plays a role analogous to temperature, resulting in a steady state behavior in the hardening region identifiable by strain rate and temperature. Following these observations, we propose a constitutive model to describe the rate- and temperature-dependent strain hardening behavior of glassy polymers using a viscous potential as a function of strain rate. To capture the elastic and yield behavior at small strains, we integrate this viscous potential with a conventional elasto-viscoplastic (EVP) model, giving rise to our V-EVP model. The V-EVP model is shown to be thermodynamically consistent and is validated by comparison to MD simulation results of glassy polymers undergoing uniaxial tension tests across a broad range of temperatures and strain rates.

The viscous force and torque on a closed irrotational surface

The force and torque on a solid body in a viscous potential flow are often taken to be independent of viscosity. Joseph et al. (Eur. J. Mech. B/Fluids, vol. 12, 1993, pp. 97–106; J. Fluid Mech., vol. 265, 1994, pp. 1–23) proved that this holds for (i) the force (not the torque) in any two-dimensional flow, and (ii) the drag force experienced by a purely translating three-dimensional body. The remaining components of the force and torque, along with general three-dimensional flows, were not considered. Importantly, the flow was assumed to be unbounded and irrotational everywhere. We eliminate this rarely satisfied assumption and consider the viscous force and torque experienced by any closed surface where the flow is irrotational locally; this can include a body's surface. Any vorticity distribution is permitted away from the closed irrotational surface. In so doing, we complete the analysis of Joseph et al. for all components of the viscous force and torque in two and three dimensions and enable application to real flows that inevitably contain regions of vorticity.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

A novel methodology in analyzing nonlinear stability of two electrified viscoelastic liquids

The aim of this study is to analyze the nonlinear stability of two viscoelastic electrified superimposed liquids immersed in porous media. Two limitless horizontal semi-infinite electrified fluids make up the present structure. The impacts of an unchanged oblique electric field (EF) and surface tension (ST) are applied. The increasing attraction of atmospheric and oceanic dynamics is fundamental to understanding this issue. The viscous potential flow (VPF) is employed to make mathematical usage easier. The concern mainly relies on combining the essential hydrodynamic equations with Maxwell's equations in an approximately quasi-static style. The linearized controlling equations are addressed to achieve the nonlinear expression under the appropriate boundary conditions (BCs). Subsequently, the influences of viscoelasticity are ignored, while solving the equations of motion. Therefore, the flat axis and the interface disturbance are interacting horizontally. The Rayleigh Helmholtz-Duffing oscillator (RHDO) describes how the two liquids in the interface spread out. He's frequency formula (HFF) converts the traditional nonlinear differential equation (NDE) into a linear one, which is analyzed through the non-perturbative approach (NPA). As shown through a non-dimensional analysis, there are diverse dimensionless physical numerals. Likewise well-known, the non-dimensional physical characteristics could be employed to investigate the fundamental aspects of a liquid structure. Additionally, they applied to degeneration the number of characteristics needed to understand the construction. A brief description of the NPA is likewise provided. The real/complex features of the NDEs are revealed via the stability research. According to the numerical simulations, the entire system is stabilized by different situations of the oblique EF versus the horizontal wavenumber. For both real and complex components, diverse sorts of polar plots are exhibited by graphs to elucidate the impacts of diverse elements and ensure the stability of the solutions. It should be noticed that all circumstances of the EFs are portrayed. It is observed that, when the EF is tangent to the interface, the Darcy and Bond numbers have a stabilized influence on the stability configuration. Supplementary, when the EF is normal to the interface, it is recognized that dynamic viscosity stabilizes the stability distribution. The density parameter has a destabilized effect on the stability zone. Finally, when the EF is inclined to the interface, it is observed that the Bond number and the viscoelastic parameter have a stabilizing influence on the stability region.

Cleaning effects due to shape oscillation of bubbles over a rigid boundary

Recent experiments have revealed the interesting cleaning effects that take place due to the shape mode oscillation of bubbles over a rigid boundary. While a microbubble was undertaking shape oscillation moving over a bacterial biofilm, it removed the contaminants from the boundary and created a clean path through the biofilm. This demonstrated much higher cleaning efficiency than that associated with the volume oscillation of cavitation bubbles; however, the mechanism is unknown. Here, we study this phenomenon using the boundary integral method with the viscous effects modeled using the viscous potential flow theory and the compressible effects using the weakly compressible theory. The viscous stress at the rigid boundary is approximated using the boundary layer theory. We observed that the natural frequencies of shape mode oscillation decrease significantly due to the presence of the boundary. The shear stress at the boundary due to the shape oscillation of a nearby bubble is at least 20 times higher than that due to volume oscillation with the same energy and is significant only within the area directly beneath the bubble. This is explained by the notably faster decay for higher shape modes of the kinetic energy in the fluid as the distance to the center of the bubble r increases with the induced velocity of mode k decaying at a rate of O(r−(k+2)) away from the bubble. These results achieve excellent agreement with the intriguing cleaning effects first observed in the experiment and explain the mechanism behind this new highly efficient method of cleaning.

Stability analysis of spherical viscous fluid-Oldroyd B viscoelastic fluid interface: A viscous potential flow approach

The present study investigates the stability of a spherical interface formed by a combination of a viscous fluid and an Oldroyd B viscoelastic fluid using the linear stability analysis. The spherical geometry consists of a viscous fluid occupying the inner sphere, while the outer sphere is filled with the viscoelastic fluid. The governing equations are derived based on the viscous-viscoelastic irrotational theory, and their solutions are obtained using mathematical methods. The analysis results in a third-degree polynomial equation that describes the growth of perturbations, which is then evaluated numerically. It is found that the perturbations grow more rapidly at the interface between the viscoelastic and viscous fluids than at the interface between the viscous fluid and the surrounding medium. The instability of the interface increases with an increase in the Weissenberg number, which is a dimensionless parameter that characterizes the viscoelasticity of the fluid.

Nonlinear Kelvin-Helmholtz instability of a horizontal interface separating two electrified Walters' B liquids: A new approach

The present study scrutinizes the nonlinear stability of a plane interface concerning two fluids of Walters' B (WB) type. An unchanging tangential electric field (EF) impact upon the two dielectric fluids in the existence of a steady relative velocities. The two fluids have different density viscoelasticity, electrical properties, and in the existence of a surface tension at the interface. The growth implication in engineering and applied physics has motivated the attention of this concern. Due to the difficulty of the mathematical process, the viscoelastic contribution is established only at the interface, which is called the viscous potential flow (VPF). Therefore, the governing equations of motion are analyzed in a linear approach , instantaneously, the nonlinear boundary circumstances (BCs) are provided. This technique creates a nonlinear illustrative equation of the interface displacement. As well-known, the linear stability approach has intensively appeared in several literatures. Consequently, our study focuses only on the nonlinear sense. A new methodology based on the non-perturbative analysis (NPA) is employed to investigate the nonlinear stability and inspect the interface deflection in different situations. The latter equation represents a partial differential equation (PDE) with complex coefficients of the border displacement. Under some restrictions, this equation represents a nonlinear hybrid Rayleigh-Helmholtz oscillator. The considered NPA produces an equivalent linear equation. A numerical methodology is employed to confirm the solutions of the two equations. As well-known, the non-dimensional physical numbers are potential to analyze the structures of a fluid flow. Additionally, they reduce the number of variables that describe the system. These quantities frequently have physical meaning which help in some physical interpretations. Therefore, the investigation reveals several non-dimensional physical numerals. The instability benchmarks are theoretically inspected and computationally illustrated through a set of diagrams. The EF strength is strategized against the parameter of the traveling wave number, where the concern of stability/instability is portrayed. We think that the present analysis is easy, promising, and powerful, and may be applied in diverse contexts.

Outlining the impact of structural properties of a multilayered porous channel with oscillating velocities and fields

In this study, we analyze the multilayered viscous potential flow, in which the effects of primary and combined resonances on the interfacial stability due to oscillating velocities and a periodic field are carried out. Fluids are assumed to be immiscible and incompressible with different electrical and dynamic properties and move through a porous nature. Viscosity occurs at the surface through the surface dynamic condition, where it is assumed to be weak in the fluid bulk and can be ignored. Given the boundary and surface conditions, the linear solutions of the motion and field equations led to simultaneous differential equations with complex periodic coefficients, which are a generalization of Mathieu’s equations. The special case of uniform velocity and the constant field is discussed where a quadruple algebraic equation has complex coefficients is obtained. The method of multiple time scales is applied to obtain analytical approximate solutions and perform the stability criteria for both the non-resonant and resonant states. The impacts of flow velocities and associated electric field properties, as well as the permeability of porous media and fluid sheet geometry, were taken into consideration. Through numerical discretization by varying the values of the quantities of the model, essential conclusions can be made that support an understanding of the stabilization process. For the primary resonance, it is found that there is an important role in increasing the thickness of the layers to the stability of the fluid sheet, while the porosity of the layers has a dual role phenomenon depending on the thickness of the upper layer. In the case of combined resonance, it was mentioned that increasing the dielectric constant between the lower layer and middle one tends to assist the system to instability, but it is worth noting that it supports it slowly, on the other hand, the electric horizontal field helps the system to be more stable.

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

This study attempts to provide an approach to studying the nonlinear stability of a vertical cylindrical interface between two Oldroyd-B prototypes. An unchanged axial electric field influences the system, and porous medium, and the effects of heat and mass transfer (MHT) are considered. Hsieh's modulation and the viscous potential flow (VPT) are used to abbreviate the mathematical analysis. The viscoelastic Oldroyd-B model significant role in geothermal, engineering and industrial enhancement motivated us to carry out this in-depth investigation. The methodology of the nonlinear technique depends mainly on solving the linear equations of motion and applying the appropriate nonlinear boundary conditions. Numerous non-dimensional physical numbers are exposed using a non-dimensional technique. The stability conditions are theoretically achieved and numerically verified. As a limiting case, the linear dispersion equation is accomplished, and a set of stability diagrams is reachable. Together with the nonlinear stability method, a Ginzburg–Landau equation is derived. Subsequently, both theoretical and numerical methods are used to achieve the nonlinear stability criteria. Furthermore, a precise perturbed approach for surface deflection is achieved theoretically and numerically using the Homotopy perturbation method and the extended frequency conception. Along with the linear approach, it is found that the structure becomes unstable by the Laplace, Reynolds, Weber, and elasticity quantities as well as the linear MHT parameter. Furthermore, the stability zones are enhanced in the nonlinear instability approach.

NONLINEAR EHD STABILITY OF ENCLOSED COAXIAL JETS WITH MASS AND HEAT TRANSMISSION IN THE EXISTENCE OF AN OSCILLATORY GAS VELOCITY PROFILE

In this paper, the present work investigates a nonlinear temporal instability of coaxial cylinders in porous media in the existence of an oscillating gaseous velocity. Heat and mass transfer (MHT), as well as a uniform axial electric field were all taken into account. The viscous potential flow (VPF) was employed to calculate liquid and gas velocities to make the mathematical manipulations easier. As a result of the analysis of the boundary-values problem, the cylindrical interface displacement provided a nonlinear characteristic equation. To achieve the stability inspection, a novel approach was created. The article designates both the oscillatory and uniform streaming gas. The nonlinear analysis was completed using the homotopy perturbation method (HPM), which resulted in a Klein-Gordan equation, to arrive the stability maps. Additionally, the resonance and non-resonance cases were accomplished. In the previous situations, the stability standards were theoretically derived and numerically proven using regular diagrams. It was found that the unchanging flowing had a twofold effect. The linear MHT parameter was identified to perform a twofold character in the stability setup. On the other hand, nonlinear parameters have opposing effects. The outcomes of the homogeneous gas velocities were substantially conforming.

Stability Characteristics of Planar Rivlin–Ericksen Fluid Interface With Mass and Heat Transfer

Abstract The interface of viscous-Rivlin-Ericksen fluids is analyzed through the linear theory of stability analysis when mass and heat is transferring across the interface. The Rivlin-Ericksen fluid lies in the upper region while the lower region of the interface contains viscous fluid. The gravitational acceleration destabilizes the top-heavy arrangement and interface instability is governed by Rayleigh–Taylor instability. The two-dimensional interface is considered, and the viscous potential flow theory is employed to establish the relationship between perturbation's growth and wave number. This relationship is analyzed, and the perturbation's growth is plotted for various flow parameters. A marginal stability condition is obtained, and it is given in terms of heat transport coefficient Λ and wave number. The marginal stability criterion is analyzed using the well-known Newton–Raphson method. The heat and mass transfer phenomenon drives the unstable interface toward stability. It is pointed out that the viscoelastic coefficient λo influences the interface to be stable while the thickness of the viscoelastic fluid makes the interface unstable. Atwood numbers and Weber numbers show destabilizing behavior.

Analytical model for viscous and elastic Rayleigh–Taylor instabilities in convergent geometries at static interfaces

Great attention has been attracted to study the viscous and elastic Rayleigh–Taylor instability in convergent geometries, especially for their low mode asymmetries that behave distinctively from the planar counterparts. However, most analyses have focused on the instability at static interfaces that excludes the studies of the Bell–Plesset effects and the elastic–plastic transition since they involve too complex mathematics. Herein, we perform detailed analyses on the dispersion relations by applying the viscous and elastic potential flow method to obtain their approximate growth rates compared with the exact ones to demonstrate: (i) The approximate growth rates based on potential flow method generally coincide with the exact ones. (ii) An alternative expression is proposed to overcome the discrepancy for the low mode asymmetries at fluid/fluid interface. (iii) Extra care must be taken in solids since the maximum discrepancies occur at the n = 1 mode and at the mode proximate to the cutoff. This analytical method of great simplicity is essential to describe the dynamic interface by including the overall motion of the interface based on the static construction, while the exact analysis involves too complex mathematics to be extended by including the Bell–Plesset effects and the elastic–plastic properties. To sum up, the approximate analytical dispersion relations derived in convergent geometries, have the potential for dealing with dynamic interfaces where Bell–Plesset effects are combined with elastic–plastic transition.

An analytical model for the Kelvin–Helmholtz instability in solids

Although Rayleigh–Taylor (RT) and Richtmyer–Meshkov(RM) instabilities in solids have long been confirmed to play a significant role in high-energy-density physics and to serve as tools to diagnose material properties under high-strain and high-strain-rate conditions, the Kelvin–Helmholtz (KH) instability in solids under extreme conditions has yet to be fully investigated. In addition, according to experiments driven by high explosives or by high-intensity lasers, the interface behavior is frequently determined by the KH instability with RT and RM instabilities, as well as by gravity decay waves. Therefore, a comprehensive analysis is required to study the mechanical properties of solids under extreme conditions and the multiple stability mechanisms that affect the interface behavior. This paper proposes a simplified and analytical mathematical model for stability analysis by considering surface tension, viscosity, elasticity, viscoelasticity, and perfectly rigid plasticity as a function of the specific physical conditions. The model is used to examine how the KH instability, RT instability, and gravity decay wave affect the evolution of the interface. We first recover the well-known dispersion relations based on the viscous potential flow method for the KH instability, and in particular investigate the stability threshold with varying shear velocities and in the presence of gravity decay waves. For the KH instability in elastic solids, once the velocity difference exceeds an asymptotic value (i.e., when the effect of elasticity cancels that of shear velocity), the interface always remains unstable for all perturbed wavelengths—a result that departs from the traditional conclusion about the RT instability between elastic solids. Unexpectedly, the viscosity in Kelvin–Voigt materials can enhance the resistance to the hydrodynamic instability, while the elasticity has the opposite effect. The growth rates and the cutoff wave numbers increase gradually as the viscoelastic parameter decreases, and the inhibition of the high-wave number disturbance by the viscoelasticity is correspondingly reduced. In addition, the cutoff wave numbers depend only on densities and the shear modulus of the material and are independent of the viscous properties of the materials. Finally, the evolution of the perturbed amplitude is studied in rigid plastic materials, which offers physical insights of interest to further study the KH instability in viscoplastic and elastoplastic materials. Based on the models developed herein, experiments are proposed for further research into the mechanical properties of materials under extreme conditions.

Temporal Instability of Liquid Jet in Swirling Gas with Axial Velocity Oscillation

In the present study, viscous potential flow theory is employed to investigate the temporal instability of a viscous liquid jet in swirling gas with axial velocity oscillation. The dispersion-relation equation is obtained between dimensionless growth rate and wave number. Because of the axial velocity oscillation of gas, there are more than one instability regions, including Kelvin–Helmholtz (K–H) instability region and parametric instability region. The results suggest that increasing gas swirling strength stabilizes the liquid jet in axisymmetric mode, while it enhances the instability in nonaxisymmetric modes. And the gas viscosity has a destabilizing effect. In addition, increasing the forcing frequency enhances instability in the K–H instability region. However, it has a stabilizing effect in the parametric instability region. Furthermore, increasing oscillation amplitude enhances instability in both the K–H instability region and the parametric instability region. Because of the competition between the parametric and K–H instabilities, the location of dominant wave number is uncertain.

Multi-fidelity Co-Kriging surrogate model for ship hull form optimization

For the simulation-based hull form optimization design, there are many methods to evaluate the hydrodynamic performance of the hull form. Although the high fidelity of the surrogate model can be guaranteed by evaluating a large number of new sample hulls based on viscous flow theory, the computational cost can be too high. Therefore, in order to release the burden of calculation, based on the traditional single-fidelity Kriging surrogate model, the multi-fidelity Co-Kriging surrogate model gives attention to both high accuracy and efficiency by combining the accuracy advantage of high-fidelity sample evaluation with the efficiency advantage of low-fidelity sample evaluation. This paper first introduces the construction process of the multi-fidelity Co-Kriging surrogate model, and then uses a series of numerical examples to illustrate the advantages of the multi-fidelity Co-Kriging surrogate model compared with the single-fidelity Kriging surrogate model in terms of fidelity and efficiency. Finally, a hull form optimization design for total drag of DTMB-5415 hull at the design speed is given in detail, where the viscous flow theory and potential flow theory are used for the hydrodynamic evaluations of the hull forms to obtain the high- and low-fidelity results respectively. Results show that the multi-fidelity Co-Kriging surrogate model can be established for hull form hydrodynamic performance optimization, which is superior to the single-fidelity Kriging surrogate model in accuracy, and the optimal hull obtained by Co-Kriging surrogate model has a better resistance optimization effect.

Electric and viscous correction for viscous potential flow analysis of electrohydrodynamic instability of an electrified leaky-dielectric jet

The electric and viscous correction of viscous potential flow (EVCVPF) is developed for analyzing the electrohydrodynamic instability of an electrified leaky-dielectric viscous jet. The EVCVPF model is based on the viscous potential flow (VPF) and the viscous correction of VPF (VCVPF), proposed by Joseph and Wang [“The dissipation approximation and viscous potential flow,” J. Fluid Mech. 505, 365–377 (2004)]. The purpose is to resolve the discrepancy between the non-zero irrotational viscous and the electric tangent stresses. The power of the pressure correction is introduced to compensate the neglected viscous dissipation in the flow bulk in VPF, which is equal to the average power of the irrotational viscous and the electric tangent stresses. The model has been validated by comparing it to the exact normal-mode solution of the linearized Navier–Stokes equations (fully viscous flow, FVF). The energy budget is also performed to assist in understanding underlying mechanisms. Results show that EVCVPF is accurate for charged jets with low and moderate viscosities, i.e., the Ohnesorge number approximately Oh ≤ 0.1. The inaccuracy for highly viscous jets are the limitations of VPF itself. The electric field has less influence compared to the fluid viscosity. To achieve more accurate approximations, VCVPF and VPF are chosen for axisymmetric and non-axisymmetric modes under weak electric fields. EVCVPF is in remarkably good agreement with FVF under moderate and strong electric fields. In general, as VCVPF extends the applicability in fluid viscosity of VPF, EVCVPF further improves the adequacy when studying the electrohydrodynamic instability.

Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

The current work examines the application of the viscous potential flow to the Kelvin-Helmholtz instability (KHI) of a planar interface between two visco-elastic Walters’ B fluids. The fluids are fully saturated in porous media in the presence of heat and mass transfer across the interface. Additionally, the structure is pervaded via a uniform, normal electrical field in the absence of superficial charges. The nonlinear scheme basically depends on analyzing the linear principal equation of motion, and then applying the appropriate nonlinear boundary-conditions. The current organization creates a nonlinear characteristic equation describing the amplitude performance of the surface waves. The classical Routh–Hrutwitz theory is employed to judge the linear stability criteria. Once more, the implication of the multiple time scale with the aid of Taylor theory yields a Ginzburg–Landau equation, which controls the nonlinear stability criteria. Furthermore, the Poincaré–Lindstedt technique is implemented to achieve an analytic estimated bounded solution for the surface deflection. Many special cases draw upon appropriate data selections. Finally, all theoretical findings are numerically confirmed in such a way that ensures the effectiveness of various physical parameters.

Association of Pepsin With Inflammatory Signaling and Effusion Viscosity in Pediatric Otitis Media.

Otitis media (OM) is a common inflammatory disease spectrum. Cytokine signaling, neutrophil activity, and mucin hypersecretion during recurrent and chronic OM contribute to persistent, viscous middle ear (ME) effusions, hearing loss, and potential for developmental delay. Extraesophageal reflux (EER), specifically pepsin, triggers inflammatory signaling in respiratory mucosa and is associated with OM. The objective of this study was to investigate the association of pepsin with ME inflammatory signaling and the outcomes and examine causality in vitro. Cross-sectional study. ME fluid (MEF) and preoperative audiometric data were collected from 30 pediatric subjects undergoing tympanostomy tube placement for recurrent OM or OM with effusion. MEF viscosity was characterized by the surgeon. Pepsin, inflammatory molecules, and mucin were assayed by enzyme-linked immunosorbent assay (ELISA). ME epithelial primary culture was exposed to 0.1 to 1 mg/ml pepsin at pH 5, 6, and 7 for 30 minutes, and cytokine expression was assayed via qPCR. Pepsin was observed in the MEF of 77% of patients (range 71-2,734 ng/ml). Pepsin correlated with effusion viscosity, interleukins -6 and -8, neutrophil elastase, and mucin 5B (P< .05). Pepsin-negative MEF was more frequently absent of interleukin 8 or mucin 5B (P< .05). Weak acid was generally insufficient to elicit cytokine expression in ME cells in vitro, however, pepsin induced IL6, IL8, and TNF at pH 7 (P< .05) and weak acid (pH 6) facilitated a response at lower pepsin concentration. Pepsin may contribute to inflammatory signaling, persistent viscous effusion, and poorer OM outcomes. 4 Laryngoscope, 132:470-477, 2022.