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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 iii 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 iv 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. |