Influence Of Surface Viscosity Research Articles

Stability and tip streaming of a surfactant-loaded drop in an extensional flow. Influence of surface viscosity

We study numerically the nonlinear stationary states of a droplet covered with an insoluble surfactant in a uniaxial extensional flow. We calculate both the eigenfunctions to reveal the instability mechanism and the time-dependent states resulting from it, which provides a coherent picture of the phenomenon. The transition is of the saddle-node type, both with and without surfactant. The flow becomes unstable under stationary linear perturbations. Surfactant considerably reduces the interval of stable capillary numbers. Inertia increases the droplet deformation and decreases the critical capillary number. In the presence of the surfactant monolayer, neither the droplet deformation nor the stability is significantly affected by the droplet viscosity. The transient state resulting from instability is fundamentally different for drops with and without surfactant. Tip streaming occurs only in the presence of surfactants. The critical eigenmode leading to tip streaming is qualitatively the same as that yielding the central pinching mode for a clean interface, which indicates that the small local scale characterizing tip streaming is set during the nonlinear droplet deformation. The viscous surface stress does not significantly affect the droplet deformation and the critical capillary number. However, the damping rate of the dominant mode considerably decreases for viscous surfactants. Interestingly, shear viscous surface stress considerably alters the tip streaming arising in the supercritical regime, even for very small surface viscosities. The viscous surface stresses alter the balance of normal interfacial stresses and affect the surfactant transport over the stretched interface.

Influence of surface viscosity on droplets in shear flow

The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq–Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number$B_{q}$. Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number$Ca$, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram$(B_{q};Ca)$of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.

Dynamics of order reconstruction in nanoconfined twisted nematic cells with a topological defect

Within the Landau-de Gennes theory, we have investigated the dynamics of s = ±1/2 twist disclinations in a twisted nematic cell, using the two-dimensional finite-difference iterative method. We explore the biaxial structure of the defect core and describe its dynamics as the cell gap decreases. At a critical value of dc* ≈ 9ξ (here ξ is the characteristic length for order-parameter changes), the exchange solution is stable, while the defect core solution becomes metastable, where the system starts to stretch the defect structure and the biaxiality starts to propagate inside of the cell. Compared to the case with no initial disclination, the value at which the exchange solution becomes stable increases relatively. At a critical separation of dc ≈ 7ξ, the system undergoes a biaxial transition, and the defect core merges into a biaxial wall with large biaxiality. This transition corresponds to the reconstruction of the nematic order already found in the bulk with no defect. The force reaches a maximum at d ≈ 9ξ and a local minimum at d ≈ 7ξ. The dynamic response shows the influence of surface viscosity.

Effect of surface viscosity, anchoring energy, and cell gap on the response time of nematic liquid crystals

An analytical expression for the relaxation time of a nematic liquid crystal is obtained for the first time by considering the influence of surface viscosity, anchoring energy strength and cell gap, validated numerically by using the so-called relaxation method. This general equation for the molecular response time (τ0) was derived for a vertical aligned cell and by solving an eigenvalue equation coming from the usual balance of torque equation in the Derzhanskii and Petrov formulation, recovering the usual equations in the appropriate limit. The results show that τ∼db, where b=2 is observed only for strongly anchored cells, while for moderate to weak anchored cells, the exponent lies between 1 and 2, depending on both, surface viscosity and anchoring strength. We found that the surface viscosity is important when calculating the response time, specially for thin cells, critical for liquid crystal devices. The surface viscosity’s effect on the optical response time with pretilt is also explored. Our results bring new insights about the role of surface viscosity and its effects in applied physics.

Surface viscosity and reorientation process in an asymmetric nematic cell

The influence of surface viscosity and anchoring energy on the reorientation process of a nematic liquid crystal cell is theoretically investigated. The cell is a slab of thickness, d, whose limiting surfaces are characterised by different anchoring strengths and present easy directions parallel to the bounding surfaces, changing with time due to some external action. The exact space-time profile of the director angle is obtained by means of integral transform techniques and a Green function approach. From this formalism, the time dependence of the optical path difference is exactly determined and its behaviour is analysed in connection with the presence of surface viscosity and different anchoring energies. The problem is also exactly solved in the presence of a constant electric field. It is shown that the compatibility problem between the time derivative of the director field on the surface and in the bulk can be avoided.

Influence of Surface Viscosity on Two-Dimensional Faraday Waves

The onset for the formation of two-dimensional Faraday waves in a liquid with a viscous surface is numerically studied. The viscous behavior of the interface due to the presence of an insoluble surfactant, affects the surface traction and this, in turns, induces changes in the flow field. It is shown that the formation of waves of a given wavenumber in the absence of elastic effects requires a force that when plotted versus the Boussinesq number increases, producing a sigmoid curve. A detailed analysis of the interfacial variables and flow fields is carried out in order to understand this behavior.

Foam drainage on the microscale II. Imaging flow through single Plateau borders.

The liquid in foam forms an interconnected network, which is composed of Plateau borders, nodes, and films. One of the dominant pathways for foam drainage is flow through Plateau borders, and we use confocal microscopy to obtain experimental results for the flow fields inside individual Plateau borders. For three types of surfactants detailed comparisons are made with a model based upon the influence of surface viscosity at free boundaries between the gas in the bubbles and the liquid in the Plateau borders. The model describes the flows well, and we find good agreement between the surface viscosity predicted by this model and representative values found in the literature. We also give a qualitative description of the flow in the nodes.

Drag of a Solid Particle Trapped in a Thin Film or at an Interface: Influence of Surface Viscosity and Elasticity

We propose a theoretical model for the motion of a spherical particle entrapped in a thin liquid film or in a monolayer of insoluble surfactant at the air/water interface. Both surface shear and dilational viscosity, surface diffusion, and elasticity of the film are taken into consideration. The drag force acting on the particle is analytically calculated and asymptotic expressions of the problem are provided. The relevance of the model is discussed by comparing the calculated “viscoelastic” drag, γvel, to the one predicted by Saffman's theory, γS, for cylindrical inclusions in membranes. Numerical analyses are performed to evaluate the contributions of the surface viscosity and the diffusion coefficient of the layer on the hydrodynamical resistance experienced by the particle.

Stability of a spherical drop with surfactant mass transfer

Interphase convection and Marangoni instability have recently become the subject of active study [1–5]. The description of a number of phenomena associated with the interaction between surfactant mass transfer and capillary effects are examined at the kinetic and hydrodynamic levels, using an experimentally realizable physical model. For this model the boundary-value problem of the stability of diffusion transfer of surfactant across an initially spherical interface between two immiscible liquids in the diffusion and adsorption kinetics regimes is solved analytically. The critical values of the dimensionless parameters of the problem at which convectionless mass transfer becomes unstable with respect to monotonic disturbances are found. The drop drift effect is examined. The change in the shape of the drop and the influence of surface viscosity and diffusion effects are taken into account. The possible practical applications of the problems solved include: modeling spontaneous emulsification, cytokinesis and chemotaxis, and estimating the effect of interphase turbulence on the rate of mass transfer across media interfaces in various industrial processes.

Hydrodynamics of thin liquid films

The influence of surface viscosity on the rate of thinning and on the critical thickness of rupture of foam films has been studied. It is shown that this effect depends strongly on the length-scale of the flow. Therefore it is possible to neglect it when calculating the rate of thinning, but to assume for the wave motion, caused by the thermic fluctuations, that the surface viscosity is infinitely great. The expression for the critical thickness, obtained in this way, agrees relatively well with the experimental results. A possible explanation of the dependence of critical thickness on surfactant concentration is suggested.