Impact of viscosity on creeping viscous fluid flow through a permeable slit: a study for the artificial kidneys

IF 1.1 Q4 BIOPHYSICS AIMS Biophysics Pub Date : 2022-01-01 DOI:10.3934/biophy.2022026
K. Maqbool, H. Mehboob, A. Siddiqui
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Abstract

The idea of this study is to present the mathematical model of two-dimensional biofluid flow having variable viscosity along the height of the channel (proximal renal tube of artificial kidney). This research describes that flow resistance is dependent on the height of the channel (proximal renal tube of artificial kidney) which makes the high flow near the centre and slow near the wall. The goal of this research is to provide the formulas to find the flow speed, average pressure, outflow flux and filtration rate of the viscous fluid having variable viscosity. The complex mathematical problem is solved by the Inverse method and results for axial velocity are plotted at the opening, central and departure region of the conduit. The numerical values for constant reabsorption and mean pressure are calculated against the filtration rate for the constant and variable viscosity. The numerical results of pressure rise show that when the viscosity of biofluid varies from centre to the boundary, then high change in pressure is required as compared with the biofluid having constant viscosity along the height of the slit. These mathematical formulas are very useful for the bioengineers to design the portable artificial kidney which works as a mechanical tool to filter the biofluid.
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粘度对通过可渗透狭缝蠕动的粘性流体流动的影响:人工肾脏的研究
本研究的思想是提出具有可变粘度的二维生物流体沿通道(人工肾脏近端肾管)高度流动的数学模型。本研究描述了流动阻力取决于通道(人工肾近端肾管)的高度,这使得靠近中心的流量大,靠近壁的流量慢。本研究的目的是提供变粘度粘性流体的流速、平均压力、流出流量和过滤速率的计算公式。用反求法求解了这一复杂的数学问题,并绘制了导管开口、中心和偏离处的轴向速度曲线。恒定重吸收和平均压力的数值是根据恒定和可变粘度的过滤速率计算的。压力上升的数值结果表明,当生物流体的黏度从中心到边界变化时,与黏度沿狭缝高度恒定的生物流体相比,需要较大的压力变化。这些数学公式对生物工程师设计便携式人工肾脏作为过滤生物流体的机械工具具有重要的指导意义。
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来源期刊
AIMS Biophysics
AIMS Biophysics BIOPHYSICS-
CiteScore
2.40
自引率
20.00%
发文量
16
审稿时长
8 weeks
期刊介绍: AIMS Biophysics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in the field of biophysics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports. AIMS Biophysics welcomes, but not limited to, the papers from the following topics: · Structural biology · Biophysical technology · Bioenergetics · Membrane biophysics · Cellular Biophysics · Electrophysiology · Neuro-Biophysics · Biomechanics · Systems biology
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