**1.5 Diffusion coefficient**

The diffusion coefficient is one of the transport properties of gas, liquids. During the diffusion process, the particles migrate from high concentrations to low concentrations. The diffusion rate can be controlled by variations of external parameters such as temperature, concentration, external electromagnetic forces (electric and magnetic). Investigations of diffusion have different purposes in liquids, such as exploring the dynamical properties and understanding the microscopic phenomena. For the CDPs research direction, the investigations of diffusion motion for applying external fields such as electric and magnetic become a hot topic in current research. Different types of diffusion motion exist in dusty plasma regimes depends on temperature and forces. Diffusion also plays an essential role in exploring the dynamical properties (structure, waves, and instabilities) of many biological, physical, and chemical systems. The diffusion motion of dust particles in CDPs continues as one of the active research topics, an essential consequence of understanding the transport and dynamical properties [12, 29–33]. It is one of the primary sources to lose energy (stopping power) in CDPs. Therefore, we can easily understand the microscopic phenomena of particles in the different states [34]. An extensive amount of previous studies have been made to understand the diffusion motion in CDPs. Molecular dynamics simulations were performed and investigate the velocity autocorrelation function for 2D WCCDPs [12], Langevin dynamics simulation for 2D SCCDPs [35] and diffusion coefficient [36]. For the investigations of self-diffusion coefficient MD simulations were performed for 3D CDPs [30, 33, 37], one-component plasma [31] and ionic mixtures [32].

The main objective of the present book chapter is to give an overview of electrorheological (ER) fluids and ER-CDPs. We have computed the effect of the external applied uniaxial electric field on the velocity autocorrelation function and self-diffusion coefficient of 3D ER-CDPs using MD simulations over a wide range of input CDPs parameters.
