Surface tension difference

Concerning function integration, for example, micro-flow membrane reactors can exhibit similar process intensification, as shown already for their large-scale counterparts [75]. Separation columns for proteomics, immobilizing enzymes, utilize the large surface-to-volume ratios. Surface tension differences can guide and transport liquids selectively. 

A current maximum of the first kind has the form of a sharp, straight line which starts to form just before the main polarographic wave (curve a in Figure 6.32). Such a maximum can be considerably larger than the wave itself, although it will usually drop suddenly back to the normal wave. Maxima of the first kind are caused by convective effects, as electrolyte flows past the surface of the mercury drop, resulting from surface tension differences at various points on the surface of the drop. 

Solution The surface tension of liquid naphthalene (1) is greater than that of solid naphthalene (3). Therefore A312 is expected to be negative for all systems having 7 values greater than 7.,. This is the case for the first six compounds listed in Table 10.6. Therefore these substances are expected to display rejection by the solidification front. This is indeed observed for five of the six cases. The case of nylon-6,12, which deviates from the predicted behavior, is best understood by examining the product (73s - 711/2)(72/2 - y]12)- Values of this product for the various systems considered are listed in Table 10.6. The factor arising from the solid-liquid (3-1) naphthalene has the constant value -0.0186 for all cases, but differs when various solids are used as component 2. For nylon-6,12, the second factor becomes -0.0022, and the product of the two, 0.41 10 4 mJ m 2, is the smallest of all such products listed in the table. As the surface tension difference decreases, the sensitivity of the behavior to variations in d0 increases. ... 

Isotherms of surface tension Ao(C) which characterise the decrease in a at the surfactant solution/air interface, are plotted as a function of surfactant concentration. Conventional techniques for a measurement are employed. However, these isotherms are not always sufficiently reliable, since these techniques offer poor accuracy and occasionally the values measured are non-equilibrium. For that reason data on surface tension differ considerably [e.g. 361,362],... 

When surface tension differences appear or are produced between some points or some small regions of an interface, the flow produced is called the Marangoni flow or flow with Marangoni effect. The Marangoni number, used to characterize the flow shown on Fig. 6.9, is a combination of the Reynolds number, the Weber number and the Schmidt number ... 

So-8X Aa Ay Ap AA (8o,xi 8ijXi) 2.2.3 local 8(x) slope 2.2.3 difference of segmental polarizabilities of two species 2.2.2 surface tension difference of pure blend components 3.1.2.2 difference of chemical potentials of species (pA-pB) 2.1 difference of Hamaker constant of species 3.1.2.1 ... 

A surface energy difference Afs and (a surface tension difference Ay) between two pure blend components may be evaluated based on a (-dfs/d( >)s vs (]>s relation calculated for measured segregation isotherm data ... 

Fig. 23. The relative surface tension difference -Ay/y(T) between components of six poly-olefinic blends grouped in three microstructurally identical pairs Xj/x2 (x1>x2) 66/52 (Q, ), 86/75 (A, ) and 75/66 (V, Y). Open and solid symbols correspond to blends with deu-terated more (x,) and less (x2) branched components, respectively. Large and small symbols correspond to previously determined whole segregation isotherms and singular surface excess data, respectively [16,120,145]. y(T) is given by Eq. (45) for polyethylene. Solid lines denote average values for each blend at Tref=100 °C (thick bar)...

In Fig. IB, the VLS process is illustrated. At reaction temperatures exceeding the eutectic. Si vapor dissolves in the Au seed to form a liquid alloy droplet. As more gaseous Si dissolves in the alloy, the droplet becomes supersaturated, and Si crystallizes on the droplet surface. The shape of the droplet interface and the surface tension difference between the liquid alloy and the solid semiconductor promote crystallization in one direction. In many cases, the liquid alloy droplet displaces off the surface and rides on the top of the vertically growing whisker—crystallization continues to occur at the liquid-solid interface as the metal seed is continuously fed with Si from the gas phase. 

Values of Yq are often taken to be the surface tension of the pure components, Y and have also been obtained by iterative procedures. Figure 4a shows a typical plot of Y as a function of x for a binary slag and the individual x Yi contributions have also been included. These methods work well for certain slag mixtures but break down when surface-active constituents, such as P205 are present. These components migrate preferentially to the surface and cause a sharp decrease in the surface tension and consequently only very small concentrations are required to cause an appreciable decrease in Y. Thus some unreported or undetected impurity could have a marked effect on the surface tension of the slag and thereby produce an apparent error in the value estimated by the model. In this respect surface tension differs from all the other physical properties which are essentially bulk properties. 

Based on such tables, it is possible to check the purity of a surfactant solution. The use of such tables requires many calculations and, therefore, their use is not very convenient. Starting from such tables, an easy relation could be derived which is very simple to use. This relation is derived under the conditions c, /Ul, =1 and =65mN/m and calculates the time t,j necessary to reach a surface tension difference... 

To decide whether a surfactant is surface-chemically pure or not, the following steps have to be made. First the characteristic time t j of Eq. (5.9) is calculated and then, the surface tension difference Ay (t ) = Y ad (tad) Yd (tad) at c, = aLi is measured. If the condition of Eq. (5.8) is fulfilled the solution is surface-chemically pure. 

At first the surface tension gradient is estimated by the ratio of the surface tension difference between y and y (r ) over a characteristic length, equal to the bubble radius. This uncertainty can be bypassed after the elaboration of a stagnant cap theory for high Reynolds number. In the... 

From the thermodynamical point of view the formation of dissipative structures is entropy driven as intensively explained by Prigogine Glansdorf (1971). The criteria for surface instabilities due to mass transfer across a liquid interface were evaluated by Stemling Scriven (1959). The typical Marangoni instability starts on surfactant concentration or temperature differences between two phases. Surface tension differences along the surface are... 

Surface self-diffusion is the two-dimensional analogue of the Brownian motion of molecules in a liquid bulk. Measurements of self-diffusion have to be performed in complete absence of any Marangoni flow caused by surface tension differences. Such experimental conditions are best established in an insoluble monolayer where one part consists of unlabelled and the other of radio-tracer labelled molecules. The movement of molecules within the surface monolayer can be now observed by using a Geiger-Miiller counter. There are possible effects of liquid convective flow in the sublayer which was discussed for example by Vollhardt et al. (1980a). With e special designed apparatus Vollhardt et al. (1980b) studied the self-difihision of different palmitic and stearic acid and stearyl alcohol and obtained self-diffusion coefficients between l-i-4 lO cm /s. 

Microphase separation and domain formation in block copolymers, which are the result of incompatibility of block chains, have been studied extensively (1,2). In addition to being incompatible, block chains in a copolymer generally have different thermal transition temperatures. The surface tensions of molten block chains also differ. When a crystalline block chain is incorporated into a block copolymer, it is expected that crystallization of the crystalline block chain causes considerable change in resultant morphology. Surface properties of a block copolymer and of its blend with a homopolymer should also be modified by the surface tension difference between block chains and the homopolymer. Since these factors determine the morphological features of a block copolymer both in bulk and at surface, a unified study of morphology, crystallization, and surface activity of any block copolymer is important to our understanding of its physical properties. 

Surface tension vs. temperature for PS and PTHF are shown in Figure 15. The data of Gains and Bender (17) on PS surface tensions (yGps) agree well with ours. However, our value for the surface tension of PTHF (yoPthf) is about 4.5 dynes/cm higher than Roe s value (18). The reason for this discrepancy is not clear. The y0i thf is always smaller than the yoPS by Ay = 3 dynes/cm, which is much smaller than the surface tension difference between the blocks of PS and polydimethylsiloxane. The time-dependent surface tensions of four blends (ST-PS, ST-PTHF, PS-PTHF, and PTHF-PS) were measured. To prepare the blends, the block or homopolymers were added in small amounts (0.3-1 wt %) to the homo-PS or PTHF. The mixture was completely dissolved in benzene, the solutions were quickly frozen by a dry ice-acetone mixture, and the samples were freeze dried. 

From these results, it is concluded that for the ST-PS blend, both the surface tension difference and the incompatibility between PTHF block and homo-PS assist in the adsorption of the PTHF block, which has lower surface tension than molten homo-PS. On the contrary, it is clear that incompatibility alone is not sufficient to force the PS block chain to the surface of the ST-PTHF blend against the increase of surface free energy. Therefore, quite an important conclusion has been reached from these studies, that is, an AB block copolymer, in which the surface tension difference between the two blocks AY = 7a - 7b is as small as 3 dynes/cm, is still sufficiently surface active when it is added in low concentration to a homopolymer corresponding to block A as long as yA > yB. 

As described earlier, Benard performed a number of careful interferometric measurements of the deformation of the liquid surface during convection, and correctly attributed the observed relief to the forces of surface tension. Benard s hexagonal cells were concave and were divided hy ridges, whose level was 1.7 p above the < 11 center when the layer of spermaceti was 1.20 mm thick and at a temperature of lOO C. Smaller thicknesses and lower temperatures yielded less pronounced ridges. Benard s thermal measurements placed the lateral temperature difference between the cell center and the cell partitions at approximately 1°C. In 1939, Hershey (HI) obtained an expression for the steady-state surface elevation due to surface tension differences caused by temperature differences on the surface. This expression reduces to... 

Surface tension differences may also develop within the paint itself during drying the solvent evaporates and this change in composition also alters the surface tension. Even slight surface tension differences lead to the formation of Benard cells which may result in visible surface defects such as orange peel and air draught sensitivity. 

In general, surface tension differences lead to material transport in the liquid paint film from the region of lower surface tension to that of higher surface tension. This movement is responsible for the above-mentioned defects. Other phenomena such as fat edges, picture framing, and ghosting can be explained in a similar way. 

Silicone additives (mainly organically modified methylalkyl polysiloxanes) lower the surface tension of coatings and minimize surface tension differences. 

---