Jayati Sarkar

A unified theory of instabilities in viscoelastic thin films: from wetting to confined films, from viscous to elastic films, and from short to long waves.

A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short- to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (gamma/mu h) are uncovered, where gamma is the surface energy, mu is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength lambda approximately = 2.96 h is obtained for gamma/mu h < 0.1, whereas long waves that depend nonlinearly on the field strength and surface energy are obtained for gamma/mu h > 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.

CFD of mixing of multi‐phase flow in a bioreactor using population balance model

Mixing in bioreactors is known to be crucial for achieving efficient mass and heat transfer, both of which thereby impact not only growth of cells but also product quality. In a typical bioreactor, the rate of transport of oxygen from air is the limiting factor. While higher impeller speeds can enhance mixing, they can also cause severe cell damage. Hence, it is crucial to understand the hydrodynamics in a bioreactor to achieve optimal performance. This article presents a novel approach involving use of computational fluid dynamics (CFD) to model the hydrodynamics of an aerated stirred bioreactor for production of a monoclonal antibody therapeutic via mammalian cell culture. This is achieved by estimating the volume averaged mass transfer coefficient (kLa) under varying conditions of the process parameters. The process parameters that have been examined include the impeller rotational speed and the flow rate of the incoming gas through the sparger inlet. To undermine the two‐phase flow and turbulence, an Eulerian‐Eulerian multiphase model and k‐ε turbulence model have been used, respectively. These have further been coupled with population balance model to incorporate the various interphase interactions that lead to coalescence and breakage of bubbles. We have successfully demonstrated the utility of CFD as a tool to predict size distribution of bubbles as a function of process parameters and an efficient approach for obtaining optimized mixing conditions in the reactor. The proposed approach is significantly time and resource efficient when compared to the hit and trial, all experimental approach that is presently used.

Contact Instability of a Soft Elastic Film Bonded to a Patterned Substrate

A linear stability analysis is presented for the contact instability of a soft thin elastic film which is rigidly bonded to a physically patterned substrate, and is in adhesive contact with a smooth rigid contactor. Increasing roughness by enhancing the substrate-amplitude produces increasingly smaller instability length-scales. The smallest wavelengths obtainable are 0.3*h, an order of magnitude smaller than that observed with films on flat substrates (3*h). Instability length-scales are found to be largely independent of substrate length-scales. For van der Waals interaction, increase in substrate roughness increases the energy penalty and, consequently, requires smaller gap distances (< 1nm for stiff films) to engender instabilities. When an externally controllable long-range electric field is employed instead, instabilities can be initiated at very low critical voltages (∼32 V) even in relatively stiff films, making it a more suitable route to produce miniaturized instability patterns.

Adhesion and Debonding of Soft Elastic Films on Rough and Patterned Surfaces

ABSTRACT With the help of simulations based on energy minimization, we have studied the effect of roughness of a rigid contactor with sinusoidal and step patterns on the adhesion-debonding cycle of a soft thin elastic film. The surface instability engendered by attractive forces between the contactor and the film produces a regularly spaced array of columns in the bonding phase. The inter-column spacing is governed largely by periodicity of the contactor pattern. Decreased periodicity of the pattern favors intermittent collapse of columns rather than a continuous peeling of contact zones. An increase in the amplitude of roughness decreases the maximum force required for debonding and increases the snap-off distance. The net effect results in a reduced work for debonding. Introduction of noise and increased step-size in simulations decreases the pull-off force and the snap-off distance, as in the case of a smooth contactor. Finally the study reveals that a patterned contactor can be used as a potential template in the patterning of soft interfaces.

Electric-field induced morphological transitions in elastic contact instability of soft solid films

A soft elastic film, when placed in adhesive proximity with a contactor in a crack-like geometry, spontaneously undergoes a surface instability to form finger patterns with a characteristic wavelength of approximately 4h, where h is the film thickness. We study the morphological evolution and control of this elastic contact instability under the influence of an external electric field. The distinct electric field induced morphological changes, leading to the formation of two-dimensional hexagonally arranged pillars, large-amplitude fingers, and straightening of contact edge, which are studied comprehensively. The conditions for the evolution of morphologically distinct patterns are governed by the film parameters, such as its shear modulus and thickness. A theoretical model and its stability analysis provide an approximate estimate of the critical voltage required for the onset of changes and its scaling with the film parameters (thickness and shear modulus). Further, three-dimensional simulations based on energy minimization are presented to provide important clues regarding the physics of pattern evolution on soft elastic interfaces.

Pattern formation in soft elastic films cast on periodically corrugated surfaces?a linear stability and finite element analysis

Length scales of instabilities exhibited by soft, thin elastic films cast on smooth and sharp corrugated surfaces and in adhesive contact with an external contactor are investigated by means of linear stability analysis (LSA) and non-linear finite element analysis. The instability length scales are found to decrease with either an increase in the amplitude β or a decrease in the wavelength λp of the substrate pattern. For same substrate parameters, a step-patterned surface with higher RMS roughness is generally found to engender smaller length scales. The linear stability analysis with sinusoidally patterned substrates shows a reduced scaling of critical wavelength with substrate amplitude: λc = 2.96(1 − β)h, where h is the mean film thickness. The largest substrate amplitudes explored with finite element analysis are limited to β = 0.7, which is found to beget instability length scales of 0.89h, that are much smaller than the 3h length scale that is obtained with flat substrates. This suggests that an increase in substrate roughness via patterning can prove to be an attractive route for the production of miniaturized patterns.

Miniaturized Pattern Formation in Elastic Films Cast on Sinusoidally Patterned Substrates

The various morphologies that are formed when van der Waals forces or electric field is induced between film cast on a sinusoidal substrate and in contact proximity with a contactor or electrode are studied. Remarkably smaller length scales are achieved (λc < 2.96h) than those obtained with films cast on flat substrates. With van der Waals interactions, the patterns are uniformly formed throughout the film but are not regularly ordered. When electric field is used at critical voltage, more ordered, localized patterns are formed at the zones of large local interaction strengths. When these patterns are evolved by increasing the applied voltage, coexistence of all three phases-cavities, stripes, and columns-is observed throughout the film. The localized patterns that are initially formed vary with the voltage applied and strongly dictate the phases of evolution. A patterned substrate/patterned contactor assembly can be made to operate like its unpatterned counterpart by making the interaction strength same everywhere and yet yield uniform, regularly ordered, highly miniaturized patterns. Such patterns are very useful in various applications like microfluidics; they are formed with great ease and can be morphologically tuned by tuning the externally applied electric field.

Kinetically engendered subspinodal length scales in spontaneous dewetting of thin liquid films.

Numerical simulations reveal emergence of subspinodal length scales in spontaneous dewetting of nonslipping unstable thin liquid films on homogeneous substrates if the liquid viscosity decreases with decrease in film thickness.

Simulating Contact Instability in Soft Thin Films through Finite Element Techniques

When a thin film of soft elastic material comes in contact with an external surface, contact instability triggered by interaction forces, such as van der Waals, engenders topologi‐ cally functionalized surfaces. Innumerable technological applications such as adhesives; microelecromechanical systems (MEMS), and nanoelectromechanical systems (NEMS) demand understanding of the physics behind the mechanical contact, relationship between the morphologies, and detachment forces in such films. Indentation tests are important experimental approach toward this; there also exist many simulation procedures to model the mechanical contact. Both atomistic level and analytical continuum simulations are computationally expensive and are restricted by the domain geometries that can be handled by them. Polymeric films also particularly demonstrate a rich variety of nonlinear behavior that cannot be adequately captured by the aforementioned methods. In this chapter we show how finite element techniques can be utilized in crack opening and in contact‐instability problems.

Erratum: Contact Instability in Adhesion and Debonding of Thin Elastic Films [Phys. Rev. Lett.97, 018303 (2006)]

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).