Naveen Tiwari

Linear stability of a volatile liquid film flowing over a locally heated surface

The dynamics and linear stability of a volatile liquid film flowing over a locally heated surface are investigated. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that leads to the formation of a pronounced capillary ridge. Lubrication theory is used to develop a model for the film evolution that contains three key dimensionless groups: a Marangoni parameter (M), an evaporation number (E), and a measure of the vapor pressure driving force for evaporation (K), which behaves as an inverse Biot number. The two-dimensional, steady solutions for the local film thickness are computed as functions of these parameters. A linear stability analysis of these steady profiles with respect to perturbations in the spanwise direction reveals that the operator of the linearized system can have both a discrete and a continuous spectrum. The continuous spectrum exists for all values of the spanwise wave number and is always stable. The discrete spectrum, which corresponds to...

Theoretical Analysis of the Effect of Insoluble Surfactant on the Dip Coating of Chemically Micropatterned Surfaces

Microfluidic flow on chemically heterogeneous surfaces is a useful technique with applications ranging from selective material deposition to the self-assembly of nanostructures. The recent theoretical analysis by Davis [Phys. Fluids 17, 038101 (2005)] of the dip coating of a pure fluid onto vertical, wetting stripes surrounded by nonwetting regions quantified the experimentally observed deviations from the classical Landau-Levich result due to lateral confinement of the fluid by chemical surface patterning. In this present work, the analysis of dip coating of these heterogeneous surfaces is extended to a liquid containing an insoluble surfactant. Using matched asymptotic expansions based on lubrication theory in the limit of a small capillary number, the thickness of the deposited liquid film and the surfactant concentration in the deposited monolayer are predicted for a wide range of fluid properties and process parameters. The increase in the deposited film thickness is shown analytically to be limited ...

Stability analysis of the rimming flow inside a uniformly heated rotating horizontal cylinder

The stability analysis is presented for a thin viscous liquid film flowing inside a uniformly heated horizontal cylinder that is rotating about its axis. The free surface evolution equation for the liquid-gas interface is obtained by simplifying the Navier-Stokes and energy equations within the lubrication approximation. Various dimensionless numbers are obtained that quantify the effect of gravity, viscous drag, inertia, surface tension, and thermocapillary stress. The film thickness evolution equation is solved numerically to obtain two-dimensional, steady state solutions neglecting axial variations. A liquid pool forms at the bottom of the cylinder when gravity dominates other forces. This liquid pool is shifted in the direction of rotation when inertia or viscous drag is increased. Small axial perturbations are then imposed to the steady solutions to study their stability behavior. It is found that the inertia and capillary pressure destabilize whereas the gravity and thermocapillary stress stabilize ...

Stability of a volatile liquid film spreading along a heterogeneously-heated substrate.

The dynamics and stability of a thin, viscous film of volatile liquid flowing under the influence of gravity over a non-uniformly heated substrate are investigated using lubrication theory. Attention is focused on the regime in which evaporation balances the flow due to gravity. The film terminates above the heater at an apparent contact line, with a microscopically thin precursor film adsorbed due to the disjoining pressure. The film develops a weak thermocapillary ridge due to the Marangoni stress at the upstream edge of the heated region. As for spreading films, a more significant ridge is formed near the apparent contact line. For weak Marangoni effects, the film evolves to a steady profile. For stronger Marangoni effects, the film evolves to a time-periodic state. Results of a linear stability analysis reveal that the steady film is unstable to transverse perturbations above a critical value of the Marangoni parameter, leading to finger formation at the contact line. The streamwise extent of the fingers is limited by evaporation. The time-periodic profiles are always unstable, leading to the formation of periodically-oscillating fingers. For rectangular heaters, the film profiles after instability onset are consistent with images from published experimental studies.

Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface

The stability of a thin, volatile liquid film falling under the influence of gravity over a locally heated, vertical plate is analyzed in the noninertial regime using a model based on long-wave theory. The model is formulated to account for evaporation that is either governed by thermodynamic considerations at the interface in the one-sided limit or limited by the rate of mass transfer of the vapor from the interface. The temperature gradient near the upstream edge of the heater induces a gradient in surface tension that opposes the gravity-driven flow, and a pronounced thermocapillary ridge develops in the streamwise direction. Recent theoretical analyses predict that the ridge becomes unstable above a critical value of the Marangoni parameter, leading to the experimentally observed rivulet structure that is periodic in the direction transverse to the bulk flow. An oscillatory, thermocapillary instability in the streamwise direction above the heater is also predicted for films with sufficiently large hea...

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

A long-wave lubrication analysis is used to study the influence of topographical features on the linear stability of noninertial coating flows over a locally heated surface. Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets even in the limit of noninertial flow. Similar fluid ridges form near topographical variations on isothermal surfaces, but these ridges are stable to perturbations. The influence of basic topographical features on the stability of the locally heated film is analyzed. In contrast to its destabilizing influence on liquid films resting on heated, horizontal walls, even such nonoptimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. Optimal topographical features that suppress variations in the free-surface sha...

A brief review of photo-orthotropic elasticity theories

The development of the theory of birefringence of annotropic composites has proceeded mainly along the following directions, strew strain models, analogy, integrated photoelasticity and tensonal nature of birefringence. All these studies have concluded that three independent photoelastic constants are needed to characterize orthotropic model materials. In the literature, there has not been uniformity of notation used in the representations of the results.In this paper, using uniform notation, existing photo-orthotropic clasticity theories are reviewed under three major headings stress-optic laws strain-optic laws and approximate strain-optic laws. The interrelation ships between stress-optic and strain-optic coefficients are brought out Interpretation of isoclinics is discussed. The steps necessary to calibrate a birefringent orthotropic composite are summarized and finally the influence of residual birefringence is also discussed.

Linear stability analysis of thin liquid film flow over a heterogeneously heated substrate

The linear stability of a thin film of volatile liquid flowing over a surface with embedded, regularly spaced heaters is investigated. The temperature gradients at the upstream edges of the heaters induce gradients in surface tension that create a pronounced non-uniformity in the film profile due to the formation of capillary ridges. The Governing equations for the evolution of the film thickness are derived within the lubrication approximation, and three important parameters that affect the dynamics and stability of the film are identified. The computed two-dimensional, steady solutions for the local film thickness reveal that due to evaporation there is a slight change in the height of capillary ridge at subsequent heaters downstream. Using a linear stability analysis, it is shown that, as for a single heater, the film is susceptible to two types of instabilities. A rivulet instability leads to spanwise-periodic rivulets, and an oscillating thermocapillary instability leads to streamwise, time-periodic ...

Asymptotic analysis of the selective dip coating of power-law fluids

The dip coating of a chemically micropatterned surface bearing alternating wetting and nonwetting vertical strips is analyzed for a non-Newtonian power-law fluid. Asymptotic matching is used to determine the thickness of liquid films deposited on the O(10μm) strips at small capillary and Bond numbers. The chemical patterning that confines the fluid laterally induces a significant transverse curvature of the free-surface. The streamwise variation in this transverse curvature along the strip provides an additional contribution to the capillary pressure gradient that is not present for uniform surfaces. Consequently, the difference in the thickness of the deposited liquid film relative to a Newtonian fluid is significantly less than for homogeneous plates or fibers.

Hydrodynamic stability of thermoviscous liquid film inside a rotating horizontal cylinder: Heating and cooling effects

Steady two-dimensional solutions and their stability analysis are presented for thin film of a thermoviscous liquid flowing inside a cylinder rotating about its horizontal axis. The inner surface of the cylinder is either uniformly hotter or colder than the enveloping air. The mass, momentum, and energy equations are simplified using thin-film approximation. The analytically obtained film thickness evolution equation consists of various dimensionless parameters such as gravitational number, Bond number, Biot number, thermoviscosity number, and Marangoni number. The viscosity of the liquid is considered as an exponential function of temperature. The viscosity increases (decreases) within the film thickness away from the inner surface of the cylinder when the surface is uniformly hotter (colder) than the atmosphere. For hotter (colder) surface, the film thickness on the rising side decreases (increases) when convective heat transfer at the free surface is increased. The surface tension gradient at the free ...