#### Date of Award

Spring 1986

#### Document Type

Dissertation

#### Degree Name

Doctor of Engineering Science in Mechanical Engineering

#### Department

Mechanical Engineering

#### First Advisor

Rong-Yaw Chen

#### Second Advisor

Hans E. Pawel

#### Third Advisor

Roman I. Andrushkiw

#### Fourth Advisor

Jui Sheng Hsieh

#### Fifth Advisor

Robert P. Kirchner

#### Abstract

The deposition of suspensions for uniform flow in convergent channels under the combined influences of inertia, viscous and electrostatic image forces was studied theorectically. The fluid phase was assumed to be two-dimensional, steady, uniform, incompressible and laminar while the particle phase was assumed to be uniform, steady, dilute and with negligible gravity effects.

Since the image force equations for convergent channels have not been derived, it becomes one of the main purposes of this study to perform the derivation of the image force equations. The lengths of the channels were chosen in a way that the exit area is only 20% of the inlet.

The governing equations were solved numerically (with Runge-Kutta fourth order algorithm) using the trajectory method to calculate the deposition of the solid particles.

Derivation and analysis of the image force equations for convergent channels revealed that the images are confined on an Image Circle and that both X and Y components of image forces are experienced. For zero angle of convergence ( 6 = 0°), the image force equations reduce to that of the parallel-plate channel.

It was found that, for a given St (100 => St => 0) and Q (100 => Q => 0), the particle deposition is higher for higher convergent angles. At a fixed convergent angle (7.5° => 6 *=> *0°), particle deposition increases with both St and Q. When St and Q are both = 0, no deposition occurs. When St

It was also observed that, for a constant convergent angle and St, particle deposition increased with increasing Q. For high Q (Q => 10) even with moderate St (10 > St => 0.01), more than 80% of the deposition rate takes place within X < 2. For small St and small Q (St < 1 and Q < 0.01) the fraction of deposition near the entrance of the channel (X < 0.3) increased from 0 to about 0.1 and then remained relatively constant.

#### Recommended Citation

Hui, Kwok Wah, "Deposition of suspensions in convergent channels due to electrostatic image forces" (1986). *Dissertations*. 1211.

https://digitalcommons.njit.edu/dissertations/1211