Measurement method of complex viscoelastic material properties

A measurement technique of viscoelastic properties of polymers is proposed to investigate complex Poisson’s ratio as a function of frequency. The forced vibration responses for the samples under normal and shear deformation are measured with varying load masses. To obtain modulus of elasticity and shear modulus, the present method requires only knowledge of the load mass, geometrical characteristics of a sample, as well as both the amplitude ratio and phase lag of the forcing and response oscillations. The measured data were used to obtain the viscoelastic properties of the material based on a 2D numerical deformation model of the sample. The 2D model enabled us to exclude data correction by the empirical form factor used in 1D model. Standard composition (90% PDMS polymer + 10% catalyst) of silicone RTV rubber (Silastic^® S2) were used for preparing three samples for axial stress deformation and three samples for shear deformation. Comprehensive measurements of modulus of elasticity, shear modulus, loss factor, and both real and imaginary parts of Poisson’s ratio were determined for frequencies from 50 to 320 Hz in the linear deformation regime (at relative deformations 10^?6 to 10^?4) at temperature 25 °C. In order to improve measurement accuracy, an extrapolation of the obtained results to zero load mass was suggested. For this purpose measurements with several masses need to be done. An empirical requirement for the sample height-to-radius ratio to be more than 4 was found for stress measurements. Different combinations of the samples with different sizes for the shear and stress measurements exhibited similar results. The proposed method allows one to measure imaginary part of the Poisson’s ratio, which appeared to be about 0.04–0.06 for the material of the present study.     

Vertical stability of bubble chain: Multiscale approach

Linear stability is investigated of a uniform chain of equal spherical gas bubbles rising vertically in unbounded stagnant liquid at Reynolds number Re = 50–200 and bubble spacing s > 2.6 bubble radii. The equilibrium bubble positions are questioned for their stability with respect to small displacements in the vertical direction, parallel to the chain motion. The transverse displacements are not considered, and the chain is assumed to be laterally stable. The bubbles are subjected to three kinds of forces: buoyant, viscous, inviscid. The viscous and inviscid forces have both pairwise (local) and distant (nonlocal) components. The pairwise forces are expressed by the leading-order formulas known from the literature. The distant forces are expressed as a linear superposition of the pairwise forces taken over several farther neighbours. The stability problem is addressed on three different length scales corresponding to: discrete chain (microscale), continuous chain (mesoscale), bubbly chain flow (macroscale). The relevant governing equations are derived for each scale. The microscale equations are a set of ODE’s, the Newton force laws for the individual discrete bubbles. The mesoscale equation is a PDE for bubbles continuously distributed along a line, obtained by taking the continuum limit of the microscale equations. The macroscale equations are two PDEs, the mass and momentum conservation equations, for an ensemble of noninteracting mesoscale chains rising in parallel. This transparent two-step process (micro → meso → macro) is an alternative to the usual one-step averaging, in obtaining the macroscale equations from microscale information. Here, the scale-up methodology is demonstrated for 1D motion of bubbles, but it can be used for behaviour of 2D and 3D lattices of bubbles, drops, and solids.It is found that the uniform equilibrium spacing results from a balance between the attractive and repulsive forces. On all three length scales, the equilibrium is stabilized by the viscous drag force, and destabilized by the viscous shielding force (shielding instability). The inviscid forces are stability neutral and generate conservative oscillations and concentration waves. The stability region in the parameter plane s − Re is determined for each length scale. The stable region is relatively small on the microscale, larger on the mesoscale, and shrinks to zero on the macroscale where the bubbly chain flow is inherently unstable.The shielding instability is expected to occur typically in intermediate Re flows where the vertical bubble interactions dominate over the horizontal interactions. This new kind of instability is studied here in a great detail, likely for the first time. Its relation to the elasticity properties of bubbly suspension on different length scales is discussed too. The shielding force takes the form of a negative bulk modulus of elasticity of the bubbly mixture.     

The high strain mechanical response of the wet Kelvin model for open-cell foams

Surface Evolver software was used to create the three-dimensional geometry of a Kelvin open-cell foam, to simulate that of polyurethane flexible foams. Finite Element Analysis (FEA) with 3D elements was used to model large compressive deformation in the [0 0 1] and [1 1 1] directions, using cyclic boundary conditions when necessary, treating the polyurethane as an elastic or elastic–plastic material. The predicted foam Young’s moduli in the [0 0 1] direction are double those of foams with uniform Plateau border cross-section edges, for the same foam density and material properties. For compression in the [1 1 1] direction, the normalized Young’s modulus increases from 0.9 to 1.1 with foam relative density, and the predicted stress–strain relationship can have a plateau, even for a linearly-elastic polymer. As the foam density increases, the predicted effects of material plasticity become larger. For foam of relative density 0.028, edge-to-edge contact is predicted to occur at a 66% strain for [1 1 1] direction compression. The foam is predicted to contract laterally when the [1 1 1] direction compressive strain exceeds 25%.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

Axisymmetric simulation of the interaction of a rising bubble with a rigid surface in viscous flow

The interaction between a rising deformable gas bubble and a solid wall in viscous liquids is investigated by direct numerical simulation via an arbitrary-Lagrangian–Eulerian (ALE) approach. The flow field is assumed to be axisymmetric. The bubble is driven by gravity only and the motion of the gas inside the bubble is neglected. Deformation of the bubble is tracked by a moving triangular mesh and the liquid motion is obtained by solving the Navier–Stokes equations in a finite element framework. To understand the mechanisms of bubble deformation as it interacts with the wall, the interaction process is studied as a function of two dimensionless parameters, namely, the Morton number (Mo) and Bond number (Bo). We study the range of Bo and Mo from (2, 6.5 × 10⁻⁶) to (16, 0.1). The film drainage process is also considered in this study. It is shown that the deformation of a bubble interacting with a solid wall can be classified into three modes depending on the values of Mo and Bo.     

Comment on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123]

By using the reciprocal theorem of elasticity, the author obtained the appropriate stress boundary conditions for the Levy solution for plate bending accurate to all order for plates of general edge geometry and loading. Two special cases of k = 0 (axisymmetric deformation of a circular plate) and k ⩾ 2 (unsymmetric deformation of a circular plate) were discussed in detail in the paper.     

Flow boiling heat transfer of R134a,R236fa and R245fa in a horizontal 1.030 mm circular channel

This research focuses on acquiring accurate flow boiling heat transfer data and flow pattern visualization for three refrigerants, R134a, R236fa and R245fa in a 1.030 mm channel. We investigate trends in the data, and their possible mechanisms, for mass fluxes from 200 to 1600 kg/m²s, heat fluxes from 2.3 kW/m² to 250 kW/m² at T_sat = 31 °C and ΔT_sub from 2 to 9 K. The local saturated flow boiling heat transfer coefficients display a heat flux and a mass flux dependency but no residual subcooling influence. The changes in heat transfer trends correspond well with flow regime transitions. These were segregated into the isolated bubble (IB) regime, the coalescing bubble (CB) regime, and the annular (A) regime for the three fluids. The importance of nucleate boiling and forced convection in these small channels is still relatively unclear and requires further research.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (∼1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e∼9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

Origin of regime transition to turbulent flow in bubble column: Orifice- and column-induced transitions

The possible events during bubble formation on an orifice were investigated using a rectangular bubble column (30 cm × 30 cm × 100 cm). The gas flow rate through a single orifice was adjusted from 0.1 dm³/min to 5.0 dm³/min covering a high flow rate regime. At the high gas flow rate, the bubble formation process was complicated by diverse events, such as wake effect, channeling, and orifice-induced turbulent flow. The detachment period could be used to discern the bubble formation steps because it was strongly affected by the above events. The bubble size distribution around the orifice was also analyzed to gain a clearer understanding of the bubble formation process. Above the rate of 3.0 dm³/min through a single orifice, the detachment period converged to a value of 25 ms irrespective of the orifice diameter. The bubble size distribution also showed little difference in this range of gas flow rate. This could be explained by the development of turbulent flow around the orifice. A 0.15 m in-diameter bubble column was tested to investigate the effect of orifice-induced turbulent flow on the regime transition in which the homogeneous flow regime is converted into the heterogeneous flow regime in the column. Obvious distinction between the orifice- and column-induced transitions was observed.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Pressure-sensitive ductile layers – I. Modeling the growth of extensive damage

Polymeric adhesives sandwiched between two elastic substrates are commonly found in multi-layers and IC packages. The non-elastic deformation and flow stress of such adhesive joints are highly pressure-sensitive. In this work, we study the effects of pressure-sensitivity, α, and plastic dilatancy, β, on void growth and coalescence ahead of a crack in ductile adhesive joints. To this end, a single layer of discrete voids is placed ahead of the crack in a pressure-sensitive dilatant adhesive sandwiched between two elastic substrates. The adhesive joint is subjected to small-scale yielding conditions. Using an associated flow rule (α = β), we show that pressure-sensitivity not only intensifies damage levels but also increases its spatial extent several fold. The damage level as well as its spatial extent is found to be even greater when a non-associated flow rule (β < α) is deployed. A reduction in the damage process zone’s thickness further increases the voiding activity in the adhesive, thereby resulting in brittle-like failure. This work also examines the fracture toughness trends using a material failure criterion for crack growth.     

Analytical and numerical techniques to predict carbon nanotubes properties

In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young’s and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young’s modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double- and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.     

Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

CFD based mini- vs. micro-system delineation in elongated bubble flow regime

Delineation of mini- and micro-scale channels with respect to two-phase flow has been the subject of many research papers. There is no consensus on when the small channel can be characterized as a mini-channel or micro-channel. The idea proposed by this paper is to use the normalized bubble nose radius, liquid film thickness top over bottom ratio, and bubble shape contour, which are found under normal gravity conditions in slug flow through a horizontal adiabatic channel, as the delineation criteria. The input parameters are bubble nose radius and bubble nose velocity as the characteristic length scale and characteristic velocity scale respectively. 3D numerical simulation with ANSYS FLUENT was used to obtain the necessary data. Following CFD practice, a mesh independence study and a numerical model validation against published experimental data were both conducted. Analysis of the numerical simulation results showed that channels with D ⩽ 100 μm can be characterized as a micro-system, while channels with D ⩾ 400 μm belong to mini-systems. The region 200 μm ⩽ D ⩽ 300 μm represents a transition from the micro-scale to mini-scale.     

Simulation of a valveless pump with an elastic tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary (IB) method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet throughout a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient (ϕ), bending coefficient (γ), the aspect ratio (l/d) of the elastic tube, and the frequency (f) of the pumping chamber. As the stretching and bending coefficients of the elastic tube increased, the net flow through the valveless pump decreased. Elastic tubes with aspect ratios in the range of 2 ⩽ l/d ⩽ 3 generated a higher flow rate than that generated for tubes with aspect rations of l/d = 1 or 4. As the frequency of the pumping chamber increased, the net flow rate of the pump for l/d = 2 increased. However, the net flow rate for l/d = 3 was nonlinearly related to the pumping frequency due to the complexity of the wave motions. Snapshots of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump to gain a better understanding of the mechanism underlying the valveless pump. The relationship between the average gap in the elastic tube and the average flow rate of the pump was analyzed. A smaller gap in the elastic tube during the expansion mode and a wider gap in the elastic tube during the contraction mode played a dominant role in generating a high average flow rate in the pump, regardless of the stretching coefficient (ϕ), the aspect ratio (l/d) of the elastic tube, or the pumping frequency of the pumping chamber (f).     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

The effects of freestream turbulence on the drag coefficient of a sphere

The effects of freestream turbulence intensity and integral length scale as freestream turbulent parameters on the drag coefficient of a sphere were experimentally investigated in a closed circuit wind tunnel. The Reynolds number, Re = Ud/ν, was varied from 2.2 × 10⁴ to 8 × 10⁴ by using spheres with diameter d of 20, 51 and 102 mm in addition to altering the freestream velocity, U. The freestream turbulence intensity Tu and flow integral length scale Λ were manipulated by the utilization of orifice perforated plates. The proper combination of orifice perforated plate hole diameter, sphere size, and sphere location along the center line of the wind tunnel enabled the independent alterations of turbulence intensity and relative integral length scale (Λ/d) from 1.8% to 10.7% and from 0.1 to 2.6, respectively, at each studied Reynolds number. Results show that over the range of conditions studied, the drag always decreases with increasing Tu and, the critical Reynolds number at which the drag coefficient is dramatically reduced is decreased by increasing Tu. Most interestingly, the drag at any particular Re and Tu may be significantly lowered by reducing Λ/d; this is particularly the case at high Re and Tu.