Chemical reactions variational formulation

Drugs in solution formulations may be more susceptible to chemical reactions leading to degradation. The most common reactions are hydrolysis, oxidation, and reduction. Usually, the reaction rate or type is inLuenced by pH. For example, the hydrolysis of acetylsalicylic acid (aspirin) is pH dependent, and its pH-rate proLle shows a large and complex variation dfrls to four distinct mechanistic patterns (Alibrandi et al., 2001). Therefore, it is essential to monitor and understand the chemical stability of the drug in pH-adjusted formulations. 

Below, we describe tbe design formulation of isothermal batch reactors with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically by applying a numerical technique such as the Runge-Kutta method, but, in some simple cases, analytical solutions are obtained. Note that, for isothermal operations, we do not have to consider the effect of temperature variation, and we use the energy balance equation to determine tbe dimensionless heat-transfer number, HTN, required to maintain the reactor isothermal. 

In addition to an external variation of the mole numbers by a transfer of molecules across the boundary of the system, there may also be an internal variation due to chemical reactions. Quite generally, a chemical reaction can be formulated as... 

A variational formulation of the dynamics of systems of chemical reactions is presented which utilizes a Rayleigh dissipation function to extend the Lagrangian approach to conservative systems to dissipative systems [l]. The formulation is valid arbitrarily far from equilibrium and is based on macroscopic, deterministic chemical kinetics. It thus stands in contrast to variational principles for dissipative systems which are based on studies of fluctuations and are restricted to the near equilibrium regime [z] or, far from equilibrium, to the vicinity of stable stationary states [3]. 

Many adhesive types can, by alteration of the precise chemistry of the basic polymer or by changing the formulation by adding catalysts or accelerators, show a very wide variation in the time required to achieve load-bearing strength. Additionally, where curing depends on a chemical reaction rather than mere loss of solvent or crystallization, it can be greatly hastened by an increase of temperature. 

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