Imposing a temperature gradient on a narrow channel can trigger an acoustic instability, driving self-sustained oscillations of the fluid. The temperature gradient required to trigger the instability is dramatically decreased when the channel wall is covered by a thin film of volatile liquid that can undergo phase change. In the present work, we consider a volatile-droplet aerosol on which a temperature

Previous studies (Watt et al. in J Eng Math 75(1):1, 2012; Cartwright and Falle in J Eng Math 115(1):157, 2019) have shown that a streamline based approach to modelling of steady state detonations can produce good results for rate laws which have maximal reaction at the shock. In this paper we consider a Variational Streamline Approximation (VSA) which introduces streamline curvature. Comparing results

Desulphurisation of flue gas is essential before it can be released safely into the atmosphere. One way of removing sulphur dioxide is to use a purification device incorporating a reactive filter, in which the flue gas stream passes in front of a porous-catalyst-filled structure which converts the gaseous sulphur dioxide into liquid sulphuric acid. In this paper, we build and solve a simple mathematical

A capillary surface bound by a solid rectangular channel exhibits dynamic wetting effects characterized by a constitutive law relating the dynamic contact-angle to the contact-line speed through the contact-line mobility \(\Lambda \) parameter. Limiting cases correspond to the free (\(\Lambda =0\)) and pinned (\(\Lambda =\infty \)) contact-line. Viscous potential flow is used to derive the governing

The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these

A review of investigations of plane steady external flows of incompressible fluid with developed separation zones at high Reynolds numbers is presented.

In the study of wave propagation through plates and laminates, there are no complete three-dimensional solutions especially if the plate or plies are made of an anisotropic material. In such cases, laminate theories are approximate and often give poor results in comparison with exact solutions. When laminae or plate is highly anisotropic, the small parameter, which is appropriate is usually the modulus

A spectral constitutive equation for finite strain viscoelastic bodies with residual stresses is developed using spectral invariants, where each spectral invariant has a clear physical meaning. A prototype constitutive equation containing single-variable functions is presented; a function of a single invariant with a clear physical interpretation is easily manageable and is experimentally attractive

The dynamic translation of a micron-sized encapsulated bubble is investigated numerically inside a horizontal tube where liquid flows under constant pressure drop, when the effect of gravity is neglected. The coating of the bubble is treated as an infinitesimally thin viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed to solve the axisymmetric flow configuration

In this study, the authors proposed one-dimensional non-Fourier heat conduction model applied to phase change problem in the presence of variable internal heat generation and this has been performed by finite element Legendre wavelet Galerkin method (FELWGM). We derived the stability analysis of the non-Fourier heat conduction model in our present case. The finite difference technique has been used

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a liquid pool. Prior to impact, viscous forces in the air act to deform the liquid free surface, inducing a flow in the pool. These interactions are then

We use perturbation methods to analyze the “asymmetric rectified electric field (AREF)” generated when an oscillating voltage is applied across a model electrochemical cell consisting of a binary, asymmetric electrolyte bounded by planar, parallel, blocking electrodes. The AREF refers to the steady component of the electric potential gradient within the electrolyte, as discovered via numerics by Hashemi

We consider a macroscale model of transport and reaction of chemical species in a porous medium with a special focus on mineral precipitation–dissolution processes. In the literature, it is frequently proposed that the reaction rate should depend on the reactive mineral surface area, and so on the amount of mineral. We point out that a frequently used model is ill posed in the sense that it admits

This paper studies the generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow over a half-infinite flat plate with a roughness element using an asymptotic approach. It is assumed that the Reynolds number (denoted Re) is large, and that the free-stream turbulence is uniform so it can be modelled as vorticity waves. Close to the plate, a Blasius boundary layer forms at a

The linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising

In this work, a semi-analytic method has been developed to perform the hydroelasticity analysis of containerships. For the solution of the hydrodynamic problem, a time-domain method is developed based on impulse response function (IRF); however, for the solution of the structural responses, modal superposition technique is used assuming the ship is based on Euler–Bernoulli beam theory. The time-domain

In this study, we develop linear and energy stable numerical schemes for the Swift–Hohenberg equation with quadratic-cubic nonlinearity. A modified scalar auxiliary variable (SAV) approach is used to construct the temporally first- and second-order accurate discretizations. Different from the classical SAV approach, the proposed schemes permit us to solve the governing equations in a step-by-step manner

The present paper investigates the receptivity of inviscid first and second modes in a supersonic boundary layer to time-periodic wall disturbances in the form of local blowing/suction, streamwise velocity perturbation and temperature perturbation, all introduced via a small forcing slot on the flat plate. The receptivity is studied using direct numerical simulations (DNS), finite- and high-Reynolds-number

We consider the optimization of a chemical microchannel reactor by means of PDE-constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software

A closed-form solution for transient thermal stress analysis of functionally graded hollow cylinder exposed to high-temperature difference is obtained under the influence of periodic rotation. All mechanical and thermal properties except the Poisson’s ratio are assumed to be graded in the radial direction as a power-law function. The transient heat conduction and equilibrium equations are solved on

The method of matched asymptotic expansions is applied to the investigation of transitional separation bubbles. The problem-specific Reynolds number is assumed to be large and acts as the primary perturbation parameter. Four subsequent stages can be identified as playing key roles in the characterization of the incipient laminar–turbulent transition process: due to the action of an adverse pressure

We investigate the dynamics of a smoothly curved convex body skimming on a layer of shallow water, with the phenomenon of skipping stones as a primary modelling motivation but also industrial applications in mind. The skimming process of such an object may consist of two successive stages: an impact stage and a conditional planing stage. The focus here is on explaining the change from one stage to

It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy

The paper is concerned with a partly analytical, partly numerical study of acoustic trapped modes in a cylindrical cavity (expansion chamber), placed in between two semi-infinite pipes acting as a waveguide. Trapped mode solutions are expressed in terms of Fourier–Bessel series, with the expansion coefficients determined from a determinant condition. The roots of the determinant, expressed in terms

In this paper, we study the dynamics of rigid particles in either viscoelastic flow or unsteady Stokes flow in 3D. We start with the Cauchy momentum equation in time domain, and apply the Fourier transform to recast the problem in frequency domain as a Brinkman equation with imaginary coefficients. The Fourier space equations are reformulated in terms of boundary integrals. This formulation allows

This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In this context, it (i) formulates the general dynamical problem of a rectangular plate with embedded a single family of straight fibres that possess bending resistance

Calcium signaling regulates and maintains plethora of complicated phenomena taking place inside the brain, the alterations in which results into devastating neuronal disorder like Alzheimer’s disease (AD). In this analysis, the calcium concentration distribution is determined where simultaneous attention is paid to the physiology behind AD and complex mathematical formulations. A system of two non-linear

We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow close to a no-slip boundary and the temperature field for a point heat source placed in a heat flow close to a temperature jump boundary. We also derive the solution

An asymptotic approach of analysis is used to analyze the antisymmetric anti-plane shear dispersion of an elastic inhomogeneous five-layered plate in the presence of material contrasts. The resultant exact dispersion relation, overall cut-off frequency and the low-frequency range are determined. Two different asymptotic contrasting material setups for layered plates are employed with regards to the

Energy stability theory is applied to the study of the nonlinear stability of natural convection in an inclined fluid layer having a uniform internal heat source (sink), with the boundaries of the layer maintained at constant temperatures. The stability limit is found in terms of the thermal Rayleigh number \(R_{1}\) and the internal Rayleigh number \(R_{2}\). The region of stability is found in \(R_{1}\)–\(R_{2}\)

In this note we examine fluid violent kinematics in a plunging breaker. The fluid motion is computed in the frame of the potential flow theory. The fluid kinematics is basically generated by forcing the motion of a rectangular tank, starting from rest. When a sufficient level of energy is injected in the fluid, the free surface has highly nonlinear behavior, here a plunging breaker. In the vicinity

This article considers a thin-walled hollow cylinder, which is composed of a fibrous and swellable hyperelastic material. The fibers are arranged in two families and they are taken to be parallel within each fiber family. The two fiber families are also assumed to be mechanically equivalent and symmetrically disposed in the ground substance material. At each instant of the homogeneous swelling, the

Two-dimensional boundary layer flows in quiet disturbance environments are known to become unstable to Tollmien–Schlichting waves. The experimental work of Liepmann et al. (J Fluid Mech 118:187–200, 1982), Liepmann and Nosenchuck (J Fluid Mech 118:201–204, 1982) showed how it is possible to control and reduce unstable Tollmien–Schlichting wave amplitudes using unsteady surface heating. We consider

The high-speed impact of a droplet onto a flexible substrate is a highly non-linear process of practical importance, which poses formidable modelling challenges in the context of fluid–structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical

The study here is concerned with a thin solid body passing through a boundary layer or channel flow and interacting with the flow. Relevant new features from modelling, analysis and computation are presented along with comparisons. Three scenarios of such fluid-body interactive evolution in two-dimensional settings are considered in turn, namely a long body translating upstream or downstream, a long

Long wavelength instabilities of boundary layers caused by centrifugal effects or wall roughness are investigated. The wall roughness is modelled by small amplitude surface waviness. The instability is described in the nonparallel regime where it develops on the same length scale as the unperturbed flow. It is shown that instabilities initiated by disturbances close to the leading edge initially deform

Detailed fibre architecture plays a crucial role in myocardial mechanics both passively and actively. Strong interest has been attracted over decades in mathematical modelling of fibrous tissue (arterial wall, myocardium, etc.) by taking into account realistic fibre structures, i.e. from perfectly aligned one family of fibres, to two families of fibres, and to dispersed fibres described by probability

A fiber-reinforced material comprised of a soft polymeric matrix reinforced with polymeric filaments is often modeled as an equivalent anisotropic nonlinearly elastic solid. Although the response of a single constituent polymeric material can be modeled by nonlinear thermo-elasticity over a large range of deformations and temperatures, there can be conditions requiring a theory that extends the range

Piezoelectric materials have a wide range of industrial applications in different branches of engineering due to their electromechanical coupling. So, investigating their responses to either mechanical or electric loadings helps engineers for efficient design of smart systems. However, most of the studies have assessed the well-known 6 mm piezoelectric materials or piezoceramics and few papers have

The flow of Bingham materials inside rectangular channels is characterized by a plug region located in the central region of the conduit and four dead zones in the vicinity of the corners of the geometry (i.e., the unyielded regions) that grow as the Bingham number is increased. In this paper, a semianalytical technique is presented for solving the flow of Bingham yield-stress materials inside straight

The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients and equipped by Neumann boundary condition, hence modeling the hard scattering of damped waves. The differential problem, which includes, besides diffusion, advection and reaction terms, is written as a space–time boundary integral equation (BIE) whose kernel is given

The present article discusses the solute transport process in steady laminar blood flow through a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits. The Darcy–Brinkman–Forchheimer drag force formulation is adopted to mimic a sparsely packed porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The conservation equations are implemented

This paper investigates the interaction of water waves with a group of submerged porous reef balls, which are hemispheres with centers lying on a plane seabed. An analytical solution based on potential theory is developed. In the solving process, the series solutions of the velocity potentials in the exterior and internal fluid domains of the reef balls are obtained by means of multipole expansions

The strain energy for incompressible anisotropic non-linearly elastic materials is decomposed into an isotropic part representing the mechanical response of an isotropic matrix and an anisotropic part representing the contribution to the mechanical response from the presence of fibres. It is the form of the anisotropic component that is of interest here. We note that the invariants can themselves be

This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric

This paper presents a Green’s function method for the modal analysis of structures with interval parameters. By introducing first order approximations, the governing equations of modal displacements for interval analysis are decomposed into two sets of governing equations for the midpoints and deviations of modal responses, respectively. Utilizing the similarity between these equations and the governing

Eccentric annular regions formed by two impermeable cylinders are considered. Flow of Newtonian fluid in the annular region in the presence of heat transfer is studied. The eccentric annulus is mapped to concentric annular region through conformal mapping. Analytical solution for both temperature and velocity is obtained and graphically depicted. An increase in eccentricity results in an increase in

Multilayered membrane filters, which consist of a stack of thin porous membranes with different properties (such as pore size and void fraction), are widely used in industrial applications to remove contaminants and undesired impurities (particles) from a solvent. It has been experimentally observed that the performance of well-designed multilayer structured membranes is markedly better than that of

The transient mixed problem for an elastic semi-strip is investigated in this article. The semi-strip is loaded by a transient load at the center of its short edge. The longitudinal sides of the semi-strip are fixed. The initial problem is reduced to a one-dimensional problem with the help of Laplace and Fourier transforms. The analytical solution of the one-dimensional boundary problem is constructed

In many micro- and macro-scale systems, collective dynamics occurs from the coupling of small spatially segregated, but dynamically active, units through a bulk diffusion field. This bulk diffusion field, which is both produced and sensed by the active units, can trigger and then synchronize oscillatory dynamics associated with the individual units. In this context, we analyze diffusion-induced synchrony

We address a boundary-value problem involving a Poisson–Boltzmann equation that models the electrostatic potential of a channel formed by parallel plates with an electrolyte solution confined between the plates. We show the existence and uniqueness of solution to the problem, with special (particular) solutions as bounds, namely, a Debye–Hückel type solution as lower bound and a Gouy–Chapman type solution

The nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites has been investigated in this paper aiming at its applications in general 3D stress conditions in a consistent manner. So far, such relationship has only been addressed in plane stress conditions. In this paper, it has been shown that its straightforward generalisation to 3D stress states lacks

We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting in a set of singular integro-differential equations on the boundary. The resulting boundary integral equations are solved numerically using a Chebyshev collocation method which is augmented by a fractional power term, derived

A stagnant free-surface flow is an instantaneous flow field of pure acceleration with zero velocity and a deformed surface. There exists a potential-flow acceleration field. With zero velocity and the acceleration field given, there is a limiting free-surface position which possesses one peak at its point of highest elevation. By complex analysis, it can be shown that the surface peak has a right angle

In his landmark paper, Keller (J Appl Phys 34:991–993, 1963) obtained an approximation for the effective conductivity of a composite medium made out of a densely packed square array of perfectly conducting circular cylinders embedded in a conducting medium. We here examine Keller’s problem for the case of square cylinders, considering both a full-pattern and a checkerboard configurations. The dense

Three weakly nonlinear but fully dispersive Whitham–Boussinesq systems for uneven bathymetry are studied. The derivation and discretization of one system is presented. The numerical solutions of all three are compared with wave gauge measurements from a series of laboratory experiments conducted by Dingemans (Comparison of computations with Boussinesq-like models and laboratory measurements. Delft

Problems of water wave propagation over an infinite step in the presence of a thin vertical barrier of four different geometrical configurations are investigated in this paper. For each configuration of the barrier, the problem is reduced to solving an integral equation or a coupled integral equation of first kind involving horizontal component of velocity below or above the barrier and above the step

Residual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular

The paper presents a study of the propagation and interaction of weakly nonlinear plane waves in isotropic and transversely isotropic media. It begins with a definition of stored energy functions of considered hyperelastic models. The equation of elastodynamics as well as the first-order quasilinear hyperbolic system for plane waves are provided. The eigensystem for this system is determined to study