Analytical solution of the droplet breakup equation by the Adomian decomposition method

Hasseine, Abdelmalek; Bellagoun, A.; Bart, Hans‐Jörg

doi:10.1016/j.amc.2011.07.041

Cited by 10 publications

(10 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…are usually represented by an infinite series of the Adomian polynomials m A and m B , respectively, we set 6 and finally we get…”

Section: The Adomian Decomposition Methodsmentioning

confidence: 99%

“…For this particular case we proceed to the solution of Eq. [6] through Adomian decomposition method with respect to v instead of t.…”

Section: Case Study Iv: Simultaneous Growth and Nucleationmentioning

confidence: 99%

“…[6] is considered where 0 B and G are constant and the initial condition is assumed zero. For this particular case we proceed to the solution of Eq.…”

Section: Case Study Iv: Simultaneous Growth and Nucleationmentioning

confidence: 99%

See 2 more Smart Citations

Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Hasseine

Bart

2015

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

Please cite this article as: A. Hasseine, H.-J. Bart, Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes, Appl. Math. Modelling (2014), doi: http:// dx. AbstractThe dynamic behavior of particulate processes under the influence of the nonlinear aggregation term, nucleation, growth and breakup is studied. Analytic solutions are obtained from the integro-differential population balance equation governing the particle size distribution density function for special cases by the Adomian decomposition method (ADM) and are compared with other analytical solutions available in the literature. It avoids the difficulty numerical stability that often characterizes general numerical techniques in this area. It generates an infinite series which converges uniformly to the exact solution of the problem. For the case where there are no previous results a comparison between the present method and projection method which include collocation techniques is made.The results obtained indicate that the Adomian decomposition method is highly accurate, efficient and are useful for further work.

show abstract

“…are usually represented by an infinite series of the Adomian polynomials m A and m B , respectively, we set 6 and finally we get…”

Section: The Adomian Decomposition Methodsmentioning

confidence: 99%

“…For this particular case we proceed to the solution of Eq. [6] through Adomian decomposition method with respect to v instead of t.…”

Section: Case Study Iv: Simultaneous Growth and Nucleationmentioning

confidence: 99%

See 1 more Smart Citation

Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Hasseine

Bart

2015

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…where the Adomian polynomials 's are defined in (11). The MDM splits ( ) + ( ) into two parts; ( ) is written with 0 ( , ) and ( ) is written with 1 ( , ) as follows:…”

Section: General Complete Second-order Singular Nonlinear Pdesmentioning

confidence: 99%

“…MDM was first developed by Wazwaz and El-Seyed [1] who applied it to solve the ordinary differential equations (ODEs). Since then the MDM has been used for solving various equations in mathematics and physics [2][3][4], boundary value problems [5][6][7][8][9], various problems in engineering [10][11][12][13], and initial-value problems [14][15][16][17]. Adomian et al [14] solved the Lane-Emden equation using the MDM.…”

Section: Introductionmentioning

confidence: 99%

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

Dalir

2014

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first-and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

show abstract

Effect of Unsaturated Flow Modes on Partitioning Dynamics of Gravity‐Driven Flow at a Simple Fracture Intersection: Laboratory Study and Three‐Dimensional Smoothed Particle Hydrodynamics Simulations

Kordilla

Noffz

Dentz

et al. 2017

Water Resources Research

View full text Add to dashboard Cite

In this work, we study gravity‐driven flow of water in the presence of air on a synthetic surface intersected by a horizontal fracture and investigate the importance of droplet and rivulet flow modes on the partitioning behavior at the fracture intersection. We present laboratory experiments, three‐dimensional smoothed particle hydrodynamics (SPH) simulations using a heavily parallelized code, and a theoretical analysis. The flow‐rate‐dependent mode switching from droplets to rivulets is observed in experiments and reproduced by the SPH model, and the transition ranges agree in SPH simulations and laboratory experiments. We show that flow modes heavily influence the “bypass” behavior of water flowing along a fracture junction. Flows favoring the formation of droplets exhibit a much stronger bypass capacity compared to rivulet flows, where nearly the whole fluid mass is initially stored within the horizontal fracture. The effect of fluid buffering within the horizontal fracture is presented in terms of dimensionless fracture inflow so that characteristic scaling regimes can be recovered. For both cases (rivulets and droplets), the flow within the horizontal fracture transitions into a Washburn regime until a critical threshold is reached and the bypass efficiency increases. For rivulet flows, the initial filling of the horizontal fracture is described by classical plug flow. Meanwhile, for droplet flows, a size‐dependent partitioning behavior is observed, and the filling of the fracture takes longer. For the case of rivulet flow, we provide an analytical solution that demonstrates the existence of classical Washburn flow within the horizontal fracture.

show abstract

Analytical solution of the droplet breakup equation by the Adomian decomposition method

Cited by 10 publications

References 32 publications

Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

Effect of Unsaturated Flow Modes on Partitioning Dynamics of Gravity‐Driven Flow at a Simple Fracture Intersection: Laboratory Study and Three‐Dimensional Smoothed Particle Hydrodynamics Simulations

Contact Info

Product

Resources

About