Determination of the aerodynamic droplet breakup boundaries based on a total force approach

The determination of the critical We_g number separating the different breakup regimes has been extensively studied in several experimental and numerical works, while empirical and semi-analytical approaches have been proposed to relate the critical We_g number with the Oh_l number. Nevertheless, under certain conditions, the Re_g number and the density ratio ε may become important. The present work provides a simple but reliable enough methodology to determine the critical We_g number as a function of the aforementioned parameters in an effort to fill this gap in knowledge. It considers the main forces acting on the droplet (aerodynamic, surface tension and viscous) and provides a general criterion for breakup to occur but also for the transition among the different breakup regimes. In this light, the present work proposes the introduction of a new set of parameters named as We_g,eff and Ca_l monitored in a new breakup plane. This plane provides a direct relation between gas inertia and liquid viscosity forces, while the secondary effects of Re_g number and density ratio have been embedded inside the effective We_g number (We_g,eff)     

Disturbance growth in two-fluid channel flow: The role of capillarity

This work examines the role of capillarity in the non-modal linear stability properties of three-dimensional disturbances in sheared two-layer flow of immiscible fluids of similar density. Capillarity reduces the transient growth of energy that occurs due to the non-normality of the linear stability problem according to a scaling of peak energy with We^1/2 over a wide range of Weber number, viscosity ratio and wavenumber. More importantly, the participation of capillary modes in non-modal growth leads to oscillatory energy growth and to larger disturbance growth rates, features that are confirmed by computing the numerical range and numerical abscissa of the non-normal disturbance evolution operator. Examination of energy components and disturbance structure reveals that early rapid growth and subsequent oscillations are due to the coupling of streamwise vortices – the two-fluid analog of lift-up – to the displaced interface.     

Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner

Here we consider the stability of flow along a streamwise corner formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the corner region have been obtained by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. An eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a corner layer as well, but away from the cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability is small and decreases the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient corner layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one. Received 17 March 1998 and accepted 28 April 1999     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Numerical investigations of drop solidification on a cold plate in the presence of volume change

We present a front-tracking/finite difference method for simulation of drop solidification on a cold plate. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–gas, and liquid–gas, that are explicitly tracked under the assumption of axisymmetry. Method validation is carried out by comparing computational results with exact solutions for a two-dimensional Stefan problem, and with related experiments. We then use the method to investigate a drop solidifying on a cold plate in which there exists volume change due to density difference between the solid and liquid phases. Numerical results show that the shape of the solidified drop is profoundly different from the initial liquid one due to the effects of volume change and the tri-junction in terms of growth angles ϕ_gr on the solidification process. A decrease in the density ratio of solid to liquid ρ_sl or an increase in the growth angle results in an increase in the height of the solidified drop. The solidification process is also affected by the Stefan number St, the Bond number Bo, the Prandtl number Pr, the Weber number We, the ratios of the thermal properties of the solid to liquid phases k_sl and C_psl. Increasing St, Bo, Pr, We, or k_sl decreases the solidified drop height and the time to complete solidification. Moreover, the solidification growth rate is strongly affected by St, k_sl and C_psl. An increase in any of these parameters hastens the growth rate of the solidification interface. Contrarily, increasing ρ_sl decreases the growth rate. However, other parameters such as ϕ_gr, Bo, Pr and We have minor effects on the solidification growth rate.     

Computations of breakup modes in laminar compound liquid jets in a coflowing fluid

We present a numerical investigation of breakup modes of an axisymmetric, laminar compound jet of immiscible fluids, which flows in a coflowing immiscible outer fluid. We use a front-tracking/finite difference method to track the unsteady evolution and breakup of the compound jet, which is governed by the Navier–Stokes equations for incompressible Newtonian fluids. Numerical results show that depending on parameters such as the Reynolds number Re (in the range of 5–30) and Weber Number We (in the range of 0.1–0.7), based on the inner jet radius and inner fluid properties, the compound jet can break up into drops in various modes: inner dripping–outer dripping (dripping), inner jetting–outer jetting (jetting), and mixed dripping–jetting. Decreasing Re or increasing We promotes the jetting mode. The transition from dripping to jetting is also strongly affected by the velocity ratios, U₂₁ (intermediate to inner velocities) and U₃₁ (outer to inner velocities). Increasing U₂₁ makes the inner jet thinner and stretches the outer jet and thus promotes jetting. In contrast, increasing U₃₁ thins the outer jet, and thus, when the inner jet is dripping, the outer jet can break up into drops in the mixed dripping–jetting mode. Continuously increasing U₃₁ results in thinning both inner and outer jets and thus produces small drops in the jetting mode. In addition, starting from dripping, a decrease in the interfacial tension ratio of the outer to inner interfaces results in the mixed dripping–jetting and jetting modes. These modes produce various types of drops: simple drops, and compound drops with a single inner drop (single-core compound drops) or a few inner drops (multi-core compound drops).     

Asymptotic Behavior of Solutions of the Compressible Navier�CStokes Equation Around the Plane Couette Flow

Asymptotic behavior of solutions to the compressible Navier–Stokes equation around the plane Couette flow is investigated. It is shown that the plane Couette flow is asymptotically stable for initial disturbances sufficiently small in some L ² Sobolev space if the Reynolds and Mach numbers are sufficiently small. Furthermore, the disturbances behave in large time in L ² norm as solutions of an n − 1 dimensional linear heat equation with a convective term.     

Conjugate natural convection heat transfer between two fluids separated by a horizontal wall: steady-state analysis

The conjugate heat transfer across a thin horizontal wall separating two fluids at different temperatures is investigated both numerically and asymptotically. The solution for large Rayleigh numbers is shown to depend on two nondimensional parameters;α/ε ², withα being the ratio of the thermal resistance of the boundary layer in the hot medium to the thermal resistance of the wall andε the aspect ratio of the plate, andβ, the ratio of the thermal resistances of the boundary layers in the two media. The overall Nusselt number is an increasing function ofα/ε ² taking a finite maximum value forα/ε ² → ∞ and tending to zero forα/ε ² → 0.     

Discrete and continuous models for in plane loaded random elastic brickwork

The aim of this paper is to study non-periodic masonries – typical of historical buildings – by means of a perturbation approach and to evaluate the effect of a random perturbation on the elastic response of a periodic masonry wall. The random masonry is obtained starting from a periodic running bond pattern. A random perturbation on the horizontal positions of the vertical interfaces between the blocks which form the masonry wall is introduced. In this way, the height of the blocks is uniform, while their width in the horizontal direction is random. The perturbation is limited such as each block has still exactly 6 neighboring blocks. In a first discrete model, the blocks are modeled as rigid bodies connected by elastic interfaces (mortar thin joints). In other words, masonry is seen as a “skeleton” in which the interactions between the rigid blocks are represented by forces and moments which depend on their relative displacements and rotations. A second continuous model is based on the homogenization of the discrete model. Explicit upper and lower bounds on the effective elastic moduli of the homogenized continuous model are obtained and compared to the well-known effective elastic moduli of the regular periodic masonry. It is found that the effective moduli are not very sensitive to the random perturbation (less than 10%). At the end, the Monte Carlo simulation method is used to compare the discrete random model and the continuous model at the structural level (a panel undergoing in plane actions). The randomness of the geometry requires the generation of several samples of size L of the discrete masonry. For a sample of size L, the structural discrete problem is solved using the same numerical procedure adopted in [Cecchi, A., Sab, K., 2004. A comparison between a 3D discrete model and two homogenized plate models for periodic elastic brickwork, International Journal of Solids Structures 41 (9–10), 2259–2276] and the average solution over the samples gives an estimation which depends on L. As L increases, an asymptotic limit is reached. One issue is to find the minimum size for L and to compare the asymptotic average solution to the one obtained from the continuous homogenized model.     

Droplet impact dynamics for two liquids impinging on anisotropic superhydrophobic surfaces

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93?% using droplets of water and a 50?%/50?% water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We?>?100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5????We????15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115????We????265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.     

Mechanism of flow instability and transition to turbulence

In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K_max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K_max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K_max of about 370.     

Finite-Amplitude Equilibrium Solutions for Plane Poiseuille–Couette Flow

Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette flow is stable at all Reynolds numbers when the Couette velocity component σ₂ exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ₂. It is found that, for small σ₂, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds number gradually increases with increasing σ₂. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ₂ values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ₂. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases slowly up to σ₂∼ 0.2 and remains constant until σ₂∼ 0.58. Beyond σ₂ > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear equilibrium solutions do not exist beyond a critical σ₂ value of about 0.59. Received: 26 November 1996 and accepted 12 May 1997     

Bulk rheology of dilute suspensions in viscoelastic liquids

A theoretical relation is derived for the bulk stress in dilute suspensions of neutrally buoyant, uniform size, spherical drops in a viscoelastic liquid medium. This is achieved by the classic volume-averaging procedure of Landau and Lifschitz which excludes Brownian motion. The disturbance velocity and pressure fields interior and exterior to a second-order fluid drop suspended in a simple shear flow of another second-order fluid were derived by Peery [9] for small Weissenberg number (We), omitting inertia. The results of the averaging procedure include terms up to orderWe ². The shear viscosity of a suspension of Newtonian droplets in a viscoelastic liquid is derived as $$\eta _{susp} = \eta _0 \left[ {1 + \frac{{5k + 2}}{{2(k + 1)}}\varphi - \frac{{\psi _{10}^2 \dot \gamma ^2 }}{{\eta _0^2 }}\varphi f_1 (k, \varepsilon _0 )} \right],$$ whereη ₀, andω ₁₀ are the viscosity and primary normal stress coefficient of the medium,ε ₀ is a ratio typically between ?0.5 and ?0.86,k is the ratio of viscosities of disperse and continuous phases, and \(\dot \gamma \) is the bulk rate of shear strain. This relation includes, in addition to the Taylor result, a shear-thinning factor (f ₁ > 0) which is associated with the elasticity of the medium. This explains observed trends in relative shear viscosity of suspensions with rigid particles reported by Highgate and Whorlow [6] and with drops reported by Han and King [8]. The expressions (atO (We ²)) for normal-stress coefficients do not include any strain rate dependence; the calculated values of primary normal-stress difference match values observed at very low strain rates.     

Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations

Ultimately, numerical simulation of viscoelastic flows will prove most useful if the calculations can predict the details of steady-state processing conditions as well as the linear stability and non-linear dynamics of these states. We use finite element spatial discretization coupled with a semi-implicit θ-method for time integration to explore the linear and non-linear dynamics of two, two-dimensional viscoelastic flows: plane Couette flow and pressure-driven flow past a linear, periodic array of cylinders in a channel. For the upper convected Maxwell (UCM) fluid, the linear stability analysis for the plane Couette flow can be performed in closed form and the two most dangerous, although always stable, eigenvalues and eigenfunctions are known in closed form. The eigenfunctions are non-orthogonal in the usual inner product and hence, the linear dynamics are expected to exhibit non-normal (non-exponential) behavior at intermediate times. This is demonstrated by numerical integration and by the definition of a suitable growth function based on the eigenvalues and the eigenvectors. Transient growth of the disturbances at intermediate times is predicted by the analysis for the UCM fluid and is demonstrated in linear dynamical simulations for the Oldroyd-B model. Simulations for the fully non-linear equations show the amplification of this transient growth that is caused by non-linear coupling between the non-orthogonal eigenvectors. The finite element analysis of linear stability to two-dimensional disturbances is extended to the two-dimensional flow past a linear, periodic array of cylinders in a channel, where the steady-state motion itself is known only from numerical calculations. For a single cylinder or widely separated cylinders, the flow is stable for the range of Deborah number (De) accessible in the calculations. Moreover, the dependence of the most dangerous eigenvalue on De≡λV/R resembles its behavior in simple shear flow, as does the spatial structure of the associated eigenfunction. However, for closely spaced cylinders, an instability is predicted with the critical Deborah number De_c scaling linearly with the dimensionless separation distance L between the cylinders, that is, the critical Deborah number De_Lc≡λV/L is shown to be an O(1) constant. The unstable eigenfunction appears as a family of two-dimensional vortices close to the channel wall which travel downstream. This instability is possibly caused by the interaction between a shear mode which approaches neutral stability for De ≫ 1 and the periodic modulation caused by the presence of the cylinders. Nonlinear time-dependent simulations show that this secondary flow eventually evolves into a stable limit cycle, indicative of a supercritical Hopf bifurcation from the steady base state.     

Bifurcation phenomena in viscoelastic flows through a symmetric 1:4 expansion

In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur. We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100), Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L² = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part I: unified mapping of flow regimes

Present research highlights the potential of apparatuses with integrated minichannel packings to intensify gas-liquid-solid contacting. Especially an operation of these devices within the Taylor flow regime gained extraordinary attention due to its excellent heat and mass transfer and the segmented flow characteristics. However, criteria for flow regime transitions are mainly developed from water-similar fluids and are contradictory which hinders uniform flow regime prediction.This work presents a systematic analysis of adiabatic gas-liquid downflow in a square minichannel of 1.0 mm hydraulic diameter. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm). Experiments were conducted using water, water-glycerol, and water-ethanol mixtures to cover a broad range of material properties. The gas and liquid superficial velocities were varied between 9.81·10^-4…2.72 m/s and 1.7·10⁻⁴…0.80 m/s, respectively. Taylor flow, Taylor-annular flow, annular flow, churn flow, and bubbly flow were observed. Using the Pi-theorem, 8 significant dimensionless groups dictating the flow transition were identified, namely u_{G, s}/u_{L, s}, Re_G, Re_L, We_G, We_L, Θ*, d_{In, CI}/d_h, and d_{Ou, CI}/d_h. Based on more than 1500 experimental data, criteria for the regime transitions of Taylor flow are provided. The derived flow regime map shows good agreement for all applied liquids and for the two larger injector geometries.     

Viscoelastic flow of polymer solutions around a periodic,linear array of cylinders: comparisons of predictions for microstructure and flow fields

Numerical simulation is used to investigate the flow of polymer solutions around a periodic, linear array of cylinders by using three constitutive equations derived from kinetic theory of dilute polymer solutions: the Giesekus model; the finitely extensible, nonlinear elastic dumbbell model with Peterlin's approximation (FENE-P); and the FENE dumbbell model of Chilcott–Rallison (CR). In the Giesekus model, intramolecular forces are described by a Hookean spring, whereas a finitely extensible spring whose modulus is given by the Warner approximation is used in both the FENE-P and CR models. Hydro dynamic drag on the beads is taken to be anisotropic for the Giesekus model and isotropic for the other two models. The CR and FENE-P models differ subtly in their approximate treatment of the nonlinear force law. The three models exhibit very similar rheological behavior in viscometric flow and steady elongational flow, with the notable exception that the viscosity for the CR model is shear-rate independent. Finite element simulations are performed by using two different formulations: the elastic-viscous split-stress gradient (EVSS-G) method and a new variant of this formulation, the discrete EVSS-G (DEVSS-G) formulation, in which the elliptic stabilization term is added only to the discrete version of the momentum equation, and the constitutive equation is solved directly in terms of the polymer contribution to the stress tensor. Calculations are performed for all models up to a Weissenberg number We, where the configuration tensor 〈QQ〉 loses positive definiteness. However, by locally refining the mesh in the gap region, the positive definiteness of 〈QQ〉 is recovered. The flow and stress fields predicted by the three constitutive equations are qualitatively similar. A `birefringent strand' of highly stretched polymer molecules, which appears to emanate from the rear stagnation point in the cylinder, strengthens as We is increased. Not surprisingly, the molecular extension computed for the Giesekus model is considerably larger than that of the two FENE spring models. The drag force on the cylinders differs for the FENE-P and CR models, because of the difference in the shear-thinning viscosity resulting from the different approximations used in these models.     

Localized collocation schemes and their applications

An in-depth study of the complicated trajectory characteristics of skipping stones is carried out in the present work. A three-dimensional numerical simulation validated by acquiring good agreement with experimental results is established. It is devoted to illustrating five different types of motion responses after the stone impacts the water surface in the o-xy plane, including “dive”, “hydroplaning trout”, “hydroplaning skip”, “stable skip”, and “skipping trout”. Then, the lateral deviations are investigated quantitatively based on dimensionless parameter sin(α+β)cosα in the o-yz plane. Steady interval and linear interval are divided for lateral deviation Z₁/D and Z₂/D based on the values of (α+β) and α, respectively. The results reveal that (1) Z₁/D increases almost linearly with the increasing sin(α+β)cosα at different slopes in different (α+β) intervals; (2) Z₂/D increases almost linearly with the increasing sin(α+β)cosα at different slopes in different α intervals; (3) in linear interval, numerical lateral deviations are much larger than the fitting values at points β/α≥4.5, and much smaller than the fitting values at points 2.3 ≤β/α<4.3. Finally, a theoretical approach is proposed to predict the maximum immersion depth of trailing edge point P.

     

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.     

Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity

An experimental investigation of viscous binary droplet collisions in a vacuum environment is conducted. The fundamental ramifications of conducting such experiments in a vacuum environment are twofold. The first, which is the motivating factor of this work, assures that the collision products are unimpeded by aerodynamic effects which tend to disrupt the collision process at a much earlier stage in the processes than if they were absent, and second, the phenomenon of encapsulation of the host medium between the colliding droplets is not present in this study; a fact that limits the scope of direct application of this study to a number of (but not all) applications. Droplets are generated from capillary stream breakup with the imposition of an amplitude-modulated disturbance which results in the generation of highly uniform pre-collision drops at separations far extending those which are possible from a standard (monochromatic) sinusoidal disturbance. Hence, the collision products are able to deform unimpeded by interactions with neighboring collision products. Measurements over a broad range of Weber number, We, indicate that the value of the critical Weber number, We_c, is more than 100 times greater for the 30-cSt fluid than the corresponding value for similarly sized water drops in a standard ambient environment. Measurements of the oblate and prolate half-cycle oscillation periods resulting from the binary collision reveal a distinct behavior that is observed and documented here for the first time. Additionally, measurements of the radial extent of the deformed mass at the instant of maximum deformation have been conducted and allow quantification of the energy dissipation. These measurements show that the energy dissipation increases with increasing fluid viscosity, which contradicts the results published by others.