# Mass Transfer: Concentration, Velocity, and Diffusion Flux

## Mass transfer process

### Mass transfer definition

Mass transfer phenomena are ubiquitous, for example, in the process of drying clothes in life, water evaporates into still air; in industrial chemical environments, there are a large number of mass transfer phenomena such as drying, humidification, absorption, and separation. Mass transfer is an important part of transport phenomena. In a mixture containing two or more components, if there is a concentration gradient, each component has a tendency to shift to a lower concentration, so as to weaken the uneven concentration.

• Mass transfer: The process of transferring components of a mixture from a high concentration to a low concentration under the action of a concentration gradient is called mass transfer.
• Mass transfer process: The process of material transfer from one phase to another phase interface in the form of diffusion is called the material transfer process, referred to as the mass transfer process.

Similar to momentum transport and heat transport, concentration gradients are the driving force for mass transfer.

### How to achieve

Mass transfer can be achieved by the random motion of particles in a stationary fluid, or it can be transferred from one location to another by combining with the dynamic characteristics of the fluid. These two different mass transfer methods are molecular mass transfer (or molecular diffusion) and convective mass transfer, which are similar to heat conduction and convective heat transfer in heat transfer, respectively.

## Concentration, Velocity, and Diffusion Flux

### Concentration

For different states of matter and systems, there are various representation methods and definitions of concentration. The amount of a substance is generally measured by mass and the amount of the substance (molar mass). Corresponding to different measurement standards, the concentration expression also has different definitions. In addition to the mass fraction and mole fraction that we are familiar with, there are mass concentration and substance concentration.
For gases, there is also a pressure-based representation, that is, partial pressure.

## Speed

It is generally believed that the speed is the speed under a certain reference system, and the speed is different in different reference systems. Therefore, the speed of fluid motion is also the speed relative to the reference system, and the diffusion flux is also the flux relative to the selected reference system.

### Flux

Similar to momentum transport and heat transport, defining the quantity of a substance passing through a unit area perpendicular to the concentration per unit of time is called flux. The flux vector of any component can be expressed by the product of its concentration and its velocity, and the direction is consistent with the velocity. Because the concentration is divided into the mass concentration and the amount concentration of the substance, the velocity of the component is also different due to the difference in the reference system. Therefore, the flux of the component also has different definitions.

## Fundamental laws of mass transfer

In essence, molecular mass transfer is caused by the random motion of microscopic particles of objects. When there is a concentration difference, the movement of the high-concentration particles destroys the equilibrium state and causes the directional movement of the particles, prompting the particles to move from the place with high concentration to the place with low concentration to achieve the same concentration, thus completing the mass transfer. The fundamental physical law describing molecular mass transfer is Fick’s first law, which is similar to Fourier’s law describing heat conduction.

Convective mass transfer is the mass transfer phenomenon that occurs between a moving fluid and a solid surface or between two immiscible moving fluids. The rate of convective mass transfer is not only related to the transport properties, but also closely related to the dynamic characteristics of the moving fluid.

## Classification of mass transfer

According to the different phase states, it can be divided into two types: fluid-phase mass transfer and fluid-solid-phase mass transfer.

### Mass transfer process between fluid phases

Gas phase-liquid phase, including unit operations such as gas absorption and liquid distillation. When gas is absorbed, the solubility of each component in the gas mixture is different in the liquid solvent, and other mixtures are contacted with the liquid solvent so that the substances that are easily soluble in the solvent are transferred from the gas phase to the liquid phase to separate the gas mixture.
Liquid distillation is based on the volatility of each component in the liquid mixture, heating to vaporize the component with a low boiling point, so as to achieve the purpose of separation.
Liquid-liquid phase, this type of mass transfer process includes operations such as liquid-liquid extraction. When a selective solvent is added to a homogeneous liquid mixture, the system forms two liquid phases. Because the solubility of each component in the original solution is different in the solvent, they will be distributed between the two liquid phases, that is, the interphase mass transfer process occurs, which is commonly referred to as liquid-liquid extraction.

### Mass transfer process between fluid and solid phases

Gas phase-solid phase, this type of mass transfer process includes solid drying, gas adsorption, and other operations. Solids containing water or other solvents (collectively referred to as moisture) are in contact with relatively dry hot gas, and the heated moisture is vaporized and leaves the solid, and enters the gas phase, thereby removing the moisture. This is the drying of the solid. During the drying process, the substance is transferred from the solid phase to the gas phase.

Liquid phase-solid phase, including liquid crystallization, solid leaching (also called solid-liquid extraction), liquid adsorption, ion exchange, and other unit operations.

When a supersaturated solution containing a certain substance is in contact with the solid phase of the same substance, its molecules will diffuse through the solution to reach the surface of the solid phase and precipitate out to make the solid grow up, which is crystallization. Solid leaching is the operation of extracting soluble components in solid raw materials by using liquid solvents. Liquid adsorption is an operation in which a solid-liquid two-phase contact makes one or some elements in the liquid phase diffuse to the surface of the solid phase and be adsorbed. Ion exchange is exchanging cations or anions in solution with the same ions on a solid phase called an ion exchanger.

## Mass transfer characteristics of supercritical CO2 fluid

### What is supercritical CO2 fluid?

Supercritical CO2 fluid refers to a compressible high-density fluid in a state above the critical temperature and critical pressure (called critical point), which is the fourth state other than the three states of gas, liquid, and solid. The space force is very small, similar to gas, but the density is very high, close to drinking, so it has the dual properties of gas and liquid between gas and liquid and has high solubility of liquid and high fluidity of gas at the same time. Compared with ordinary liquid solvents, the mass transfer rate is higher, and the diffusion coefficient is between liquid and gas. It has better permeability and no interphase effect, so it helps to improve extraction efficiency and greatly saves energy.

### Mass transfer characteristics of supercritical CO2 fluid

The physical and chemical properties of supercritical CO2 are quite different from those of liquids and gases in a noncritical state. Since density is the solubility, viscosity is fluid resistance, and diffusion coefficient is the main parameter of mass transfer rate, the special properties of supercritical CO2 determine the supercritical CO2 extraction technology has a series of important features.

#### Four characteristics of supercritical CO2 fluid

• The viscosity of supercritical CO2 is one percent of that of liquid, and the self-diffusion coefficient is 100 times that of liquid, so it has good mass transfer characteristics, which can greatly shorten the time required for phase equilibrium, and is an ideal medium for efficient mass transfer;
• It has a much faster rate of dissolving solutes than liquids, and has a much greater dissolving and carrying capacity for solid substances than gases;
• It has unusually large compressibility, and near the critical point, small changes in pressure and temperature will cause great changes in the density of CO2, so the solubility of CO2 can be adjusted by simply changing the temperature or pressure of the system to increase the CO2 Extraction selectivity;
• CO2 and dissolved products are separated by reducing the pressure of the system, eliminating the need to eliminate solvents.