Inter-Bubble Interactions in Ultrasonically Excited Microbubble 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.

Inter-Bubble Interactions in Ultrasonically Excited Microbubble 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

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.

Solvability of the Caldeira–Leggett model

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.

Existence theory of fractional coupled differential equations via Ψ-Hilfer fractional derivative

In this paper, we analyze existence results for coupled differential equations via ψ- Hilfer fractional derivative. The proof relies on the Schaefer fixed point theorem.

Hybrid approach for treating the depolarization of the solar lines of the Ba ii, Ca ii, and Mg ii ions by collisions

ABSTRACT Isotropic collisions between atoms of hydrogen and solar ions emitting polarized light contribute to reducing the observed polarization (depolarization). The aim of this work is to apply a hybrid method in order to provide new collisional depolarization rates of the 2P1/2 and 2P3/2 states of the Mg ii, Ca ii, and Ba ii ions. The hybrid method proposed in this work takes into account the spin effects in the calculation of the interaction potential and in the treatment of the collision dynamics. We detect the region of the interaction potential that is of importance in the determination of the depolarization rates. We conclude that the best strategy is to combine semiclassical and quantum potentials in order to build the so-called hybrid potentials. The dynamics of collisions proposed in this work is based on coupled differential equations that take into account the effects of the spins of the Mg ii, Ca ii, and Ba ii ions and the spin of the hydrogen. Hybrid depolarization rates are then inferred by solving the dynamics of collisions and using hybrid potentials. Comparison with previous quantum and semiclassical rates is presented. Our results should be of use for interpreting solar spectropolarimetric observations and our method can be applied to other ions.