#### Title

The Thermal Dielectrophoretic Force on a Dielectric Particle in Electric and Temperature Fields

#### Date of Award

2015

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Graduate Group

Mechanical Engineering & Applied Mechanics

#### First Advisor

Howard H. Hu

#### Abstract

Many microfluidic devices use an applied electric field to control and manipulate particles immersed in a fluid through the electrostatic force caused by dielectrophoresis (DEP). Additionally, electrothermal flow in the fluid can be caused by the effects of nonuniform temperature and the temperature-dependent electrical permittivity and conductivity material properties. We examine the effects on a particle immersed in a fluid subjected simultaneously to an electric and a nonuniform temperature field and find that the particle experiences an electrostatic force given by not only classical dielectrophoresis, but also an additional force, which we term thermal DEP. Assuming the change in the background electric field across the particle is small, and the relative change of temperature-dependent electric properties across the particle is also small, we develop a linearized model to solve the electric field analytically and integrate the Maxwell stress tensor to find an expression for the thermal DEP force. This thermal DEP force is proportional to the temperature gradient, the square of the electric field strength, and the particle's volume. We solve two special cases, one where the electric field and temperature gradient are aligned, and a second case where they are perpendicular to each other. The general case for an arbitrary angle can be found simply by a superposition of these two cases. We compute the fully-coupled system in COMSOL to determine a range of validity for our linearized model and show a practical way to superimpose the classical DEP and thermal DEP forces to find the total electrostatic force on the particle relative to the fluid. Due to the high electrical conductivity of common biological buffers, the thermal DEP force can play an important role when an electric field is used to control and manipulate cells or bacteria. The thermal DEP force may also modify the heat transfer rates in nucleate boiling applications, where large temperature gradients are present.

#### Recommended Citation

Shaparenko, Barukyah, "The Thermal Dielectrophoretic Force on a Dielectric Particle in Electric and Temperature Fields" (2015). *Publicly Accessible Penn Dissertations*. 1129.

https://repository.upenn.edu/edissertations/1129