In recent years, dielectrophoresis based microfluidics systems have been used to manipulate colloids, inert particles, and biological microparticles, such as red blood cells, white blood cells, platelets, cancer cells, bacteria, yeast, micro?organisms, proteins, DNA, etc. In the current study the governing electric potential equations have been solved in the presence of cell for the purpose of studying particle-electric field dielectrophoretic interaction. Immersed Interface Method (IIM) which is a modified finite difference method is used to solve the governing 2D elliptic electrostatic equations with irregular boundaries. A neutral particle polarizes under the application of an electric field and causes local nonuniformity in electrostatic potential distribution. So cells experience electric stresses on its surface. The electric stress on cell surface is calculated by Maxwell Stress Tensor (MST) on both sides of cell. DEP force is calculated by integrating electric stress on particle surface. In the present study calculated electric stresses is validated by DEP force calculated using EDM method and exact solution. we neglect other electrokinetic effects such as electrophoresis and electro-osmosis. Electrophoresis can be neglected if the particles are not charged. The effect of applied voltage, dielectric constants of cells and cells orientation on particle-particle interaction force has been studied.

Assuming arbitrary boundary and initial conditions, a transient thermo-elastic analysis of a rotating thick cylindrical pressure vessel made of functionally graded material (FGM) subjected to axisymmetric mechanical and transient thermal loads is presented. Time-dependent thermal and mechanical boundary conditions are assumed to act on the boundaries of the vessel. Material properties of the vessel are assumed to be graded in the radial direction according to a power law function. The Poisson’s ratio is assumed to be constant. Method of separation of variables has been used to analytically calculate the time dependent temperature distribution as a function of radial direction. In a case study, the distribution of radial and hoop stresses along the thickness is derived and plotted. In order to validate the model, the analytical results have been compared with finite element method modeling results presented in literature. Any arbitrary boundary and initial conditions can be handled using the equations derived in the present research. In order to investigate the inhomogeneity effect on time dependent stress distribution and displacements, values of the parameters have been set arbitrary in the present study. To the best of the authors’ knowledge, in previous researches, transient thermo-elastic analysis of thick cylindrical FGM pressure vessels is investigated by numerical methods, while in the present research, an exact solution is derived for the same problem.