In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.
Molecular diffusion, often simply called diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules. The result of diffusion is a gradual mixing of material such that the distribution of molecules is uniform. Since the molecules are still in motion, but an equilibrium has been established, the result of molecular diffusion is called a "dynamic equilibrium". In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.
In continuum mechanics, the Péclet number is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of species or mass transfer, the Péclet number is the product of the Reynolds number and the Schmidt number. In the context of the thermal fluids, the thermal Péclet number is equivalent to the product of the Reynolds number and the Prandtl number.
In fluid mechanics, the Grashof number is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number.
The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate to the rate of diffusive mass transport, and is named in honor of Thomas Kilgore Sherwood.
The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler, who worked in the fields of chemical engineering, thermodynamics, and fluid dynamics. The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka.
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
The plug flow reactor model is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.
In physics and engineering, permeation is the penetration of a permeate through a solid. It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.
The Marangoni number (Ma) is, as usually defined, the dimensionless number that compares the rate of transport due to Marangoni flows, with the rate of transport of diffusion. The Marangoni effect is flow of a liquid due to gradients in the surface tension of the liquid. Diffusion is of whatever is creating the gradient in the surface tension. Thus as the Marangoni number compares flow and diffusion timescales it is a type of Péclet number.
Diffusivity, mass diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species. More accurately, the diffusion coefficient times the local concentration is the proportionality constant between the negative value of the mole fraction gradient and the molar flux. This distinction is especially significant in gaseous systems with strong temperature gradients. Diffusivity derives its definition from Fick's law and plays a role in numerous other equations of physical chemistry.
In electrochemistry, the Butler–Volmer equation, also known as Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction, considering that both a cathodic and an anodic reaction occur on the same electrode:
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds.
Diffusion is the net movement of anything generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing.
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e. at these conditions the adsorbate's partial pressure, , is related to the volume of it, V, adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule and an empty sorption site, S. This reaction yields an adsorbed species with an associated equilibrium constant :
The Maxwell–Stefan diffusion is a model for describing diffusion in multicomponent systems. The equations that describe these transport processes have been developed independently and in parallel by James Clerk Maxwell for dilute gases and Josef Stefan for liquids. The Maxwell–Stefan equation is
In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics, it places a heavy emphasis on the commonalities between the topics covered. Mass, momentum, and heat transport all share a very similar mathematical framework, and the parallels between them are exploited in the study of transport phenomena to draw deep mathematical connections that often provide very useful tools in the analysis of one field that are directly derived from the others.
The Thiele modulus was developed by Ernest Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939. Thiele reasoned that a large enough particle has a reaction rate so rapid that diffusion forces can only carry the product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would experience any reaction.
Equimolar counterdiffusion is an instance of molecular diffusion in a binary mixture, and occurs when equal numbers of molecules of the two substances are moving in opposite directions.
