Surface Dilatational Viscosity Research Articles

Relationship between surface dilational properties and foam stability

The knowledge of the stability of foams and emulsions is very important for the control of a large number of technological processes. However, in spite of much intense research, the mechanism of foam stability is still not completely clear. Foam stability depends on many parameters but the type of the added surfactant and the surface rheological properties of the adsorption layers play the most important role. Because of the lack of reliable surface rheological data a comprehensive investigation of this problem was not yet possible. However, we can now present measurements of surface dilational properties of soluble adsorption layers in a frequency range of 1–500 Hz using a new version of the oscillating bubble method. The results are compared with measurements of foam stability. This indicates that the surface dilational viscosity plays an important role in the stability of foam films. A direct relation between surface dilational elasticity values and foam stability could not be detected for the examined systems. Pure elastic adsorption layers were not able to stabilize foam lamellas.

Negative Pressure in the Oil Film of Journal Bearing. 1st Report: Modelling of Negative Pressure Development and Influences of Parameters on Pressure Distribution.

Using a bubble theory which takes into account the surface dilatational viscosity κ, influences of eccentricity ε, 4 bubble and 4 bearing parameters on pressure distribution are studied for the oil film in journal bearing : When κ is neglected, the maximum negative pressure is given by a formula containing only a dimensionless surface tension. For small ε, pressure distribution scarcely depends on bubble parameters, and coincides nearly with that calculated by conventional theory under Reynolds condition. For large ε, it changes also with bubble parament values. Whether ε is small or large, the maximum pressure hardly depends on bubble parameters, but depends only on bearing parameters. It is nearly equal to that calculated by conventional theory under Reynolds condition. For increasing ε, κ and shaft speed, the pressure distribution tends to that of Sommerfeld type.

The shape oscillations of a two-dimensional drop including viscous effects

The implementation of a boundary integral method for potential flow is presented for the case of a two-dimensional drop freely oscillating in a vacuum. Calculations using a standard boundary integral formulation and a double-layer potential boundary integral formulation are compared for the case of an inviscid drop with a clean interface. Additional comparisons are made using a least-squares spectral transform method for interpolating and differentiating versus more common methods using cubic splines and central differences. The boundary integral method for potential (i.e. inviscid) flow is extended in two viscous examples to approximate (i) the weak viscous effects in the bulk fluid far from the clean interface, or (ii) the surface viscous effects in an inviscid drop arising from an interface that is highly contaminated with an insoluble surfactant. The addition of an incompressibility constraint, implemented in a least-squares sense, to the standard boundary integral formulation is shown to significantly improve its ability to preserve the conserved quantities of volume and total energy. Nevertheless, the double-layer potential boundary integral formulation, despite its more complicated form, is found to be computationally more efficient than the standard formulation. The use of the least-squares spectral transform method is shown to be more accurate, and in certain conditions more efficient, than using cubic splines and sixth-order central differences for time-evolution of this system. Simulations approximating the damping effects of clean viscous drop are found to be consistent with small deformation theory while the calculations incorporating the damping effects of surface dilatational viscosity are shown to dissipate the energy of the oscillations at a rate that is neither exponential nor algebraic.

Theoretical analysis of free-shape oscillations of surfactant-bearing drops

A theoretical analysis is presented for the free-shape oscillations of surfactant-bearing drops suspended in air using the method of spherical harmonic expansions. Two extreme types of surfactant mass transfer between the bulk and the surface of drops are considered: (1) no surfactant transport as the drop oscillates; and (2) the surfactant transport is so fast that the surface surfactant concentration remains constant and homogeneous. It is found that the shear viscosity of bulk phase, surface elasticity, surface shear viscosity and surface dilatational viscosity have the same order of influence on the free-damping constant when the surface shear viscosity is smaller than a certain value. Otherwise, the free-damping constant is determined by the surface shear viscosity, and the influence of the surface dilatational viscosity, the surface elasticity, and the shear viscosity of the bulk phase on the drop oscillation is negligible.

Stress relaxation behaviour of dipalmitoyl phosphatidylcholine monolayers spread on the surface of a pendant drop

Dipalmitoyl phosphatidylcholine (DPPC) monolayers were characterised by surface pressure/area isotherms ( π/ A) and surface dilational rheological parameters at temperatures 20–40°C. The methods used were the Langmuir trough and the pendant drop micro-film balance. The latter allows accurate measurements at higher temperatures and transient drop deformation. Stable DPPC monolayers were found only for low surface pressures, π<15 mN m −1. At higher monolayer compression π decreases over a long time, mainly caused by molecular rearrangement processes in the monolayer starting in the coexisting region. At π>25 mN m −1 and 20°C relaxation experiments give evident of rupturing, brittle monolayer structures. At higher temperatures the monolayers became more fluid-like. π/ A-isotherms determined by using both methods principally agree with each other, but show also remarkable differences, which cannot be explained so far satisfactory. Transient drop relaxation experiments were analysed for the short time range (600 s). At 20°C the dilational modulus ( ε r) and the surface dilational viscosity ( ξ r) passes a stationary maximum at 0.54 nm 2 molecule −1 and increase strongly at higher surface coverage, thus indicating crystalline monolayer structure. Increasing temperature from 20 to 30°C causes a rapid decrease of ε r and ξ r and a shift of the stationary maximum to lower surface coverage. No evidence for crystalline structure is found. Further increase of temperature causes ε r and ξ r increase again. This increase is caused by a rising relaxation time, while the elasticity does not change in the same manner. Such intermediate decrease of ε r and ξ r in the range 30–40°C appears to be unusual and can be interpreted as a consequence of strong DPPC interactions and strongly pronounced retardation of monolayer deformation. The study is discussed in connection to the physiology of breathing. For pulmonary surfactants the observed behaviour seems to be understandable. It is however interesting that such complex behaviour is observed for monolayers consisting of DPPC only.

Surface visco-elastic modes in a spread film of a block copolymer

A linear diblock copolymer of polymethyl methacrylate and poly-4-vinyl pyridine quaternised with ethyl bromide has been spread as a thin film at the air/water interface and the properties of the capillary waves obtained using surface quasi-elastic light scattering. The data have been analysed for surface visco-elastic parameters on the basis of the complete absence of any transverse shear viscosity in the spread film. A resonance between capillary and dilatational modes was observed at a block copolymer surface concentration of 0.8 mg m-2. At this surface concentration the frequency dependence of the surface tension, dilatational modulus and dilatational viscosity exhibited behaviour which suggested that spread film could be represented as a Maxwell fluid with a relaxation time of ca. 3 µs. This Maxwell fluid model also described the dependence of an ‘apparent’ relaxation time of the dilatational mode on the surface concentration for a capillary wave of fixed wavenumber. A comparison of the observed dispersion behaviour (damping as a function of capillary wave frequency) with that predicted by theoretical forms of the dispersion equation, showed that there was no need to include a postulated coupling factor. This observation concurred with the modest dimensions of the surface region occupied by the quaternised vinyl pyridine blocks.

Direct Determination of the Dependence of the Surface Shear and Dilatational Viscosities on the Thermodynamic State of the Interface: Theoretical Foundations

Recent developments in nonlinear optical techniques for noninvasive probing of a surfactant influenced gas/liquid interface allow for the measurement of the surfactant surface concentration,c,and thus provide new opportunities for the direct determination of its intrinsic viscosities. Here, we present the theoretical foundations, based on the Boussinesq–Scriven surface model without the usual simplification of constant viscosities, for an experimental technique to directly measure the surface shear(μs)and dilatational(κs)viscosities of a Newtonian interface as functions of the surfactant surface concentration. This ability to directly measure the surfactant concentration permits the use of a simple surface flow for the measurement of the surface viscosities. The requirements are that the interface must be nearly flat, and the flow steady, axisymmetric, and swirling; these flow conditions can be achieved in the deep-channel viscometer driven at relatively fast rates. The tangential stress balance on such an interface leads to two equations; the balance in the azimuthal direction involves onlyμsand its gradients, and the balance in the radial direction involves bothμsandκsand their gradients. By further exploiting recent developments in laser-based flow measuring techniques, the surface velocities and their gradients which appear in the two equations can be measured directly. The surface tension gradient, which appears in the radial balance equation, is incorporated from the equation of state for the surfactant system and direct measurements of the surfactant surface concentration distribution. The stress balance equations are then ordinary differential equations in the surface viscosities as functions of radial position, which can be readily integrated. Sincecis measured as a function of radial position, we then have a direct measurement ofμsandκsas functions ofc.Numerical computations of the Navier–Stokes equations are performed to determine the appropriate conditions to achieve the requisite secondary flow.

Surfactant-bearing drop dynamics in microgravity

Experiments of large amplitude nonlinear oscillations of axially symmetric surfactant-bearing (triton or bovine serum albumin) water drops with different initial aspect ratios and drop volumes were performed during the second United States Microgravity Laboratory, USML-2 in November 1995. Through the numerical simulation of the oscillations of these surfactant-bearing water drops using the boundary integral method, the surface dilatational viscosity and the surface shear viscosity are found to play a major role in these oscillations. How they influence the damping coefficient and the drop oscillation frequency will be presented. The numerical and analytical results and a physical picture of the relation between the surface viscosities and the damping coefficient will be described. In addition, the relation between the initial drop aspect ratio, the surface viscosities, and the surface rotational velocity will also be presented. [Work supported by NASA through JPL, Contract No. 958722.]

Numerical simulation of superoscillations of a BSA-bearing drop in microgravity

Large-amplitude nonlinear oscillations of a water drop, radius 2.53 cm and aspect ratio 2.10, with surfactant BSA (bovine serum albumin) 1.0×10−5 g/ml(1CMC), is numerically simulated based on the boundary integral method. BSA is a globular, large molecular-weight protein. Two surface viscosities, surface dilatational viscosity and surface shear viscosity, as well as the Marangoni effect, are considered. The high-surface viscosities make the rotational velocity the same order as the irrotational velocity in the boundary layer. A boundary-layer method is used to calculate the rotational velocity. When the surface dilatational viscosity is 0.5 sp and the surface shear viscosity is 0.15 sp, the numerical simulation results are in good agreement with the experiment results observed in the space shuttle during the second United States Microgravity Laboratory, USML-2, in October, 1995. The evolution of the drop oscillation for both experiment and simulation is given. The change of the BSA distribution along the surface, and the relative importance of the rotational and irrotational velocities, as the drop oscillates is also shown. [Work supported by NASA through JPL, Contract No. 958722.]

Experimental comparisons with a numerical model of surfactant effects on the burst of a single bubble

A high-speed photographic study of gas bubbles bursting at a gas/liquid interface in the presence of surfactant is described. Bubbles were burst in a variety of media typical of those used in mammalian cell culture. In order to test the hypothesis that surfactant reduces cell damage as a result of moderation of the bubble burst, a numerical simulation of the surfactant effect was compared with the experimental data. Surface tension, surface shear and dilatational viscosities were measured in a variety of media containing a surfactant. The rate of bubble jet rise, a readily measured property of a burst, which depends strongly on the presence of surfactant, was measured. Experimental observations in the presence of surfactant broadly agree with the theory in the reduction in jet rise rate, if it is assumed that dilatational viscosity plays a major role. However, measured values for surface dilatational viscosity were an order of magnitude less than those required for an observable effect in the model. A reason for this discrepancy is proposed.

Determination of Surface Viscosities by Surfactant Concentration and Velocity Field Measurements for an Insoluble Monolayer

A new technique has been developed to determine the sum of the surface (excess) shear viscosity and surface dilatational viscosity for insoluble monolayers on a gas−liquid interface. The flow on the interface is produced by the rise and the subsequent spread of a laminar vortex pair which dilates the interface. The terms in the tangential component of the stress boundary condition equation for the interface are directly evaluated through measurements of the velocity in the liquid and on the interface, obtained through digital particle image velocimetry, and measurements of the unsteady surfactant concentration on the interface, made with the nonlinear optical technique of second-harmonic generation. For the experiments, the water surface was initially covered by a uniform monolayer of hemicyanine dye, 4-[4-(dimethylamino)styryl]-1-docosylpyridinium bromide, which was chosen for its strong nonlinear optical response. The sum of the surface viscosities for hemicyanine was found to be 1.2 (±0.5) sp at a conc...

Oscillations of a water drop with surfactant Triton X-100 in zero gravity

Large amplitude nonlinear oscillations of an axially symmetric water drop of 2.51-cm diameter, initial aspect ratio 3.4, with surfactant Triton X-100 of 0.5 mM, in zero gravity are studied by a boundary element method. Included in the analysis are surface-shear and dilatational viscos- ity, under the assumption that the shear viscosity of the bulk phase is small. Numerical simulations of the drop oscillations are in good agreement with the experimental results of drop oscillations measured in space during the second United States Microgravity Laboratory, USML-2. The evolution of the drop oscillations for both experiment and simulation is given. The simulation provides predictions for the values of both surface dilatational viscosity and shear viscosity of 0.20 sp and 0.10 sp, respectively. In addition, with the simulated data, the damping constants, frequencies, and decomposed oscillation modes are computed. [Work supported by NASA through JPL, Contract No. 958722.]

Light scattering study of viscoelastic properties of a liquid Gallium surface

High frequency capillary waves on a liquid Gallium surface were studied by quasi-elastic light scattering spectroscopy. The observed damping constants of the waves differ greatly from the predictions of classical theoretical treatment of the surface as that of a simple liquid. This is explained in terms of the presence of a surface layer possessing visco-elastic properties which are extracted from the fit of experimental spectra using different theoretical forms. One of the most important results of the data analysis is that the surface dilational viscosity appears to be negative. This result implies that the widely used phenomenological theoretical model should be replaced by one taking into account processes of adsorption and diffusion.

Investigation of Liquid Surface Rheology of Surfactant Solutions by Droplet Shape Oscillations: Experiments

The experimental results of droplet shape oscillations are reported and applied to the analysis of surface rheological properties of surfactant solutions. An acoustic levitation technique is used to suspend the test drop in air and excite it into quadrupole shape oscillations. The equilibrium surface tension, Gibbs elasticity, and surface dilatational viscosity are determined from the measurements of droplet static shape under different levitation sound pressure, oscillation frequency, and free damping constant. Aqueous solutions of sodium dodecyl sulfate, dodecyltrimethylammonium bromide, andn-octyl β-d-glucopyranoside are tested with this system. The concentrations of the solutions are below the critical micelle concentration. For these solutions it is found that the surface Gibbs elasticity approaches a maximum at a moderate concentration, and its value is less than that directly calculated from the state equation of a static liquid surface. The surface dilatational viscosity is found to be in a range around 0.1 cps.

Light-scattering spectroscopy of a liquid gallium surface

High-frequency capillary waves at a liquid gallium surface have been studied by means of quasi-elastic light-scattering spectroscopy. The observed frequencies and damping constants of waves differed greatly from the classical theoretical treatment of a liquid Ga surface as that of a simple liquid. This effect was explained in terms of the presence of the surface layer, possessing visco-elastic properties which were, in turn, extracted, for the first time, from the fit of experimental spectra with an appropriate theoretical form. A negative value of the surface dilational viscosity has been derived for all wavenumbers studied and the effect of the visco-elasticity on the strong coupling and mixing between the capillary and dilational mode on the surface of liquid Ga has been demonstrated.

A Note on the Formation and Rise of a Bubble from a Submerged Nozzle, Including Effects of Bulk- and Surface-Dilatational Viscosity

A model of the formation, detachment, and rise of a bubble from a submerged orifice is derived, based upon a study using a modified form of the Rayleigh–Plesset equation. Similar models have previously been proposed by Oguz and Prosperetti (1), Avramidis and Jiang (2), and also Chakraborty and Tuteja (3). We seek to re-examine these models and implement a number of additional physical features. In particular, we demonstrate the relative importance of the surface dilatational viscosity of surfactant added to the liquid in the growth and detachment of the bubble from the orifice. It is found that “large” surface dilatational viscosities significantly increase the time to detachment of the bubble. In addition, through a drastic reduction in the rate of radial expansion of the bubble in the early stages of development (given an initial condition on the radial velocity for “fast” bubble growth), the rise velocity of the bubble centroid at this time is greater with a large surface dilatational viscosity than when this property is neglected.

Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory

A theoretical analysis is presented for the shape oscillations of drops suspended in air. For drops of surfactant solution, the oscillation frequency is basically determined by the surface tension; the free-damping constant depends on the surface viscoelasticities. Different types of surfactant mass transfer at the droplet surface produce different surface rheological behaviors. Analytical approximate solutions for free-oscillation frequency and damping constant are derived by a perturbation method as functions of surface compositional elasticity, surface dilatational viscosity, and surface shear viscosity. These solutions are verified with exact numerical solutions. The existence of a second oscillation mode due to surface elasticity is illustrated. The phase relationships between the external driving forces and the droplet shapes for forced oscillations are discussed. It is found that at the 90° phase shift, the driving frequency and the slope of the phase diagram are equivalent to the free-oscillation frequency and damping constant.

The effect of surfactant on bursting gas bubbles

A numerical technique, based on the boundary integral method, is developed to allow the modelling of unsteady free-surface flows at large Reynolds numbers in cases where the surface is contaminated by some surface-active compound. This requires the method to take account of the tangential stress condition at the interface and is achieved through a boundary-layer analysis. The constitutive relation that forms the surface stress condition is assumed to be of the Boussinesq type and allows the incorporation of surface shear and dilatational viscous forces as well as Marangoni effects due to gradients in surface tension. Sorption kinetics can be included in the model, allowing calculations for both soluble and insolube surfactants. Application of the numerical model to the problem of bursting gas bubbles at a free surface shows the greatest effect to be due to surface dilatational viscosity which drastically reduces the amount of surface compression and can slow and even prevent the information of a liquid jet. Surface tension gradients give dilatational elasticity to the surface and thus also significantly prevent surface compression. Surface shear viscosity has a smaller effect on the interface motion but results in initially increased surface concentrations due to the sweeping up of surface particles ahead of the inward-moving surface wave.

Slow motions of a solid spherical particle close to a viscous interface

In order to investigate the hydrodynamic interaction between an interface and a spherical particle and its dependence on the type of interface, it is essential to compute the drag and torque exerted on the sphere in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stationary movement of a spherical particle next to a solid, viscous or free interface is considered. For low capillary numbers and different values of surface dilatational and shear viscosities in a curvilinear co-ordinate system of revolution with bicylindrical co-ordinates in meridian planes, the problem reduces from three to two dimensions. The model equations and boundary conditions, which contain second-order derivatives of the velocities, transform to an equivalent well-defined system of second-order partial differential equations which is solved numerically for medium and small values of the dimensionless distance to the interface. Very good agreement with the asymptotic equation for a translating sphere close to a solid interface could be achieved. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity.

Influence of the Surface Viscosity on the Hydrodynamic Resistance and Surface Diffusivity of a Large Brownian Particle

The present paper treats the problem of the slow motion of a spherical particle, partially immersed in a viscous liquid. It relates to the theory of Brenner and Leal concerning the surface diffusivity of a large Brownian particle and provides important basic information on the so-called "drag-out problem." The numerical investigation yields the local velocity and pressure distribution, the hydrodynamic resistance, and the surface diffusion coefficient. The computations are carried out for low Reynolds and capillary numbers considering a stationary floating macroparticle on a viscous liquid-gas interface. Results are presented for different values of surface dilatational and shear viscosity and contact angles. Brownian motion of the particle is taken into account by integrating the resultant second-order partial differential equations with an alternating direct implicit method. The numerical results reveal for all contact angles a strong decrease of the surface diffusion coefficient when the surface viscosity increases.