This force is due to the E-field inducing dipoles in the particles, and the dipoles subsequently interacting with the gradient of the field. Particle dielectrophoresis has been widely utilized to control the positioning and motion of particles -in the case of positive dielectrophoresis, the particles are attracted to regions of higher field intensity. This is typical of highly polarizable particles, such as metallic or other conducting particles. In the above equation, 𝜀𝜀 𝑚𝑚 refers to the permittivity of the medium, r refers to the radius of the particle (which is approximated as a sphere) and 𝑅𝑅𝑅𝑅|𝛼𝛼| refers to the real part of the Clausius-Mosotti function, which represents the effective polarizability of the particle and is approximated by