Physico-Chemical Aspect of the Dyeing Process:Physico-chemical aspect of the dyeing process is one kind of system or way which shows how to a dye penetrates or enter into the fiber. It also describes how many process and time a dye molecules follow to enter completely onto the fiber. 

Successive Stage in the Dyeing:   Dye dispersed in the dye bath 

↓↑(Convective diffusion) Dye in the diffusion layer(boundary layer) 

↓↑ (Molecular diffusion) Dye in the electrical double layer 

↓↑ (Adsorption) Dye absorbed on the fiber surface 

↓↑ (Diffusion) Dye diffused in the fiber 

↓↑ (Fixation) Dye physically or chemically bond in the fiber

The dyeing process is essentially a distribution process. The dye is distributed over at least two phase systems, the dye bath and textile materials. When equilibrium dyeing is reached, the following subsidiary equilibrium is established. 

1. Dye Dispersed in the Dye Bath:Most of the dyes in solution are in molecular and partially ionized state or exist in the form of ionic micells. 

2. Dye in the Diffusion Layer: When a substrate is brought into a dye bath, a concentration gradient is created which will-make the dye molecules move or diffuse to the fiber. The dye which approaches the fiber surface must eventually diffuse through a thin liquid layer, the so-called diffusion layer, towards or onto the fiber surface. 

3. Dye in the Electrical Double Layer: All textile fibers when immersed in water or aqueous solution, acquire an electrical potential after referred to as Beta potential. At the fiber surface the dye molecules must pass the electrical double layer, consists of non-solvated anions(mostly) and solvated cat ions. These positive and negative ions try to approach the fiber surface as close as possible. This layer is about 1nm thin. 

4. Dye Absorbed on the Fiber Surface: The dye molecules reach the fiber surface ( and the first layer of the fiber ). This dye take-up at the fiber surface (absorption) occurs very rapidly and leads to a reduction of dye molecules in the immediate vicinity of this surface. 

5. Dye Diffused in the Fiber: 

After absorption, dye diffused in the fiber. Owing to the high temperature , there is always an abundance of dye stuff molecules in the vicinity of the fiber and agitation has little effect upon the time of half dyeing. 

6. Dye Physically or Chemically Bond in the Fiber: The last step of dyeing is fixation. In case of reactive dyes, the fixation is one-way. Because here dye molecules become attached to the fiber polymer by strong co-valent bonds. In case of all other dyes this fixation is two ways. Because they are fixed with fiber by weak hydrogen or salt linkage. 

The following factors are responsible for the anchoring of the dye molecules to the fiber:  

1. Salt linkage/ionic bonds for protein fibers.2. Co-ordination linkage3. Hydrogen bonds4. Co-valent bonds ; for cellulose fibers5. Physical forces6. Dispersion forces

Read more: http://textilelearner.blogspot.com/2012/03/theory-of-dyeing-stagesteps-of-dyeing.html#ixzz46uv2vxV5