nicholas goble
DESCRIPTION
Equilibrium Shape of a Dielectric Droplet in an Electric FieldTRANSCRIPT
Equilibrium shape of a dielectric droplet in an electric field
Nicholas Goble - Illinois Wesleyan University
Dr. Philip Taylor - Case Western Reserve University
Research problem
droplet of dielectric fluid
Research problem
droplet of dielectric fluid uniform electric field
When do conical tips form?
Methods: Shape approximation
The shape of the droplet is approximated by .
Methods: Energy calculation
Total Energy = Surface Energy Electrostatic Energy+
Methods: Energy calculation
Total Energy = Surface Energy Electrostatic Energy+
Surface Energy Volume Surface Energy Density= x
Methods: Energy calculation
Total Energy = Surface Energy Electrostatic Energy+
Surface Energy Volume Surface Energy Density= x
Methods: Optimization
Results: Shape of Droplet
For a given dielectric constant and electric field, we are able to find the shape of the droplet.
Results: Development of Points
When pointed ends form, a1=0. To determine whether the development of points is gradual or sudden, we study how a1 changes with E0.
Results: Development of Points
As the bin count increases, the electric field at which the droplet forms points approach a real value.
Results: Development of Points
Results: Hysteresis
By changing the point at where we search for a minimum, we find different local minima, which indicates hysteresis.
Results: Critical Dielectric Constant
Our approach to this problem finds no critical dielectric constant below which no points develop. However, this may be due to the third-order polynomial approximation.
Results: Angle of Pointed Ends
The relationship between the electric field and the angle of the pointed ends is not linear.
Conclusion
Our methods have given us an expression for a dielectric droplet in an electric field.
Future goals include using a fourth-order polynomial in hopes of finding a critical dielectric constant.
We are also able to explore the angle of the points, hysteresis, and the formation of conical tips.
NSFCWRU Physics Department
Dr. Philip TaylorGareth Kafka
Acknowledgements: