Length-tension curve

Just as important as the maximum active force a muscle can exert at various lengths, is the rate at which the muscle shortens as a function of the force load, i.e., the force-velocity curve. Both the length-tension curve and the force-velocity curve vary according to the degree of activation of a muscle. The rate at which crossbridges cycle is an inverse function of the load force (Figure 4). 

Figure 1.16 Temperature dependence of the water/oil interfacial tension

A serious point is the neglect of surface tension and anisotropy in these derivations. In the experiments analyzed so far the relation VX const, seems to hold approximately, but what happens when the capillary anisotropy e goes to zero Numerically, tip-splitting occurs at lower velocities for smaller e. Most likely in a system with anisotropy e = 0 (and zero kinetic coefficient) the structures show seaweed patterns at velocities where the diffusion length is smaller than the short wavelength hmit of the neutral stability curve, as discussed in Sec. V B. 

What characterizes surfactants is their ability to adsorb onto surfaces and to modify the surface properties. At the gas/liquid interface this leads to a reduction in surface tension. Fig. 4.1 shows the dependence of surface tension on the concentration for different surfactant types [39]. It is obvious from this figure that the nonionic surfactants have a lower surface tension for the same alkyl chain length and concentration than the ionic surfactants. The second effect which can be seen from Fig. 4.1 is the discontinuity of the surface tension-concentration curves with a constant value for the surface tension above this point. The breakpoint of the curves can be correlated to the critical micelle concentration (cmc) above which the formation of micellar aggregates can be observed in the bulk phase. These micelles are characteristic for the ability of surfactants to solubilize hydrophobic substances in aqueous solution. So the concentration of surfactant in the washing liquor has at least to be right above the cmc. 

The uniformity of the particles as measured by the standard deviation for a normal probability curve was found to be a function of flow rate, nozzle size (better for smaller nozzles), nozzle length (decrease in nozzle length decreases uniformity), etc. A decrease in interfacial tension is insufficient to cause change in uniformity. 

For solutions of AEg with different distributions of hydrocarbon chain lengths, the Y log C curves appear to be different than mono-component system. The surface pressure at critical micelle concentration (iTcjic) AEg with a long hydrocarbon chain (C gEg) is Increased by adding the short AEg, but the effect is not significant if the hydrocarbon chain is in a wide distribution (i.g. coconut fatty radical) (Figure 2,3,4). As for the efficiency of surface tension reduction there is a synergestic effect for the mixed... 

Takahashi et al.67) prepared ionene-tetrahydrofuran-ionene (ITI) triblock copolymers and investigated their surface activities. Surface tension-concentration curves for salt-free aqueous solutions of ITI showed that the critical micelle concentration (CMC) decreased with increasing mole fraction of tetrahydrofuran units in the copolymer. This behavior is due to an increase in hydrophobicity. The adsorbance and the thickness of the adsorbed layer for various ITI at the air-water interface were measured by ellipsometry. The adsorbance was also estimated from the Gibbs adsorption equation extended to aqueous polyelectrolyte solutions. The measured and calculated adsorbances were of the same order of magnitude. The thickness of the adsorbed layer was almost equal to the contour length of the ionene blocks. The intramolecular electrostatic repulsion between charged groups in the ionene blocks is probably responsible for the full extension of the... 

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