الفهرس 
Chapter 1 . Historical background, main concepts and fundamental theories ofOnly 14 pages are availabe for public view
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Abstract
The study for growth of bubbles in two-phase (gas-liquid) flow is
important in several fields of sciences such as geophysics, chemical
engineering, physiology and other fields of sciences, which have important
applications in industries such as water purification instruments, food
industries, carbonated beverages, mixing, thermal ink-jet printers, many
medical applications like damaging tumors and shock wave lithotripsy.
Peristalsis is produced by successive waves of contraction in elastic, tubular
structures which push their fluid or fluid-like contents forward. The most
common industrial use is in pumping. In the urinary system, peristalsis is due
to involuntary muscular contractions of the ureteral wall which drives urine
from the kidneys to the bladder through the ureters. Mathematical analyses of
peristaltic flow with application to the ureter are presented. Also included are
results from an experimental peristalsis simulator. The aim of this thesis is to
study some cases of the growth of vapour/gas bubbles in two main different
dynamical systems. In each chapter, we obtain a relation between the bubble
wall radius and the time, this explicit relation contains some physical
parameters that affect on the growth process. The numerical implementation is
preceded with real and proposed values of the parameters to indicate the effects
of change of these parameters on the growth of the bubble via the produced
graphs, discussion of the results is presented and some concluded remarks
entail each chapter. Different analytical methods were used. In the problems;
which describe the growth of a vapour bubble in a viscous, superheated liquid,
the modified Plesset-Zwick method [57] was used, on the other hand in the
problem of the growth of a gas bubble in a non-Newtonian fluid under the
effect of shearing stress and magnetic field. The method of combined variables
[55, 56, 82] was used for solving the ordinary and partial differential equations
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such as, similarity parameter in chapter six. In the previous works, the study of
peristaltic motion in different shapes of tubes, the dynamic of bubbles not
considered in any textbook or any journal in case of peristaltic two-phase fluid
flow. In this thesis, we make consideration of growth and shrinking of bubbles
in the peristaltic two-phase flow. The physical problem, and then in the
proposed mathematical model with boundary conditions, includes the physical
meaning of bubble dynamic. This thesis consists of seven chapters.
Chapter one introduced a survey of historical background, the main concepts
and some fundamental theories and studies that describe the growth of bubbles
in different cases. It also includes a short survey on the theoretical and
experiential studying of peristaltic motion.
In Chapter two and Chapter three, we discuss the problem of the growth of
a vapour bubble in a vertical cylindrical tube between two-phase density under
the effect of peristaltic motion of long wavelength and low Reynolds number.
The mathematical model is formulated by mass, momentum, and heat
equations. The problem solved analytically to estimate the growth of vapour
bubbles, temperature and velocity distributions.
In Chapter four, we study the behavior of vapour bubble radius with the
peristaltic flow in a curved channel with the permeability porous medium. The
temperature distribution, velocity distribution, and the radius of bubble are
studied under the effect of some physical parameters, such as, amplitude ratio
e , density ratio , curvature parameter 1 k , and permeability of porous medium
0 k .
In Chapter five, the problem of growth of a gas bubble in the biotissues which
the concentration of the oversaturated, dissolved gas vary with time (unsteady
case) the diffusion equation [123], is solved analytically by the method
similarity parameter. The growth of gas bubble is affected by initial
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concentration difference Δ𝐶0, diffusivity of gas in tissue T D , the constant 𝐾𝑑 at
decompression, surface tension , initial void fraction 0 . The relation between
the growth of gas bubble Rt and time t is obtained from the definition of the
concentration distribution around a growing gas bubble in biotissues. The
problem is described by a system of three equations (mass, Rayleigh, and
concentration equations) .The relation between the growth of gas bubble Rt
and time t is studied under the effect of two different values of initial void
fraction 0 , critical bubble radius c R . The proposed model is compared with
Mohammadein and Mohammed model [123].
In Chapter six, the growth of gas bubble in a non-Newtonian fluid under the
effect of shearing stress rr is studied. The growth process is affected by shear
stress, coefficient of consistency f m , surface tension , and void fraction 0 in
order to derive the growth of a gas bubble between two-phase in non-
Newtonian fluids. The results that are obtained in a non-Newtonian fluid are
compared with Foster and Zuber [55] and Scriven theory [155].
Chapter seven, we investigate the effect of magnetic field B , and shearing
stress rr on a growing of gas bubble in a non-Newtonian fluid. The
mathematical model consists of mass and momentum equations. The governing
equations are analytically solved by using modified Plesset and Zwick method.
The growth process with different values of void fraction 0 , Jacob number *
a J ,
and the initial temperature difference 0 T are studied. The growth of gas bubble
in a non-Newtonian fluid under the effect of magnetic field and shearing stress
is compared with the previous works without the presence of magnetic field.
The behavior of gas bubble growth remains decreasing with the magnetic field
B and liquid electrical conductivity. Finally, the seven chapters are followed
by a general conclusions extracted from the thesis and some appendices.
Selected references and Arabic summary appear at the end of this thesis.