Noyes-Whitney equations

This dissolution process can be considered to be diffusion-layer controlled. This is best explained by considering the rate of diffusion from the solid surface to the bulk solution through an unstirred liquid film as the rate-determining step. This dissolution process at steady state is described by the Noyes-Whitney equation ... 

The relevance of particle size to solid dosage formulations has been determined by a number of individuals [54,190-196], As is illustrated in Table 13, particle size affects the solid dosage formulation in numerous ways. For instance, particle size can have a profound effect on the dissolution of a formulation within the GI tract. This is most notably characterized by the Noyes-Whitney equation ... 

The higher thermodynamic activity, a, of the amorphous form compared to that of the crystalline form explains the higher initial dissolution rate per unit surface area (intrinsic dissolution rate, J) and the higher solubility, s, of the amorphous form compared to that of the crystalline form, according to a simple form of the Noyes-Whitney equation [15],... 

Also, hydrates are more soluble in water-miscible solvents than are the corresponding anhydrous forms. For example, the solubility of caffeine hydrate is lower than that of anhydrous caffeine in water but higher in ethanol. The maximum concentration seen may be due to the solubility of the anhydrous crystalline phase or due to a temporary steady state in which the rate of dissolution of the metastable anhydrous form and the rate of crystallization of the stable hydrate are equal. The decreasing concentration represents crystallization of the stable hydrate from a solution supersaturated with respect to it. If the maximum concentration of the solute in the dissolution experiment corresponds to the solubility, then the initial increase in concentration follows the Noyes-Whitney equation [15]. Van t Hoff plots of log solubility versus the reciprocal of temperature give linear relationships (Fig. 16). 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

Although the Noyes-Whitney equation has been used widely, it has been shown to be inadequate in modeling either S-shape experimental data or data with a steeper initial slope. Therefore, a more general function, based on the Weibull distribution [8], was proposed [9] and applied empirically and successfully to all types of dissolution curves [10] ... 

The dissolution of drugs has been described by the Noyes-Whitney equation as later modified by Nernst and Brunner [21, 22] ... 

Dissolution rate, or simply dissolution, refers to the rate at which a compound dissolves in a medium. The dissolution rate may be expressed by the Nernst-Brunner diffusion layer form of the Noyes-Whitney equation ... 

A nanosuspension is a submicron colloidal dispersion of pure drug particles, which possess a large surface area for enhanced dissolution. Dissolution rate, depending on surface area and other factors, can be represented by the Noyes-Whitney equation ... 

The Noyes-Whitney equation forthe dissolution of solids into a solvent (Noyes and Whitney, 1897) can be used to calculate the rate of drug concentrati iin Dease with time jjt... 

Increased saturation solubility and as a consequence of the Noyes-Whitney equation... 

For water-insoluble drugs, dissolution-controlled systems are an obvious choice for achieving sustained-release because of theirslow dissolution rate characteristics. Theoretically, the dissolution process at steady state can be described by the Noyes-Whitney equation as shown in Equation 22.7. The rate of dissolution of a compound is a function of surface area, saturation solubility, and diffusion layer thickness. Therefore, the rate of drug release can be manipulated by changing these parameter. 

Particle size is a key factor that influences drug dissolution rate. The smaller the particle size, the greater is the surface area for dissolution. The Noyes-Whitney equation describes the influence of surface area (S) and other factors on the dissolution rate ... 

From these gradient situations, the well-known Noyes-Whitney equation is given as... 

Since powder dissolution is influenced by changing surface area, it is not useful for delineating the effects of polymorphs, hydrates, and pharmaceutical salts. Instead, the intrinsic dissolution rate (IDR) is used. The IDR studies are conducted at a constant surface area and hence the dissolution rate observed is only a function of the intrinsic solubility of the drug. The Noyes-Whitney equation is modified for IDR, where the surface area is kept constant, and Equation (17) reduces to... 

The Noyes-Whitney equation shows that dissolution rate is influenced by the physicochemical characteristics of the drug, the formulation, and the solvent. In addition, the temperature of the medium also affects drug solubility and dissolution rate. 

Particle size reduction is typically used to enhance dissolution rate and/or bioavailability of APIs with limited in vivo solubility. Because the rate of dissolution of a particle is not only directly proportional to solubility, but also directly proportional to particle surface area (Pick s first law, Noyes-Whitney equation), increasing the surface area by reducing the average particle size increases dissolution rate. 

One important particle property affected by total surface area is solute dissolution, i.e., drug release rate. The drug release rate from a solid as described by the Noyes-Whitney equation is ... 

One equation, which you will find on page 22, is the Noyes-Whitney equation, which relates the surface area of a drug powder to its rate of solution. Some equations are phenomenological (that is they are derived as a result of experiment and observation) and do not necessarily have a deep theoretical base, so there is no need to be frightened of them. These are often intuitive equations, quite logical, as this one is ... 

So, by thinking of a process logically, one can almost formulate the equation. Noyes and Whitney did this for us, and precisely, although each equation operates only under certain boundary conditions. Nevertheless, from the Noyes-Whitney equation one can predict accurately what the effect on dissolution will be if the solubility of the dmg in the medium is increased, for example, by a change in pH. There are other equations for calculating the effect of pH on the equilibrium solubility, so this helps us get a quantitative view of the world. 

The Noyes-Whitney equation demonstrates that solubility is one of the main factors determining rate of solution. When the rate of solution is less than the rate of absorption, the solution process becomes rate limiting. Generally speaking, it should become so only when the dmg is of low solubility at the pH of the stomach and intestinal contents. The rate of absorption, the speed of onset of effect and... 

As the drug particle dissolves, a saturated solution (stagnant layer) is formed at the immediate surface around the particle. The dissolved dmg in the saturated solution gradually diffuses to the surrounding regions. The overall rate of drug dissolution may be described by the Noyes-Whitney equation which models drug dissolution in terms... 

The first step to drug absorption is dissolution of the solid drug into aqueous media. A concise relationship defining this process is the Noyes-Whitney equation ... 

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