Vertical concentration profile of nonuniform sediment

2021 ◽  
Vol 36 (1) ◽  
pp. 120-126
Author(s):  
Zhilin Sun ◽  
Haolei Zheng ◽  
Dan Xu ◽  
Chunhong Hu ◽  
Chaofan Zhang
Keyword(s):  
Concentration Profile ◽  
Nonuniform Sediment ◽  
Vertical Concentration Profile

scholarly journals An Efficient Model for Predicting the Segregation Profile of Binary Fluidized Beds

2018 ◽  
Vol 63 (1) ◽  
pp. 147-159
Author(s):  
Mohamed Sobhi Al-Agha ◽  
Pál Szentannai
Keyword(s):  
Concentration Profile ◽  
Fluidized Beds ◽  
Vertical Axis ◽  
3D Models ◽  
Data Sets ◽  
Two Phase ◽  
Main Work ◽  
Fitting Procedure ◽  
Segregation Profile ◽  
Vertical Concentration Profile

In most cases, the stationary fluidized beds are composed of two different particle classes (inert and active particles), and the concentration profile of these binary beds along the vertical axis is crucial regarding the effectiveness of the reactor. The present study introduces a semi-empirical 1D mathematical model for predicting the vertical concentration profile of binary fluidized beds. The proposed model is a developed and applicable version of the so-called Gibilaro and Rowe two-phase model, in which the differential equations describing the jetsam movement in the bulk and wake phases were solved numerically. The main work was to determine the parameters of the basic model, which was carried out by means of an advanced multi-step parameter fitting procedure. A more general form was established, which is based on direct linkage with the operating parameters that can be directly set and measured on the system. Comparisons with very diverse measured data sets available in the literature prove the accuracy of this model. Additional comparisons pointed out that the realization of this model is numerically inexpensive as it is several orders of magnitude faster than the available 2D and 3D models.

Modeling of temporal variations of vertical concentration profile of 7Be in the atmosphere

2009 ◽  
Vol 43 (12) ◽  
pp. 2000-2004 ◽  
Author(s):  
Jan Simon ◽  
Jana Meresova ◽  
Ivan Sykora ◽  
Miroslav Jeskovsky ◽  
Karol Holy
Keyword(s):  
Concentration Profile ◽  
Temporal Variations ◽  
Vertical Concentration Profile

Nonlinear filter properties of the thick ascending limb

1997 ◽  
Vol 273 (4) ◽  
pp. F625-F634 ◽  
Author(s):  
H. E. Layton ◽  
E. Bruce Pitman ◽  
Leon C. Moore
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Transit Time ◽  
Concentration Profile ◽  
Tubuloglomerular Feedback ◽  
Thick Ascending Limb ◽  
Transport Parameters ◽  
Nodal Structure ◽  
Nacl Concentration ◽  
Fluid Transit Time

A mathematical model was used to investigate the filter properties of the thick ascending limb (TAL), that is, the response of TAL luminal NaCl concentration to oscillations in tubular fluid flow. For the special case of no transtubular NaCl backleak and for spatially homogeneous transport parameters, the model predicts that NaCl concentration in intratubular fluid at each location along the TAL depends only on the fluid transit time up the TAL to that location. This exact mathematical result has four important consequences: 1) when a sinusoidal component is added to steady-state TAL flow, the NaCl concentration at the macula densa (MD) undergoes oscillations that are bounded by a range interval envelope with magnitude that decreases as a function of oscillatory frequency; 2) the frequency response within the range envelope exhibits nodes at those frequencies where the oscillatory flow has a transit time to the MD that equals the steady-state fluid transit time (this nodal structure arises from the establishment of standing waves in luminal concentration, relative to the steady-state concentration profile, along the length of the TAL); 3) for any dynamically changing but positive TAL flow rate, the luminal TAL NaCl concentration profile along the TAL decreases monotonically as a function of TAL length; and 4) sinusoidal oscillations in TAL flow, except at nodal frequencies, result in nonsinusoidal oscillations in NaCl concentration at the MD. Numerical calculations that include NaCl backleak exhibit solutions with these same four properties. For parameters in the physiological range, the first few nodes in the frequency response curve are separated by antinodes of significant amplitude, and the nodes arise at frequencies well below the frequency of respiration in rat. Therefore, the nodal structure and nonsinusoidal oscillations should be detectable in experiments, and they may influence the dynamic behavior of the tubuloglomerular feedback system.

Sign in / Sign up

Export Citation Format

Share Document