Interfacial tension model for catalytically driven nanorods

We present an analysis of the interfacial tension model for the movement of the catalytically driven nanorod. The model considers the convective reaction-diffusion equation for the production and diffusion of oxygen around the bimetallic nanorod. We solve the equation and find the concentration difference, which drives the nanorod. We use our expression to calculate the force on the nanorod and find that the result is within 20% of the results found earlier [ W. Paxton et al., J. Am. Chem. Soc. 128, 14881 (2006) ] by an approximate method. Unlike the earlier results, our results are valid from short to long lengths of the nanorod.

Peculiar morphological transitions induced by nanoparticles in polymeric blends: retarded relaxation or altered interfacial tension?

Nanoparticles of different shapes can induce peculiar morphologies in binary polymer blends depending on their position. It is envisaged that the increased yield stress of the filled phase slows down the relaxation resulting in arresting the peculiar morphologies which otherwise is thermodynamically unfavourable due to the increased interfacial area. This essentially means that the highly irregular structures can be preserved even without altering the interfacial tension between the phases! On the other hand, in the case of interfacially adsorbed particles, the resulting solid-like interface can also preserve the irregular structures. These phenomenal transitions in filled blends are very different from the classical copolymer compatibilized polymer blends. Moreover, these irregular structures can further pave way in designing conducting polymer blends involving conducting nanoparticles and revisiting our understanding of the concept of double percolation!

PE/PEO blends compatibilized by PE brush immobilized on MWNTs: improved interfacial and structural properties

Polyolefin based blends have tremendous commercial importance in view of their exceptional properties. In this study the interface of a biphasic polymer blend of PE (polyethylene) and PEO (polyethylene oxide) has been tailored to reduce the interfacial tension between the phases and to render finer morphology. This was accomplished by employing various strategies like addition of maleated PE (PE grafted maleic anhydride), immobilizing PE chains, ex situ, onto MWNTs by covalent grafting, and in situ grafting of PE chains onto MWNTs during melt processing. Multiwalled nanotubes (MWNTs) with different surface functional groups have been synthesized either a priori or were facilitated during melt mixing at higher temperature. NH2 terminated MWNTs were synthesized by grafting ethylene diamine (EDA) onto carboxyl functionalized carbon nanotubes (COOH(MWNTs) and further, was used to reactively couple with maleated PE to immobilize PE chains on the surface of MWNTs. The covalent coupling of maleated PE with NH2 terminated MWNTs was also realized in situ in the melt extruder at high temperature. Both NH2 terminated MWNTs and the in situ formed PE brush on MWNTs during melt mixing, revealed a significant improvement in the mechanical properties of the blend besides remarkably improving the dispersion of the minor phase (PEO) in the blends. Structural properties of the composites were evaluated and the tensile fractured morphology was assessed using scanning electron microscopy.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.

Breakage of viscoelastic drops in turbulent stirred dispersions

The existing models of drop breakage in stirred turbulent dispersions are applicable only to purely viscous dispersed phases. In their present form, they are found to underpredict the diameters of the largest stable drops formed when a viscoelastic fluid is dispersed into a Newtonian liquid. In purely viscous fluids, the turbulent stresses are opposed both by the stresses due to interfacial tension and the viscous stresses generated as the drop deforms. In viscoelastic fluids, drop deformation produces additional retractive elastic stresses which also oppose turbulent stresses. As the deformation rates are large, the retractive stresses can be large in magnitude. Assuming that these additional stresses decay with time, a model of viscoelastic drop breakage in turbulent stirred dispersions has been developed. The new model quantitatively predicts the dmax of viscoelastic fluids. The model, however, does not predict the observation that when the time constant of the fluid becomes large (λ > 0.5 s), the fluid can not be dispersed into droplets up to agitator speeds of about 10 rps in our equipment.

Breakage of viscous and non-Newtonian drops in stirred dispersions

A model of breakage of drops in a stirred vessel has been proposed to account for the effect of rheology of the dispersed phase. The deformation of the drop is represented by a Voigt element. A realistic description of the role of interfacial tension is incorporated by treating it as a restoring force which passes through a maximum as the drop deforms and eventually reaching a zero value at the break point. It is considered that the drop will break when the strain of the drop has reached a value equal to its diameter. An expression for maximum stable drop diameter, dmax, is derived from the model and found to be applicable over a wide range of variables, as well as to data already existing in literature. The model could be naturally extended to predict observed values of dmax when the dispersed phase is a power law fluid or a Bingham plastic.

Replacement of water on a steel substrate by a surrounding oil reservoir

With an objective to replace a water droplet from a steel surface by oil we study here the impact of injecting a hydrophilic/lipophilic surfactant into the droplet or into the surrounding oil reservoir. Contact angle goniometery, Grazing angle FTIR spectroscopy and Atomic force microscopy are used to record the oil/water interfacial tension, surface energetics of the substrate under the oil and water phases as well as the corresponding physical states of the substrates. Such energetics reflect the rate at which the excess surfactant molecules accumulate at the water/oil interface and desorb into the phases. The molecules diffuse into the substrate from the phases and build up specific molecular configurations which, with the interfacial tension, control the non-equilibrium progress of and the equilibrium status of the contact line. The study shows that the most efficient replacement of water by the surrounding oil happens when a surfactant is sparingly soluble in the supplier oil phase and highly soluble in the recipient water phase.

Drop formation studies in liquid—liquid systems

Benzene drops were formed in continuous media of water and glycerine of varying physical properties. The effect on drop volumes of variables like volumetric flow-rate, interfacial tension, continuous phase viscosity and capillary diameter was studied. An equation has been developed, based on a two stage drop formation mechanism, which predicts drop volumes within an average error of 7 per cent for the range of physical properties employed in this investigation.

Effect of surfactants on drop breakage in turbulent liquid dispersions

The existingm odels of drop breakage in stirred dispersions grossly overpredict the maximum drop size when surface active agents are present inspite of using the lowered value of interfacial tension. It is shown that the difference in the values of dynamic and static interfacial tension, aids the turbulent stresses in drop breakage. When the difference is zero, e.g. for pure liquids and for high concentration of surfactants, the influence of the addition of surfactant is merely to reduce the interfacial tension and can be accounted for by existingm odels. A modified model has been developed, where the drop breakage is assumed to be represented by a Voigt element. The deforming stresses are due to turbulence and the difference between dynamic and static interfacial tensions. The resisting stresses arise due to interfacial tension and the viscous flow inside the drop. The model yields the existing expressions for dmax as special cases. The model has been found to be satisfactory when tested against experimental results using the styrene-water-teepol system.

Breakup of drops around the edges of Rushton turbine

A detailed experimental and simulation study has been carried out in the present work to understand drop breakup in regions around the edge of the Rushton turbine in agitated vessels. The effect of impeller speed, impeller size, interfacial tension, and the viscosities of the two phases is studied on drop breakup through their effect on dmax, the size of the largest drop in the system, and the whole size distribution. The measurements were carried out using Galai particle size analyser and optical microscope. Experimental analysis shows that the dmax, maximum stable drop diameter varies with impeller tip velocity to the power -1. The variation of dmax with interfacial tension is studied using different surfactants. The effect of viscosity ratio, achieved by changing the dispersed phase viscosity, on dmax is captured. For the same dmax values obtained from two different dispersed phases show that the wider drop size distribution is observed for higher dispersed phase viscosity.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

Breakage of a drop of inviscid fluid due to a pressure fluctuation at its surface

In this work, an attempt is made to gain a better understanding of the breakage of low-viscosity drops in turbulent flows by determining the dynamics of deformation of an inviscid drop in response to a pressure variation acting on the drop surface. Known scaling relationships between wavenumbers and frequencies, and between pressure fluctuations and velocity fluctuations in the inertial subrange are used in characterizing the pressure fluctuation. The existence of a maximum stable drop diameter d(max) follows once scaling laws of turbulent flow are used to correlate the magnitude of the disruptive forces with the duration for which they act. Two undetermined dimensionless quantities, both of order unity, appear in the equations of continuity, motion, and the boundary conditions in terms of pressure fluctuations applied on the surface. One is a constant of proportionality relating root-mean-square values of pressure and velocity differences between two points separated by a distance l. The other is a Weber number based on turbulent stresses acting on the drop and the resisting stresses in the drop due to interfacial tension. The former is set equal to 1, and the latter is determined by studying the interaction of a drop of diameter equal to d(max) with a pressure fluctuation of length scale equal to the drop diameter. The model is then used to study the breakage of drops of diameter greater than d(max) and those with densities different from that of the suspending fluid. It is found that, at least during breakage of a drop of diameter greater than d(max) by interaction with a fluctuation of equal length scale, a satellite drop is always formed between two larger drops. When very large drops are broken by smaller-length-scale fluctuations, highly deformed shapes are produced suggesting the possibility of further fragmentation due to instabilities. The model predicts that as the dispersed-phase density increases, d(max) decreases.

A note on the damping and oscillations of a fluid drop moving in another fluid

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.