Flow past a sphere straddling the interface of a two-phase system

1981 ◽  
Vol 32 (4) ◽  
pp. 474-477
Author(s):  
M. E. O'Neill ◽  
K. B. Ranger
Keyword(s):  
Phase System ◽  
Two Phase ◽  
Flow Past ◽  
Flow Past A Sphere

scholarly journals Analytical solutions of compacting flow past a sphere

2014 ◽  
Vol 746 ◽  
pp. 466-497 ◽  
Author(s):  
John F. Rudge
Keyword(s):  
Analytical Solutions ◽  
Stokes Flow ◽  
Solid Matrix ◽  
Rigid Sphere ◽  
Deformable Solid ◽  
Two Phase ◽  
Low Viscosity ◽  
Flow Past ◽  
Phase Medium ◽  
Flow Past A Sphere

AbstractA series of analytical solutions are presented for viscous compacting flow past a rigid impermeable sphere. The sphere is surrounded by a two-phase medium consisting of a viscously deformable solid matrix skeleton through which a low-viscosity liquid melt can percolate. The flow of the two-phase medium is described by McKenzie’s compaction equations, which combine Darcy flow of the liquid melt with Stokes flow of the solid matrix. The analytical solutions are found using an extension of the Papkovich–Neuber technique for Stokes flow. Solutions are presented for the three components of linear flow past a sphere: translation, rotation and straining flow. Faxén laws for the force, torque and stresslet on a rigid sphere in an arbitrary compacting flow are derived. The analytical solutions provide instantaneous solutions to the compaction equations in a uniform medium, but can also be used to numerically calculate an approximate evolution of the porosity over time whilst the porosity variations remain small. These solutions will be useful for interpreting the results of deformation experiments on partially molten rocks.

On the Problem of “Two-Phase” Activated Sludge

1991 ◽  
Vol 24 (7) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Szetela
Keyword(s):  
Activated Sludge ◽  
Single Phase ◽  
Phase System ◽  
Two Phase ◽  
Wastewater Treatment Process ◽  
Sludge Stabilization ◽  
Technological Advantage ◽  
In Series ◽  
State Models ◽  
Activated Sludge Systems

Steady-state models are presented to describe the wastewater treatment process in two activated sludge systems. One of these makes use of a single complete-mix reactor; the other one involves two complete-mix reactors arranged in series. The in-series system is equivalent to what is known as the “two-phase” activated sludge, a concept which is now being launched throughout Poland in conjunction with the PROMLECZ technology under implementation. Analysis of the mathematical models has revealed the following: (1) treatment efficiency, excess sludge production, energy consumption, and the degree of sludge stabilization are identical in the two systems; (2) there exists a technological equivalence of “two-phase” sludge with “single-phase” sludge; (3) the “two-phase” system has no technological advantage over the “single-phase” system.

Interphase distribution of 2-furylethylenes

1985 ◽  
Vol 50 (8) ◽  
pp. 1642-1647 ◽  
Author(s):  
Štefan Baláž ◽  
Anton Kuchár ◽  
Ernest Šturdík ◽  
Michal Rosenberg ◽  
Ladislav Štibrányi ◽  
...  
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Transport Rate ◽  
Phase System ◽  
Two Phase ◽  
Interphase Distribution ◽  
Distribution Kinetics ◽  
System 1 ◽  
Kinetics Of

The distribution kinetics of 35 2-furylethylene derivatives in two-phase system 1-octanol-water was investigated. The transport rate parameters in direction water-1-octanol (l1) and backwards (l2) are partition coefficient P = l1/l2 dependent according to equations l1 = logP - log(βP + 1) + const., l2 = -log(βP + 1) + const., const. = -5.600, β = 0.261. Importance of this finding for assesment of distribution of compounds under investigation in biosystems and also the suitability of the presented method for determination of partition coefficients are discussed.

Enhancing the Sensitivity of DNA and Aptamer Probes in the Dextran/PEG Aqueous Two-Phase System

2021 ◽  
Author(s):  
Qiaoshu Chen ◽  
Yanwen Zhang ◽  
Hui Chen ◽  
Jianbo Liu ◽  
Juewen Liu
Keyword(s):  
Phase System ◽  
Two Phase ◽  
Aqueous Two Phase System

Development of an ethanolic two-phase system (ETPS) based on polypropylene glycol 2000 + ethylene glycol + ethanol for separation of hydrophobic compounds

2021 ◽  
Author(s):  
Filipe Smith Buarque ◽  
Cleide Mara Faria Soares ◽  
Ranyere Lucena de Souza ◽  
Matheus Mendonça Pereira ◽  
Álvaro Silva Lima
Keyword(s):  
Ethylene Glycol ◽  
Phase System ◽  
Polypropylene Glycol ◽  
Two Phase ◽  
Hydrophobic Compounds ◽  
Ethanol Content ◽  
Coexisting Phases ◽  
Phase Water ◽  
High Ethanol

Two-phase water-free systems containing high ethanol content in the coexisting phases can selectively partition hydrophobic molecules from natural biomass.

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