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We investigate the curvature-dependence of the visco-elastic Taylor–Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined. Experiments are performed with a variety of polymer solutions and the scaling of the critical Weissenberg number with the curvature against the prediction of the Pakdel–McKinley criterion is assessed. We revisit the linear stability analysis based on the Oldroyd-B model and find, surprisingly, that the experimentally observed scaling is not as clearly recovered. We extend the constitutive equation to a two-mode model by incorporating the PTT model into our analysis to reproduce the rheological behaviour of our fluid, but still find no agreement between the linear stability analysis and experiments. We also demonstrate that that conclusion is not altered by the presence of inertia or viscous heating. The Pakdel–McKinley criterion, on the other hand, shows a very good agreement with the data. [ABSTRACT FROM AUTHOR]

The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear-thinning fluids, these results connect trends in capillary ridge and contact line finger formation in 2D models, LSA, and 3D simulations. The results can provide us insights on how to optimize non-Newtonian fluid properties to minimize a fingering instability in many industrial and biological applications. [ABSTRACT FROM AUTHOR]

The temporal linear stability analysis of shear flow of two-layer viscoelastic fluids, both described using the upper convected Maxwell (UCM) model, is carried out. The plane Couette flow under creeping flow conditions both in the absence and presence of pressure gradient is examined to study the role of unmatched elasticities in the interfacial instability. As the most critical disturbance is known to be of finite wavelength of the order of channel width, the numerical analysis examines the entire range of disturbance wavenumbers and the stability map is constructed in the parametric space of fluid Weissenberg numbers to indicate the region of stable interface. With a focus on optical fiber coating process, the analysis investigates the role of pressure gradient imposed on the plate-driven flow. Both the adverse and favorable pressure gradients are analyzed to identify the region for stable coating flow. In the presence of pressure gradient, the region of stable interface broadens when the high elasticity fluid occupies the region of low shear rate, which is the bottom (top) layer for the adverse (favorable) pressure gradient. For the two fluids of unmatched rheology, in addition to elastic instability, the role of viscosity stratification leading to a jump in the shear rate at interface is also examined. The adverse pressure gradient has a stabilizing effect when more viscous fluid is more elastic, whereas the favorable pressure gradient tends to stabilize the interface when the less viscous fluid has higher elasticity than the more viscous fluid. [ABSTRACT FROM AUTHOR]

Highlights: [•] Linear stability of Taylor–Couette flow of polymeric solutions is assessed. [•] The thermal sensitivity leads to a drastic reduction in Critical Weissenberg, Wi c . [•] A reduction in Critical Weissenberg, Wi c is observed as gap ratio is enhanced. [•] In general, lower chain extensibility gives rise to higher Wi c . [ABSTRACT FROM AUTHOR]

Abstract: The effect of shear-thinning on the onset of miscible viscous fingering in porous media is analyzed theoretically. Using the Carreau model, new stability equations are derived in the similar domain and solved analytically and numerically with and without the quasi-steady state approximation (QSSA). Through the initial growth rate analysis without the steady state approximation, it is shown that initially the system is unconditionally stable even in the unfavorable viscosity distribution and there exists the most unstable initial condition, which is quite different from the previous analyses based on the conventional QSSA. A flow where displacing fluid is a shear-thinning (nN–N) is always more unstable than the Newtonian counterpart (N–N). For the case of a Newtonian fluid displacing a Newtonian one (N–nN), the shear-thinning effect in general makes the system stable. [Copyright &y& Elsevier]

Abstract: We investigate surface-tension-driven fingering of a thin layer of viscoplastic fluid. Using standard lubrication theory we derive an equation for the flow of the film which includes effects of surface tension and yield stress. We obtain traveling-wave solutions to model the advance of a steadily propagating front and then apply a linear stability analysis to model finger growth and to determine the effect of the yield stress. Qualitative agreement is demonstrated between the numerical results and experiments. [Copyright &y& Elsevier]

Abstract: We examine the film blowing process (FBP), which is widely used for manufacturing biaxially stretched films of polymeric materials. The viscoelastic property of the material is taken into account by employing the Upper Convected Maxwell, the Oldroyd-B or the Phan-Thien and Tanner constitutive model. In contrast to all previous theoretical works, which followed the now classical method developed by Pearson and Petrie [J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular film. Part 1. Formal mathematical representation, J. Fluid Mech. 40 (1) (1970) 1–19; J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular film. Part 2. Interpretation of the model and discussion of solutions, J. Fluid Mech. 42 (3) (1970) 609–625], we analyze the process by starting with the general three-dimensional mass and momentum balances and by formally and systematically applying the thin-film approximation. This procedure results in two-dimensional dynamic balances in both the axial and azimuthal directions. Although these balances are highly non-linear and more complicated than the original momentum balance, they are reduced by one spatial dimension and, more importantly, they are more general than the classical ones, whereas they are developed in a rigorous and straightforward manner. When we assume axial symmetry and steady state, we recover the earlier model equations. However, this new methodology allows us to examine not only axisymmetric, but also non-axisymmetric disturbances to this base flow and to retain the time derivatives in all the governing equations. This procedure is an extension of our earlier one used to study transient annular extrusion [K. Housiadas, J. Tsamopoulos, Unsteady flow of an axisymmetric annular film under gravity, Phys. Fluids 10 (10) (1998) 2500–2516; K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic annular film: I. General model and its numerical solution, J. Non-Newton. Fluid Mech. 88 (3) (2000) 229–259], which also involved the thin-film approximation and three moving interfaces, but under the assumption of axial symmetry. Viscous, elastic, inertial, gravitational and capillary forces are included in our model. The base state is computed using finite differences to simultaneously predict bubble shape, film thickness, velocity, pressure and polymer extra-stress profiles. Subsequently, its linear stability is examined to two- and three-dimensional disturbances by solving the full eigenvalue problem to determine the stability regions of the process. It is shown that under typical operating conditions the bubble becomes unstable first to non-axisymmetric disturbances, although two-dimensional instability is also predicted by our model, in agreement with recent experiments. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The stability of plane Couette flow of a power-law fluid past a deformable solid of finite thickness is considered in this work. The solid is a neo-Hookean or linear elastic material which is incompressible and impermeable to the fluid, and linear stability analysis is applied in the creeping-flow limit. Four key dimensionless parameters govern the problem: an imposed shear rate, a solid-to-fluid thickness ratio, an interfacial tension, and a power-law index. The neo-Hookean solid exhibits a first normal stress difference, not present in linear elastic solids, which is strongly coupled to the imposed shear rate and the power-law index. For large thickness ratios, , the shear rate necessary to induce an instability, , scales as , where n is the power-law index. This scaling can be understood in terms of a simple balance between viscous shear stresses in the fluid and elastic shear stresses in the solid. For small thickness ratios, shear-thinning has a stabilizing effect, in contrast to what is observed for thick solids. Whereas a shortwave instability is always observed with Newtonian fluids and neo-Hookean solids when interfacial tension is absent, it can be suppressed with power-law fluids for certain values of n. These results are potentially of interest for enhancing mixing in microfluidic devices and understanding the rheology of worm-like micelle solutions. [Copyright &y& Elsevier]

Abstract: The existence of optimal cooling conditions with respect to process stability has been experimentally found in film blowing, in a sharp contrast to other extensional deformation processes such as fiber spinning and film casting where maximum, not optimal, cooling always unequivocally enhances process stability. The same simulation model of film blowing of Hyun et al. [J.C. Hyun, H. Kim, J.S. Lee, H.-S. Song, H.W. Jung, Transient solutions of the dynamics in film blowing processes, J. Non-Newtonian Fluid Mech., 121 (2004) 157–162] proven quite accurate in portraying the transient dynamic behavior of the film blowing as compared with experimental data, has been used in this study to carry out a linear stability analysis, which then clearly confirms the experimentally found optimal cooling conditions. These optimal cooling conditions in film blowing stemming from the multiplicity of steady states of the process thus make the strategies for stabilization and optimization of the process quite a challenging task in both industry and academia because of their common relevance to the important process productivity issue. [Copyright &y& Elsevier]

Abstract: The linear stability of plane Couette flow of an upper convected Maxwell (UCM) fluid of viscosity , density , relaxation time and thickness R flowing past a linear viscoelastic solid of shear modulus G and thickness HR is analyzed using a combination of asymptotic analysis (at low Reynolds number) and numerical solution (at finite Reynolds number). The asymptotic analysis is used to analyze the effect of wall deformability on a class of high frequency modes in the UCM fluid with at first studied by Gorodtsov and Leonov [J. Appl. Math. Mech. 31 (1967) 310–319; abbreviated GL here], who showed that these modes are stable in a rigid channel. Here, c is the wavespeed of perturbations (nondimensionalised by V), is the Reynolds number, V is the velocity of the moving plate. Our asymptotic results show that all the high frequency–low Re modes of GL are rendered unstable by solid wall deformability. The variation of the growth rate with the nondimensional solid elasticity parameter shows an oscillatory behavior alternating between stable and unstable regions, and the variation for upstream traveling waves is completely antiphase with that for downstream waves. The parameter is shown to be proportional to at for neutrally stable downstream waves. Numerical continuation shows that the instability at low Re continues to finite Re, and typically the instability ceases to exist above a critical Re. This critical Re increases with an increase in the Weissenberg number . In some cases, however, the instability continues to very high Re, and in that limit for neutrally stable modes. Neutral stability curves in the –W plane show that the predicted instability of the high frequency GL modes exists only at finite and large W, and is absent in the Newtonian fluid () limit. The asymptotic analysis for the Oldroyd-B model shows that the ratio of solvent viscosity to total viscosity of the solution should be in order for the instability to exist at low Re, meaning the instability is absent for realistic values of solvent viscosity at low Re. However, numerical results show that the instability of the high-frequency GL modes is present at finite Re in an Oldroyd-B fluid, and increasing solvent viscosity ratio has a stabilizing effect on the instability. Similarly, the solid to fluid viscosity ratio also has a stabilizing effect at finite Re, but in the limit of low Re, in order for the instability to exist. Our study thus demonstrates the presence of an instability in viscoelastic plane Couette flow past a deformable wall which is primarily due to the viscoelastic nature of the fluid, and is absent in Newtonian fluids. [Copyright &y& Elsevier]

Abstract: The linear stability of two-layer plane Couette flow of upper-convected Maxwell (UCM) fluids of thicknesses and , with viscosities and , and relaxation times and past a linear viscoelastic solid layer (of thickness , shear modulus , and viscosity ) is determined using a combination of low wavenumber asymptotic analysis and a numerical method. The asymptotic analysis is used to determine the effect of the deformable solid layer on the two-fluid interfacial instability due to elasticity and viscosity stratification in the low wavenumber limit. The asymptotic results show that as the solid layer is made more deformable, the two-fluid interfacial instability could be completely stabilized in the long wave limit, when the non-dimensional parameter exceeds a certain critical value. Here, is the dimensional velocity of the moving top plate. In marked contrast with the previous results obtained for matched fluid viscosities [V. Shankar, J. Non-Newtonian Fluid Mech., 117 (2004) 163], the present asymptotic results show that the stabilizing or destabilizing nature of the solid layer on the two-fluid interfacial instability is controlled only by the fluid viscosity ratio and is independent of the relaxation times of the two UCM fluids. In general, it is found that the solid layer has a stabilizing effect for and , while it has both stabilizing and destabilizing effects (depending on its thickness H, and the fluid thickness ratio ) for and . In the absence of the solid layer, the two-fluid interfacial mode is unstable or stable depending on the ratio of relaxation times between the two fluids and the thickness ratio . It is thus possible, under appropriate combinations of relaxation times, viscosities, and thicknesses of the two fluids, to stabilize (destabilize) the two-fluid interfacial mode by the deformable solid layer while it is unstable (stable) in the absence of the solid layer. Another important result from the present low wavenumber (denoted by ) analysis is that the non-dimensional solid elasticity parameter required to stabilize or destabilize the two-fluid interfacial mode is an quantity in the low--limit when , with numerical values of significantly smaller than for . Whereas when our asymptotic analysis (as well as the earlier study) shows that for . The results from the low--asymptotic analysis are continued numerically to finite values of and Reynolds number, and the numerical results confirm that the stabilization of the two-fluid interfacial mode by the solid layer extends to finite values of . However, for short wavelength fluctuations with , the fluid velocity perturbations are localized near the two-fluid interface, so the solid layer has no effect on these fluctuations. These short wavelength unstable modes can be stabilized only by the presence of a sufficiently strong interfacial tension between the two fluids. Thus, the present study shows that the viscosity mismatch between the two fluids profoundly changes the stabilizing or destabilizing effect of the deformable solid layer on the two-fluid interfacial mode in viscoelastic fluids when compared to the conclusions reached using matched fluid viscosities. [Copyright &y& Elsevier]

The transient behavior and stability of film blowing have been investigated solving the governing equations consisting of the moving-boundary partial differential equations. Incorporating an orthogonal collocation on finite elements and a coordinate transformation, a new numerical scheme was devised to obtain previously unavailable transient solutions. The scheme overcomes severe numerical problems, that are encountered especially when the process is in a periodic oscillation called draw resonance. These simulation results provide, for the first time, temporal pictures which are close to those observed experimentally, and enable a systematic analysis of the process as regards its stability, multiplicity, sensitivity and stabilization strategies. [Copyright &y& Elsevier]

The stability of two-layer plane Couette flow of upper-convected Maxwell (UCM) fluids of thicknesses (1−β)R and βR, with matched viscosities η, and relaxation times τ1 and τ2 past a soft, deformable solid layer (modeled here as a linear viscoelastic solid fixed to a rigid plate) of thickness HR, shear modulus G and viscosity ηw is determined using a temporal linear stability analysis in the creeping-flow regime where the inertia of the two fluids and the solid layer is negligible. Interfaces with and without the interfacial tension between the two fluids are considered, while the interfacial tension between the UCM fluid and the deformable solid is neglected. It is well known that the two-layer Couette flow of UCM fluids with different relaxation times undergoes a purely elastic interfacial instability (referred here as mode 1) in rigid-walled channels, even in the creeping flow limit. It was recently shown [J. Non-Newtonian Fluid Mech 116 (2004) 371] that the plane Couette flow of a single UCM fluid past a deformable solid layer also undergoes an instability (referred here as mode 2) in the creeping flow limit when the nondimensional solid elasticity parameter Γ=Vη/(GR) exceeds a certain critical value, for a given Weissenberg number W=τV/R. In this study, the respective effects of solid layer deformability and fluid elasticity stratification on mode 1 and mode 2, and the concomitant interaction of these two qualitatively different interfacial modes are analyzed in detail. It is shown that the deformability of the solid layer has a dramatic effect on the purely elastic (mode 1) interfacial instability between the two UCM fluids: When the more elastic UCM fluid is present in between the less elastic UCM fluid and the solid layer, the layer deformability has a stabilizing effect. In this configuration, if the thickness of the more elastic fluid is smaller than the less elastic fluid, it is shown that it is possible to stabilize the mode 1 purely elastic instability (except for very long and very short waves, the latter being stabilized usually by the nonzero interfacial tension between the two fluids) by making the solid layer sufficiently deformable (i.e., Γ exceeding a critical value), while such a configuration is unstable in the case of two-layer flow in rigid channels (i.e., in the absence of the deformable solid layer). Increase in the solid layer deformability, on the other hand, destabilizes the interfacial mode between the UCM fluid and the deformable solid (mode 2). It is demonstrated that it is possible to choose the solid elasticity parameter Γ and viscosity ratio ηw/η such that both mode 1 and mode 2 are completely stable in finite experimental geometries. In marked contrast, when the less elastic fluid is present in between the more elastic fluid and the solid layer, it is shown that solid layer deformability has a destabilizing effect on mode 1. For this configuration, if the thickness of the less elastic fluid is smaller, it is shown that mode 1 can be rendered unstable by increasing solid layer deformability, while it is stable in rigid channels (in the absence of the solid layer). In both of the above configurations, the nondimensional solid layer elasticity required respectively to stabilize or destabilize mode 1 varies as Γ∝(k*R)−1 for (k*R)≪1, where k* is the wavenumber of perturbations. However, for finite experimental geometries the minimum allowed k* is dictated by the system length, and in such cases, it is argued that complete stabilization or destabilization can be achieved for realistic values of Γ. In both the configurations, our results show that deformable solid layer coatings, by design or default, can completely suppress or induce purely elastic interfacial instabilities in two-layer flow of viscoelastic fluids past a deformable solid surface. [Copyright &y& Elsevier]

The stability of plane Couette flow of an upper-convected Maxwell (UCM) fluid of thickness R, viscosity η and relaxation time τR past a deformable wall (modeled here as a linear viscoelastic solid fixed to a rigid plate) of thickness HR, shear modulus G and viscosity ηw is determined using a temporal linear stability analysis in the creeping-flow regime where the inertia of the fluid and the wall is negligible. The effect of wall elasticity on the stable modes of Gorodtsov and Leonov [J. Appl. Math. Mech. 31 (1967) 310] for Couette flow of a UCM fluid past a rigid wall, and the effect of fluid elasticity on the unstable modes of Kumaran et al. [J. Phys. II (Fr.) 4 (1994) 893] for Couette flow of a Newtonian fluid past a deformable wall are analyzed. Results of our analysis show that there is only one unstable mode at finite values of the Weissenberg number, W=τRV/R (where V is the velocity of the top plate) and nondimensional wall elasticity, Γ=Vη/(GR). In the rigid wall limit, Γ≪1 and at finite W this mode becomes stable and reduces to the stable mode of Gorodtsov and Leonov. In the Newtonian fluid limit, W→0 and at finite Γ this mode reduces to the unstable mode of Kumaran et al. The variation of the critical velocity, Γc, required for this instability as a function of W¯=τRG/η (a modified Weissenberg number) shows that the instability exists in a finite region in the Γc−W¯ plane when Γc>Γc,Newt and W¯, where Γc,Newt is the value of the critical velocity for a Newtonian fluid. The variation of Γc with W¯ for various values of H are shown to collapse onto a single master curve when plotted as ΓcH versus W¯/H, for H≫1. The effect of wall viscosity is analyzed and is shown to have a stabilizing effect. [Copyright &y& Elsevier]

In this paper we present a new time marching scheme for the time dependent simulation of viscoelastic flows governed by constitutive equations of differential form. Based on the ideas of Carvalho and Scriven [J. Comput. Phys. 151 (1999) 534], a domain perturbation technique is introduced that can be applied to viscoelastic flows with fluid/fluid interfaces or free surfaces. This work mainly focuses on the development and, consequently, benchmarking of finite element algorithms (FEM) that can efficiently handle the stability problems of complex viscoelastic flows. Since spurious or non-physical solutions are easily generated for this type of analysis using finite element techniques, both the new time stepping scheme and the domain perturbation technique are benchmarked in simple shear flows of upper convected Maxwell (UCM) fluids. Both single and two layer flows are considered for which the dominating mode and associated growth rate of a perturbation are solutions of the one-dimensional generalized eigenvalue problem (GEVP). We show that both the growth rate and the most dangerous eigenmode of the simple shear flows can be accurately captured by our transient algorithm. [Copyright &y& Elsevier]

In order to better understand the sources of numerical instabilities occurring in the simulation of time-dependent flows of viscoelastic fluids at high Weissenberg numbers, we have used various types of linear stability analyses. In complement to the limited number of investigations related to the well-posedness of problems involving the flows of viscoelatic fluids, linear stability studies of steady viscoelastic flows have been carried out by various authors in both theoretical and numerical fields. In contrast to most published work where the equations have only been discretized in the cross-stream direction using a formulation with the stream function, we have used the full spatial discretization with spectral elements since we are more interested in computing the eigenvalue spectra generated by the spatial and temporal discretizations than the ones inherent in the partial differential equations. Our analysis enables us to investigate the influence of the spatial discretization, the time schemes, the various operators present in the conservation and constitutive equations and boundary conditions on the linear stability of the constitutive models. [Copyright &y& Elsevier]

We present an investigation of the phenomenon of stress-induced polymer migration for dilute polymer solutions in the Taylor–Couette device, consisting of two infinitely long, concentric cylinders rotating at constant angular velocities. The underlying physical model is represented by the dilute limit of a two-fluid Hamiltonian system involving two components: one (the polymer) is viscoelastic and obeys the Oldroyd-B constitutive equation, and the other (the solvent) is viscous Newtonian. The two components are considered to be in thermal, but not mechanical equilibrium, interacting with each other through an isotropic drag coefficient tensor. This allows for stress-induced diffusion of polymer chains. The governing equations consist of the continuity and the momentum equations for the bulk velocity, the constitutive model for the polymer chain conformation tensor and the diffusion equation for the polymer concentration. The diffusion equation contains an extra source term, which is proportional to gradients in the polymer stress, so that polymer concentration gradients can develop even in the absence of externally imposed fluxes in the presence of stress inhomogeneities. The solution to the steady-state purely azimuthal flow is obtained first using a spectral collocation method and an adaptive mesh formulation to track the steep changes of the concentration in the flow domain. The calculations show the development of strong polymer migration towards the inner cylinder with increasing Deborah number (De) in agreement with experimental observations. The migration is enhanced for increasing values of the gap thickness resulting in concentration changes by several orders of magnitude in the area between the inner and outer cylinder walls. The extent of the migration also depends strongly on the ratio of the solvent to the polymer viscosity. In addition to a strongly inhomogeneous polymer concentration, significant deviations from the homogenous flow are also observed in the velocity profile. Next, results are reported from a linear stability analysis around the steady-state solution against axisymmetric disturbances corresponding to various wavenumbers in the axial direction. The calculations show that the steady-state solution remains stable up to moderate values of the Deborah number, explaining why some of the predicted stress-induced migration effects should be experimentally observable. The role of the Peclet number (Pe) on the stability of the system is elucidated. [Copyright &y& Elsevier]

An intriguing process, known as lithographically induced self-assembly (LISA), is initiated by positioning a template parallel to a flat silicon wafer-coated with a thin polymeric film and then raising the temperature above the glass transition/melting temperature of the film. Electric fields exert a force on charges induced at the polymer–air interface, placing the film in tension. The static equilibrium that results is unstable to disturbances with wavelengths for which the electrostatic force overcomes the surface tension. Flow ensues, generating a pattern in the film with periodicity reflecting the characteristic length of the instability.Though the initiation of the process as outlined above is generally accepted, the forces guiding the evolution of the film into the remarkably periodic microstructures observed are not. Our goal here is to create a sound understanding of the mechanism through quantitative modeling to facilitate the conversion of these microstructures into nano-structures. Given the apparent importance of conductivity in the film we adopt the “leaky dielectric model”, which also allows for re-distribution of charges on the interfaces, and undertake a linear stability analysis to explore the effects of various process parameters, particularly the conductivity and the film thickness. The linear stability analysis with the leaky dielectric model for the polymer film yields growth exponents and characteristic wavenumbers much larger than that for the perfect dielectric model. The differences are striking in that the slightest conductivity increases the growth exponent by a factor of 2–20 and decreases the fastest growing wavelength by a factor of 2–4. [Copyright &y& Elsevier]