Measuring the mutual diffusion coefficient for dodecyl acrylate in low molecular weight poly(dodecyl acrylate) with laser line deflection (Wiener's Method) and the fluorescence of pyrene

Diffusion of small molecules into glassy polymers is quite complicated and almost always non-Fickian. Little work has been done with the diffusion of low molecular weight polymers that are liquids at room temperature (such as poly(dodecyl acrylate)) into their miscible monomers. We have studied three molecular weights under 20 000 to determine if poly(dodecyl acrylate) diffusion into dodecyl acrylate could be treated with Fick's law and if so to determine the values of the diffusion coefficients. We compare two methods for measuring the diffusion of dodecyl acrylate into poly(dodecyl acrylate): We used laser line deflection (Wiener's method) and improved upon the method from published reports. We also used the dependence of pyrene's fluorescence on the viscosity to measure the concentration distribution, and thus to extract the diffusion coefficient. After an initial relaxation period, diffusion in all cases followed Fick's law with a single concentration-independent diffusion coefficient. Comparison of the diffusion coefficients obtained by both methods yielded the same order of magnitude for the diffusion coefficients (10(-7) cm2/s) and showed the same trend in the dependence on the average molecular weight of the polymer (a decrease in the diffusion coefficient with an increase in the molecular weight).     

黏弹性对介观液珠聚并的影响——液珠-细丝-液珠聚并现象及其分析

在四辊流变仪中,黏弹性高分子介观液滴经反复拉伸和松弛形成了有细丝相连的两个黏弹液珠,研究了黏弹液珠的聚并过程,依形状叫做BSB(bead-string-bead,液珠-细丝-液珠)聚并.BSB现象与常见的通过滴间液膜破裂实现的液滴聚并过程大不相同.根据界面上的Laplace力、液珠移动时的黏性阻力和细丝中黏弹应力之间的平衡,推导出一个力学模型来描述BSB现象,理论分析与实验结果相符较好.细丝直径的变化和稳定性由过程参数和物料参数共同决定,尤其是液滴的黏弹性有较大影响.这一效应对多相高分子与复杂流体加工过程的基础理解富有启发.     

Experimental evidence of the motion of a single out-of-equilibrium drop

We show experimentally that when a single, neutrally buoyant drop is injected into a binary mixture either it remains quiescent or it moves, depending on whether the composition of the drop and that of the surrounding phase coincide with the equilibrium concentrations. In general, the movement of out-of-equilibrium drops, which is called diffusiophoresis, is induced by the Korteweg body force. This force is proportional to the chemical potential gradient and is therefore nonzero only when the system is in chemical nonequilibrium. In this letter, we show experimentally that this movement occurs for a single drop as well, even when the initial condition is (almost) isotropic. This instability, although it does not have a complete analytical explanation, has been predicted in the numerical simulations by Vladimirova et al. (Vladimirova, N.; Malagoli, A.; Mauri, R. Phys. Rev. E 1999, 60, 2037).     

Emulsification in turbulent flow: 3. Daughter drop-size distribution

Systematic set of experiments is performed to clarify the effects of several factors on the size distribution of the daughter drops, which are formed as a result of drop breakage during emulsification in turbulent flow. The effects of oil viscosity, etaD, interfacial tension, sigma, and rate of energy dissipation in the turbulent flow, epsilon, are studied. As starting oil-water premixes we use emulsions containing monodisperse oil drops, which have been generated by membrane emulsification. By passing these premixes through a narrow-gap homogenizer, working in turbulent regime of emulsification, we monitor the changes in the drop-size distribution with the emulsification time. The experimental data are analyzed by using a new numerical procedure, which is based on the assumption (supported by the experimental data) that the probability for formation of daughter drops with diameter smaller than the maximum diameter of the stable drops, d相似文献   

Coalescence during emulsification. 2. Role of small molecule surfactants

An oil-soluble hexadecyl pyrene (HDP) probe is used to monitor coalescence of hexadecane oil-in-water emulsions, during emulsification, in stirred systems and in a high-pressure homogenizer (microfluidizer), when small molecule surfactants are used as emulsifiers. The effect of sodium dodecyl sulfate concentration and salt concentration on the amount of coalescence and final drop size is studied. The behavior of oil-soluble surfactants and mixtures of oil-soluble and water-soluble surfactants on emulsification performance is also discussed. For high-pressure homogenizers, the drop sizes obtained are found to depend mostly on the ability of surfactants to stabilize the drops against coalescence, rather than their ability to reduce the interfacial tension. Increasing oil phase fractions increase the coalescence rate, because of the increase in collision frequency, which, in turn, impacts the drop size of the homogenized emulsion.     

Suspension of water droplets on individual pillars

We report results of extensive experimental and numerical studies on the suspension of water drops deposited on cylindrical pillars having circular and square cross sections and different wettabilities. In the case of circular pillars, the drop contact line is pinned to the whole edge contour until the drop collapses due to the action of gravity. In contrast, on square pillars, the drops are suspended on the four corners and spilling along the vertical walls is observed. We have also studied the ability of the two geometries to sustain drops and found that if we compare pillars with the same characteristic size, the square is more efficient in pinning large volumes, while if we normalize the volumes to pillar areas, the opposite is true.     

Experiments on the motion of drops on a horizontal solid surface due to a wettability gradient

Results from experiments performed on the motion of drops of tetraethylene glycol in a wettability gradient present on a silicon surface are reported and compared with predictions from a recently developed theoretical model. The gradient in wettability was formed by exposing strips cut from a silicon wafer to dodecyltrichlorosilane vapors. Video images of the drops captured during the experiments were subsequently analyzed for drop size and velocity as functions of position along the gradient. In separate experiments on the same strips, the static contact angle formed by small drops was measured and used to obtain the local wettability gradient to which a drop is subjected. The velocity of the drops was found to be a strong function of position along the gradient. A quasi-steady theoretical model that balances the local hydrodynamic resistance with the local driving force generally describes the observations; possible reasons for the remaining discrepancies are discussed. It is shown that a model in which the driving force is reduced to accommodate the hysteresis effect inferred from the data is able to remove most of the discrepancy between the observed and predicted velocities.     

Breakup of a Multiple Emulsion Drop in a Uniform Electric Field

The steady deformation and breakup of emulsion drops in a uniform electric field are considered experimentally. Due to the low volume fraction of inner drops, the emulsions can be effectively assumed as Newtonian fluids with spatial nonuniformity. The measurements of the electrical properties show that the oil-in-water (o/w) emulsion drop behaves like a conducting drop. On the other hand, the water-in-oil (w/o) emulsion drops can be regarded as inhomogeneous leaky dielectric drops. It is found that the viscosity ratio is not an important parameter within the small deformation limit and breakup mode of the o/w emulsion drops. In the case of w/o emulsion drops, however, the breakup mode depends on the viscosity ratio. Inherent nonuniformity of the emulsion drops makes drop more deformable and unstable. The tip-streaming is the dominant breakup mode of o/w emulsion drops when the nonuniformity of drop phase is appreciable. Copyright 1999 Academic Press.     

Sequential injection analysis with dynamic surface tension detection High throughput analysis of the interfacial properties of surface-active samples

A sequential injection analysis (SIA) system is coupled with dynamic surface tension detection (DSTD) for the purpose of studying the interfacial properties of surface-active samples. DSTD is a novel analyzer based upon a growing drop method, utilizing a pressure sensor measurement of drop pressure. The pressure signal depends on the surface tension properties of sample solution drops that grow and detach at the end of a capillary tip. In this work, SIA was used for creating a reagent concentration gradient, and for blending the reagent gradient with a steady-state sample. The sample, consisting of either sodium dodecyl sulfate (SDS) or poly(ethylene glycol) at 1470 g mol⁻¹ (PEG 1470), elutes with a steady-state concentration at the center of the sample plug. Reagents such as Brij®35, tetrabutylammonium (TBA) hydroxide and β-cyclodextrin were introduced as a concentration gradient that begins after the sample plug has reached the steady-state concentration. By blending the reagent concentration gradient with the sample plug using SIA/DSTD, the kinetic surface pressure signal of samples mixed with various reagent concentrations is observed and evaluated in a high throughput fashion. It was found that the SIA/DSTD method consumes lesser reagent and required significantly less analysis time than traditional FIA/DSTD. Four unique chemical systems were studied with regard to how surface activity is influenced, as observed through the surface tension signal: surface activity addition, surface activity reduction due to competition, surface activity enhancement due to ion-pair formation, and surface activity reduction due to bulk phase binding chemistry.     

Modeling diffusion in miscible polymer blend films

Recent experiments designed to probe polymer transport in the bulk and in the vicinity of surfaces have examined the interdiffusion of multilayer sandwiches of isotopically labeled polymers. The measured time dependent concentration profiles normal to the surface are typically fit to Fick's law, with a single fitting parameter, the mutual binary diffusion coefficient (MBDC). The resulting MBDCs are found to vary over a broad range of film thicknesses and time, with the time dependence being viewed as a unique signature of the reptation mechanism of long chain motion, and the thickness dependence being attributed to the slowing down of chain dynamics near surfaces. Since the experiments are conducted at finite concentration, the MBDC, which is a product of the bare mobility and the concentration derivative of the chemical potential, could be dominated by the time and thickness dependence of this second term (which is ignored in Fick's law). To quantify this conjecture we consider the more rigorous Cahn formulation of the diffusion problem in terms of chemical potential gradients. We use square gradient theory to evaluate chemical potentials, and fit the resulting time dependent concentration profiles to the analytical solution of Fick's law. By thus mimicking the experimental analysis we find that the apparent MBDCs vary with time as t(-1/2) at short times, in good agreement with existing experiments. We show that this time dependence reflects the system's desire to minimize concentration gradients, a fact ignored in Fick's law. Since these arguments make no reference to the mechanism of chain motion, we argue that the time dependence of MBDC derived from interdiffusion experiments does not provide unequivocal support for the reptation mechanism of long chain transport. The MBDC values, which also vary with the degree of confinement, are predicted to increase with decreasing thickness for model parameters corresponding to experimental systems. In contrast, since the experimental fits yield an opposite trend, we suggest that the bare mobility of the chains decreases strongly with decreasing thickness. These findings strongly support the idea that the chains are "pinned" irreversibly to the surfaces, in good agreement with other, independent experiments.     

Fog deposition and accumulation on smooth and textured hydrophobic surfaces

We investigated the deposition and accumulation of droplets on both smooth substrates and substrates textured with square pillars, which were tens of micrometers in size. After being coated with a hydrophobic monolayer, substrates were placed in an air flow with a sedimenting suspension of micrometer-sized water droplets (i.e., fog). We imaged the accumulation of water and measured the evolution of the mean drop size. On smooth substrates, the deposition process was qualitatively similar to condensation, but differences in length scale revealed a transient regime not reported in condensation experiments. Based on previous simulation results, we defined a time-scale characterizing the transition to steady-state behavior. On textured substrates, square pillars promoted spatial ordering of accumulated drops. Furthermore, texture regulated drop growth: first enhancing coalescence when the mean drop size was smaller than the pillar, and then inhibiting coalescence when drops were comparable to the pillar size. This inhibition led to a monodisperse drop regime, in which drop sizes varied by less than 5%. When these monodisperse drops grew sufficiently large, they coalesced and could either remain suspended on pillars (i.e., Cassie-Baxter state) or wet the substrate (i.e., Wenzel state).     

Contact line dynamics in the late-stage coalescence of diethylene glycol drops

We investigated the contact line dynamics of a composite drop formed as a result of the coalescence during the condensation of two diethylene glycol (DEG) drops at -4 degrees C on a silicon surface. The composite drop relaxes exponentially toward equilibrium with a typical relaxation time, tc, which depends on the equilibrium radius, R, of the composite drop. The value of tc is found to be in the range of 10-100 s for R approximately 1-4 microm. The relaxation dynamics is found to be larger by 6 orders of magnitude than that predicted by bulk hydrodynamics because of high dissipation in the contact line vicinity. Similar to low viscous liquids (water), this high dissipation can be attributed to an Arrhenius factor resulting from the phase change in the contact line vicinity and to the influence of surface defects that pin the contact line.     

Rheo-optical determination of the interfacial tension in a dispersed blend

In this work, we present two novel methods to determine the interfacial tension of a disperse polymer blend through rheo-optical measurements of flow-induced single drop distortions. A counter-rotating shearing device with transparent plates is used to measure drop distortions. The cell geometry allows for a top view of the deforming drop, i.e., along the velocity gradient direction. Such a view is the only possible option for all currently available commercial rheo-optical instruments. Two different quantities are monitored, namely, the drop axis along the vorticity direction, and the rotation period of the drop surface. We use drops of a polyacrilamide aqueous solution (a shear thinning liquid) immersed in a polyisobutene matrix. Experimental results are interpreted in terms of theories for Newtonian liquids, where the relevant parameter is the Capillary number. If an appropriate viscosity ratio is chosen, that accounts for the shear thinning behaviour of the drop phase, good agreement is found between measurements and theoretical predictions. As a result, a robust estimate of the blend interfacial tension, that makes use only of the information acquired from top view experiments, is obtained.     

Contact line dynamics in drop coalescence and spreading

The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.     

Spontaneous formation of an "antidrop"

We have observed, with great surprise, the spontaneous formation of a quite unusual drop. Because of its similarity to the antibubble [(a) Hughes, W.; Hughes, A. R. Nature 1932, 129 (3245), 59. (b) Skogen, N. Am. J. Phys. 1956, 24, 239. (c) Strong, C. L. Sci. Am. 1974, 230 (4), 116.], we describe our find as an "antidrop", a thin spherical shell of an aqueous salt solution, surrounded by an inner and outer organic liquid phase. Two of these antidrops, about 8 mm in diameter, are shown in the present paper resting on a bed of smaller conventional drops. Drops of this size do not normally appear so spherical, however the antidrop is a mere shell, and hence its geometry is dominated by the interfacial tension. We found these drops to be remarkably stable, given it was possible to reversibly deform the drops and even slice through a drop with a glass rod to produce two antidrops. Ultimately, after some finite time period, the antidrops simply disintegrated into clouds of tiny droplets of the aqueous salt solution because of the drainage and concomitant rupturing of the liquid comprising their thin spherical shells.     

Total Gaussian curvature,drop shapes and the range of applicability of drop shape techniques

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.     

A unique behavior of water drops induced by low-density polyethylene surface with a sharp wettability transition

A low-density polyethylene (LDPE) surface with a sharp wettability gradient and high hysteresis was prepared, on which a unique behavior of water drops was found. The water contact angle of one water drop on the less hydrophobic region was larger than that on the more hydrophobic end, which was much different from the general phenomenon. The unique behavior is believed to be induced by the high hysteresis of the LDPE surface and the sharp change in wettability. The driving and hysteresis forces acting on the water drops were calculated and analyzed in detail. The reasons resulting to such a unique phenomenon were further explained.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

Primary electroviscous effect in a dilute suspension of charged mercury drops

The standard theory of the primary electroviscous effect in a dilute suspension of charged spherical rigid particles in an electrolyte solution (Watterson, I. G.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1115) is extended to cover the case of a dilute suspension of charged mercury drops of viscosity eta(d). A general expression for the effective viscosity or the electroviscous coefficient p of the suspension is derived. This expression tends to that for the case of rigid particles in the limit of eta(d) --> infinity. We also derive an approximate analytical viscosity expressions applicable to mercury drops carrying low zeta potentials at arbitrary kappaa (where kappa is the Debye-Hückel parameter and a is the drop radius) and to mercury drops as well as rigid spheres with arbitrary zeta potentials at large kappaa. It is shown that the large-kappaa expression of p for rigid particles predicts a maximum when plotted as a function of zeta potential. This result for rigid particles agrees with the exact numerical results of Watterson and White. It is also shown that in the limit of high zeta potential the effective viscosity of a suspension of mercury drops tends to that of uncharged rigid spheres given by Einstein's formula (Einstein, A. Ann. Phys. 1906, 19, 289), whereas in the opposite limit of low zeta potential the effective viscosity approaches that of a suspension of uncharged liquid drops derived by Taylor (Taylor, G. I. Proc. R. Soc. London, Ser. A 1932, 138, 41).