scholarly journals Inter-Bubble Interactions in Ultrasonically Excited Microbubble Clusters

2021 ◽  
Author(s):  
Hossein Haghi ◽  
Michael C. Kolios
Keyword(s):  
Differential Equations ◽  
Collective Behavior ◽  
Pressure Waves ◽  
Theoretical Studies ◽  
Bubble Interactions ◽  
Coupled Differential Equations ◽  
Large Clusters

Microbubbles (MBs) have been utilized in a variety of applications ranging from medicine to chemistry. There have been extensive studies on many aspects of microbubble dynamics. The majority of previous theoretical studies examine the oscillations of single microbubbles. In most applications multiple microbubbles form clusters. Oscillating microbubbles generate secondary pressure waves in the medium which have been shown to modify the dynamics of neighboring MBs. Large microbubble clusters have not been studied due to the complexity of solving many coupled differential equations governing the dynamics of a large number of microbubbles. This work expands on previous works conducted on the study of multiple bubble interactions. Two approaches are introduced to simulate large clusters. Inter-bubble interactions are classified and used to explain and predict collective behavior within large polydisperse clusters. This work shows that even identical MBs within a monodisperse cluster do not necessarily exhibit identical behavior.

scholarly journals Inter-Bubble Interactions in Ultrasonically Excited Microbubble Clusters

2021 ◽  
Author(s):  
Hossein Haghi ◽  
Michael C. Kolios
Keyword(s):  
Differential Equations ◽  
Collective Behavior ◽  
Pressure Waves ◽  
Theoretical Studies ◽  
Bubble Interactions ◽  
Coupled Differential Equations ◽  
Large Clusters

Microbubbles (MBs) have been utilized in a variety of applications ranging from medicine to chemistry. There have been extensive studies on many aspects of microbubble dynamics. The majority of previous theoretical studies examine the oscillations of single microbubbles. In most applications multiple microbubbles form clusters. Oscillating microbubbles generate secondary pressure waves in the medium which have been shown to modify the dynamics of neighboring MBs. Large microbubble clusters have not been studied due to the complexity of solving many coupled differential equations governing the dynamics of a large number of microbubbles. This work expands on previous works conducted on the study of multiple bubble interactions. Two approaches are introduced to simulate large clusters. Inter-bubble interactions are classified and used to explain and predict collective behavior within large polydisperse clusters. This work shows that even identical MBs within a monodisperse cluster do not necessarily exhibit identical behavior.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

Nonlinear stationary whistler waves and whistler solitons (oscillitons). Exact solutions

2003 ◽  
Vol 69 (4) ◽  
pp. 305-330 ◽  
Author(s):  
E. DUBININ ◽  
K. SAUER ◽  
J. F. MCKENZIE
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Wave Packets ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Transverse Motion ◽  
System Of Nonlinear Equations ◽  
Whistler Waves ◽  
Coupled Differential Equations ◽  
Consistent Manner

A fully nonlinear theory for stationary whistler waves propagating parallel to the ambient magnetic field in a cold plasma has been developed. It is shown that in the wave frame proton dynamics must be included in a self-consistent manner. The complete system of nonlinear equations can be reduced to two coupled differential equations for the transverse electron or proton speed and its phase, and these possess a phase-portrait integral which provides the main features of the dynamics of the system. Exact analytical solutions are found in the approximation of ‘small’ (but nonlinear) amplitudes. A soliton-type solution with a core filled by smaller-scale oscillations (called ‘oscillitons’) is found. The dependence of the soliton amplitude on the Alfvén Mach number, and the critical soliton strength above which smooth soliton solutions cannot be constructed is also found. Another interesting class of solutions consisting of a sequence of wave packets exists and is invoked to explain observations of coherent wave emissions (e.g. ‘lion roars’) in space plasmas. Oscillitons and periodic wave packets propagating obliquely to the magnetic field also exist although in this case the system becomes much more complicated, being described by four coupled differential equations for the amplitudes and phases of the transverse motion of the electrons and protons.

Solvability of the Caldeira–Leggett model

2020 ◽  
Vol 98 (7) ◽  
pp. 683-688
Author(s):  
Smail Bougouffa ◽  
Lazhar Bougoffa
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Wigner Distribution ◽  
Partial Differential ◽  
Coupled Differential Equations

In this paper, we illustrate the use of the method of the characteristics in various dissipative models of a single harmonic oscillator. The master equation governing the process can be transformed to a partial differential equation on the Wigner distribution, which in turn can be split to a system of coupled differential equations. We present a useful technique that can be used to separate the system without increasing the order and then the solutions can be obtained. The obtained solutions are used to calculate the average of energy observable of the system. This procedure can be extended to solve some other complex similar problems.

Investigation of photoionization and photodissociation of an oxygen molecule by the method of coupled differential equations

2007 ◽  
Vol 102 (3) ◽  
pp. 318-329 ◽  
Author(s):  
Ph. V. Demekhin ◽  
D. V. Omel’yanenko ◽  
B. M. Lagutin ◽  
V. L. Sukhorukov ◽  
L. Werner ◽  
...  
Keyword(s):  
Differential Equations ◽  
Oxygen Molecule ◽  
Coupled Differential Equations
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