Henry’s function

Ohshima [17] has derived the following simple approximate formula for Henry s function/(ka) with relative errors less than 1% ... 

Ohshima, H., A simple expression of Henry s function for the retardation effect in electrophoresis of spherical colloidal particles, J. Coll. Interf. ScL, 168, 269-271, 1994. 

The first term on the right-hand side of Equation (2.26) corresponds to an approximate Equation (2.10) for Henry s function (Equation (2.6)). Equation (2.26) excellently agreed with exact numerical results [15] especially for small Ka, in which region no simple analytic mobility formula is available other than Henry s equation (2.6). Thus Equation (2.26) is a considerable improvement of Henry s equation (2.8). Eor example, the relative error is less than 1% for < 7 at ka = 0.1 and for < 3 at ka = 1. 

Ohshima, H., Henry s function for electrophoresis of a cyhndrical colloidal particle, J. Colloid Interface Set, 180, 299, 1996. 

Here, p is defined as the electrophoretic mobility (particle velocity/ applied electric field) of a particle of radius a. C is the zeta potential, and q is the viscosity of the suspending solution./(A ), a) is Henry s function and depends on the Debye length (see Section 5.5.2). This variable represents the thickness of the electric double layer. 

In everyday measurements, estimates for Henry s function can be used to simplify analysis of the zeta potential. If the Debye length is small... 

In contrast, if the size of the electric double layer is large or the particles are small, then Henry s function tends to 2/3. This gives us the Huckel formula ... 

Zeta potential measurements are typically in the millivolt range, and a colloidal suspension with a zeta potential of less than 30 mV is usually considered stable, that is, the suspension will not aggregate spontaneously over a reasonable timescale. Of course, there are complications to this simple colloidal picture. Particles with complex charge distributions such as proteins or with an interesting surface topology (i.e., polymer brushes) may exhibit very different behavior compared to the ideal hard spherical colloid considered in this section. In these cases, a more detailed model for Henry s function is required. 

Eq. 6.3 with f(Kr) taking the value of either 3/2 for large partilces when Kr > 200, called the Smoluchowski equation, which was derived even earlier than Henry s function [20], or 1 for small particles when Kr <0.01, called the Hiickel equation, is still the most popular way to convert a mobility distribution to a zeta potential distribution. Electrophoretic mobility can also be presented by particle s surface charge density s [21]... 

In the present study we try to obtain the isotherm equation in the form of a sum of the three terms Langmuir s, Henry s and multilayer adsorption, because it is the most convenient and is easily physically interpreted but, using more a realistic assumption. Namely, we take the partition functions as in the case of the isotherm of d Arcy and Watt [20], but assume that the value of V for the multilayer adsorption appearing in the (5) is equal to the sum of the number of adsorbed water molecules on the Langmuir s and Henry s sites ... 

The solvophobic model has been used to deduce a functional form for a Henry s constant correlation based on molecular coimectivity index and polarizabiHty (42). Accurate predictions are reported over a span of seven log units in Henry s constant. A reHable solvophobic model of aqueous solubiHty has also been reported (45,46). 

Fiend s Constant. Henry s law for dilute concentrations of contaminants ia water is often appropriate for modeling vapor—Hquid equiHbrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of temperature (35—39,49). 

In the range of operating temperatures and compositions, the equilibrium relations are monotonic functions of temperature of the MSA. This is typically true. For instance, normally in gas absorption Henry s coefficient monotonically decreases as the temperature of the MSA is lowered while for stripping the gas-liquid distribution coefficient monotonically increases as the temperature of the stripping agent is increased. 

In general, gas solubilities are measured at constant temperature as a function of pressure. Permanent gases (gases with critical temperatures below room temperature) will not condense to form an additional liquid phase no matter how high the applied pressure. However, condensable gases (those with critical temperatures above room temperature) will condense to form a liquid phase when the vapor pressure is reached. The solubilities of many gases in normal liquids are quite low and can be adequately described at ambient pressure or below by Henry s law. The Henry s law constant is defined as... 

Carroll [82] discusses Henry s Law in detail and explains the limitations. This constant is a function of the solute-solvent pair and the temperature, but not the pres-... 

In Eq. (128), the superscript V stands for the vapor phase v2 is the partial molar volume of component 2 in the liquid phase y is the (unsym-metric) activity coefficient and Hffl is Henry s constant for solute 2 in solvent 1 at the (arbitrary) reference pressure Pr, all at the system temperature T. Simultaneous solution of Eqs. (126) and (128) gives the solubility (x2) of the gaseous component as a function of pressure P and solvent composition... 

Fugacity in Liquid Mixtures Raoult s Law and Henry s Law Each component in a liquid mixture has an equilibrium vapor pressure, and hence, a vapor fugacity. These fugacities are functions of the composition and the nature of the components, with the total vapor fugacity equal to the sum of the fugacities of the components, That is,... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

When Kh is a function of composition, the concept of overall mass transfer coefficient stops being useful. Instead, the overall resistance to mass transfer is divided between two him resistances, one for each phase. This is done by assuming that equilibrium is achieved at the interface. The equilibrium values are related by a function having the form of Henry s law ... 

The mass transfer equations, Equations (ll.l)-(ll.lO), remain valid when A, replaces A,. Equations (11.27) and (11.28) contain one independent variable, 2, and two dependent variables, ai and Ug. There are also two auxiliary variables, the interfacial compositions a and a. They can be determined using Equations (11.5) and (11.6) (with A, replacing A). The general case regards K/f in Equation (11.4) as a function of composition. When Henry s law applies throughout the composition range, overall coefficients can be used instead of the individual film coefficients. This allows immediate elimination of the interface compositions ... 

Rice CP, Chernyak SM, McConnell LL. 1997. Henry s law constants for pesticides measured as a function of temperature and salinity. J Agric Food Chem 45 2291-2298. 

In O Connell s paper, the plate efficiency is correlated with a function involving Henry s constant, the total pressure, and the solvent viscosity at the operating temperature. 

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