Harkin s equation

Hagen-Poiseuille law, 72 Hagenbach coefficient, 74 correction, 73, 75 hanging drop, 183, 189 level viscometer, 80 Hare s apparatus, 12 Harkins s equation, 155 heat capacity of electrolyte solution, 225 content of electrolyte and non-electrolyte solutions, 225-6 content of vapour, 348 Heilborn s specific heat formula, 218 Henning s latent heat formula, 307 Herwig s method for density of saturated vapour, 325... 

Equation (468) is equivalent to Harkins s equation (Equation (460)). However, we must also consider the effect of the mutual saturation of the liquids on the equilibrium spreading coefficient, S /2. After the initial contact of oil and water molecules [or liquids (1) and (2)], they will become mutually saturated within each other after a while, so that yw will change to y o) and y0 to y)(W). At equilibrium, Equations (460) and (461) turn into... 

Multiple purpose systems also include multiple wall or layered microspheres. An interesting multilayer microcapsule (microsphere) was first prepared by Mathiowitz and Langer " in a single step process. The approach relies in on a modification of Harkin s equation for spreading equilibrium... 

For a three-component polymer blend in which polymer A is the matrix and polymers (or lower molar weight liquids) B and C are dispersed phases, the tendency of C to spontaneously spread around dispersed phase B can be expressed in terms of the interfacial tension between the components, using Harkin s equation [18, 19] ... 

In the following table are given the limiting values of A calculated from Milner s and v. Szyszkowski s equations by Langmuir and Harkins. 

The early kinetic model by Smith and Ewart was based on Harkin s mechanistic understanding of the batch process. The particle population balances were written for a stationary state assuming that the rate of formation of particles with n radicals equals the rate of their disappearance (see equation at the bottom of this page). Where / , is the rate of radical entry into a particle (m /sec) is the rate constant for radical exit (m/sec) S is the particle surface area (m ) ktp is the rate constant for bimolecular termination in the particles (m /sec) and o is the particle volume. According to Smith and Ewart three limiting cases can be identified ... 

Harkins and Livingston [12] have proposed a correction to Young s equation when the surface of the solid carries a film of the liquid s vapor. The surface energy of a solid surface that contains an adsorbed vapor layer (7sa) is less than that of a clean surface. This concept has practical significance because clean surfaces tend to adsorb the ambient vapors and oils and must therefore be protected prior to the application of adhesive. Harkins and... 

The surface tension may be quickly calculated from the weight of a falling drop, formed with the precautions described below, by the following equation and table, which embody the results of Harkins and Brown s measurements. The weight and volume or density of a number of drops are measured, and the radius of the tip from which the drop falls. F is... 

Equation (5) or (5b) is the highly important deduction of Harkins-Smith-Ewart theory. Its validity has been fully confirmed for many cases of polymerization (19). Furthermore, although it is difficult to determine the nvimber of particles, Np, accurately (19) this simple relationship has been used to determine the absolute value of the rate constant, kp, satisfactorily for the polymerization of butadiene and isoprene by Smith (20) and by Morton et al.(21). Conditions where the rate of polymerization is not proportional to the number of particles are where Trommsdorff s effect (22-24) or Gordon s unsteady state (25) principles apply. However, the existence of linear portions of the conversion-time plots proves the absence of these principles in this system. 

The primary thermodynamic consideration involved is that of welting or spreading. For the adhesive to achieve the molecular closeness to the substrate required for strong van der Waals forces to develop, it must wet the substrate. In order for this to happen, the spreading coefficient S (Harkins, 1941) as defined by the equation... 

More extensive and accurate data and additional calculations are necessary to obtain s , e , and from isotherm data over what is required to get the differential energy and entropy from the isosteric equation. The first complete calculation of ss, e and , as well as the differential quantities, has recently been made by Hill, Emmett, and Joyner (95). This paper shows in detail how the methods of this section can be applied in practice. Using heats of immersion, Harkins and Jura (96) made earlier equivalent calculations, but the relationship of their calculated quantities to the thermodynamic functions of the adsorbed molecules was not pointed out until recently by Jura and Hill (92). 

The antifoaming action can be rationalised [28] in terms of the balance between the entering coefficient E and the Harkins [29] spreading coefficient S, which are given by the following equations. 

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