Henry’s equation

The above result (Equations (47a)-(47c)) is known as Henry s equation. Two specific assumptions underlying its derivation should be pointed out ... 

It should also be noted that in the limit of kRs - 0, Equation (47a) reduces to the Hiickel equation, and in the limit of kRs - oo, it reduces to the Helmholtz-Smoluchowski equation. Thus the general theory confirms the idea introduced in connection with the discussion of Figure 12.1, that the amount of distortion of the field surrounding the particles will be totally different in the case of large and small particles. The two values of C in Equation (40) are a direct consequence of this difference. Figure 12.5a shows how the constant C varies with kRs (shown on a logarithmic scale) according to Henry s equation. 

We noted above that many systems of interest in colloid chemistry involve intermediate values of kRs, so Henry s equation fills an important gap. At the same time it explicitly introduces additional restrictions (a) low potentials and (b) undistorted double layers. A topic of consid-... 

What is Henry s equation, and what are the assumptions implicit in its derivation ... 

Henry [3] derived the mobility equations for spheres of radius a and an infinitely long cylinder of radius a, which are applicable for low ( and any value of Ka. Henry s equation for the electrophoretic mobility p of a spherical colloidal particle of radius a with a zeta potential C is expressed as ... 

Membrane phase concentration of component i in the feed side, Cg, can be calculated from its bulk concentration by Henry s equation (Equation 5.8) provided it is present in trace amount in the feed solution. For higher concentration of component i, Cg can be obtained from experimental sorption data. Membrane phase concentration on the permeate side of component i, i.e., Cpi may be neglected due to the low pressure the activity of the component in the downstream side is very low. Thus, Equation 5.28 can be readily solved to calculate the theoretical flux and diffusion coefficient of i or j component employing any of the above equations relating the diffusion coefficient and concentration. Equations 5.14 through 5.25 depending on its best matching with the experimental data. 

Henry s equation (2.6) assumes that is low, in which case the double layer remains spherically symmetrical during electrophoresis. For high zeta potentials, the double layer is no longer spherically symmetrical. This effect is called the relaxation elfect. Henry s equation (2.6) does not take into account the relaxation effect, and thus this equation is correct to the first order of Ohshima et al. [19] derived an accurate analytic mobility expression correct to order 1/ka in a symmetrical electrolyte of valence z and bulk concentration (number density) n with the relative error less than 1% for 10 < Ka < 00, which is... 

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. 

For rjd 00, Equation (2.34) reduces to Henry s equation (2.6) for a rigid sphere. Ohshima [33] has shown that Equation (2.34) is further approximated well by... 

Henry [25] was the first author who solved the problem for spheres of any radius (also for infinite cylinders), that is, of any Ka value, although for small zeta potentials. Restricting ourselves to the case of spheres, Henry s equation for nonconducting particles reads... 

Both are limiting cases of Henry s equation. Equation 5.78 has been widely employed however, it is valid only for large particles. For sufficiently small particles, Equation 5.79 holds, and for intermediate cases (which may be the greatest... 

Eq. (4) and (5) can only be valid if the reciprocal of Debye length (Kr)" is very high >100 or very low 1. If the zeta potential is not so high, e.g., smaller than 50 mV, Henry s equation should be used ... 

The simplest classical model to fit adsorption results consists of the equation of Langmuir [160] for localized adsorption and the equation of Henry for the nonlocaUzed case. In particular, Henry s equation may be written as... 

Water sorption in the polyethylene terephthalate can be described by Henry s equation ... 

Meastuements were performed at 20°C as a function of pH in the range of 3-10 by addition of 0.01 M HCl or 0.01 M NaOH using a Malvern Zetasizer Nano ZS. Microgel solutions with a concentration of 5 mg/mL were dialyzed in standard 1 mM KCl solution and measured in disposable polystyrene cuvettes. One hundred scans were made for each sample and the zeta potential was calculated using Henry s equation. Expert System software was used for data interpretation. 

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