A Mathematical Analysis and Simulation of the F-L Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue Virendra Upadhyay, Pooja Maurya, Surya Kant Chaturvedi, Vikas Chaurasiya, Dinesh Kumar Symmetry, 2024 In this paper, we have provided a mathematical analysis of an empirical result, namely, the Fahraeus–Lindqvist effect, a phenomenon that occurs in capillary tubes with a diameter lower than 0.3 mm. According to this effect, in capillary tubes under 0.3 mm in diameter, the apparent viscosity of blood decreases as the diameter of the tube decreases, making flow possible in these vessels. A two-phase blood flow mathematical model for human capillaries has been presented here. According to Haynes’ theory, blood is separated into two layers when it flows from the capillary. It is assumed that the first layer is plasma, and the second layer is the core layer. The plasma layer flows near the wall of the capillary, and the core layer flows along the axis of the capillary. Further, the core layer is assumed to be a mixture of two phases: one is the plasma, and the other is that of RBCs. For mathematical modeling purposes, a curvilinear coordinate system has been adopted, with physical quantities used in tensorial form. Derived equations are solved to find the effective viscosity, which depends upon the radius of the capillary; that is, it reduces viscosity to make blood flow possible. A comparative study was conducted with the experimental result of this effect, and it was observed that the proposed two-phase blood flow model is much closer to the experimental data than the single-phase blood flow model, and both have the same trends. After validation of the model with the experimental result, this model was applied to human capillaries (diameter lower than 10 μm) to show the F-L effect, and the impact of various physiological quantities that are relevant to the flow of blood into human capillaries are also discussed here. The impact of hematocrit on various parameters has been demonstrated explicitly.
Mathematical study and simulation on stenosed carotid arteries with the help of a two-phase blood flow model Pooja Maurya, Virendra Upadhyay, Surya Kant Chaturvedi, Dinesh Kumar Canadian Journal of Chemical Engineering, 2023 The present study is focused on a medical problem called stenosed carotid artery. The problem is formulated with the help of a two‐phase blood flow model. The non‐Newtonian nature of blood is considered that hold power law. Physical quantities were expressed in tensorial form. Analytical and numerical methods are used to solve equations under given boundary conditions. The effects of various parameters on blood flow like stenosis size, flow flux, resistance, haematocrit, pressure drop, etc. were studied and shown through various graphs. Parameter , which ensures that the fluid is Newtonian or non‐Newtonian; its impact on pressure drop; resistance to flow; and flow flux were obtained during the disease and presented through the graph. A relationship between pressure drop and haematocrit was obtained, which was helpful to predict fluctuation in blood flow during stenosis. We have also given a medical use for this model with the help of pathological data. We also analyzed steady and laminar flow in a carotid artery for different heights of stenosis. The study of various physiological parameters has been performed on the basis of blockage percentage and concentration of haematocrit. The nature of the red blood corpuscle (RBC) phase is considered liquid packets in a semi‐permeable membrane, which makes this model close to reality.
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RECENT SCHOLAR PUBLICATIONS
A mathematical model on stenosed artery with its application in arterial diseases P Maurya, V Upadhyay, D Kumar, SK Chaturvedi The European Physical Journal Plus 140 (10), 1028 , 2025 2025
Use of Ficus religiosa and Ficus benghalensis as habitat and food resources by peri-urban forest dwelling fauna in Chitrakoot SK Chaturvedi International Journal of Zoology Studies , 2025 2025 Citations: 1
A Mathematical Analysis and Simulation of the FL Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue V Upadhyay, P Maurya, SK Chaturvedi, V Chaurasiya, D Kumar Symmetry 16 (6), 728 , 2024 2024 Citations: 1
A Mathematical Analysis and Simulation of the FL Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue. Symmetry 2024, 16 … V Upadhyay, P Maurya, SK Chaturvedi, V Chaurasiya, D Kumar 2024
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Mathematical study and simulation on Stenosed Carotid Arteries with the help of a two‐phase blood flow model P Maurya, V Upadhyay, SK Chaturvedi, D Kumar The Canadian Journal of Chemical Engineering 101 (10), 5468-5481 , 2023 2023 Citations: 6
A Mathematical Modelling of Two-phase Coronary Blood Flow in Arterioles with Special Reference to Silent Ischemia P Gupta, V Upadhyay, SK Chaturvedi AIJR Abstracts, 77 , 2022 2022
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First record of Mango blossom midge Procystiphora mangiferae (Felt, 1927) from Satna, Madhya Pradesh RC Tripathi, SK Chaturvedi, G Bhaskar International Journal of Entomology Research 5 (Issue 3; 2020), 87-89 , 2020 2020 Citations: 1
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Status and distribution of Indian flying fox (Pteropus giganteus) in district Chitrakoot, Uttar Pradesh, India SK Chaturvedi, S Singh Int. J. Zool. Stu 3, 126-128 , 2018 2018 Citations: 3
Analysis of Two Phase Blood Flow in Human Pulmonary Artery during Lung Cancer by Mathematical Modeling PNP Dheerendra Kumar, Surya Kant Chaturvedi, V. Upadhyay American International Journal of Research in Science, Technology … , 2017 2017 Citations: 4
Study on seasonal density of zooplanktons in Ken River of Panna district (M.P.) AKT Surya Kant Chaturvedi, Lankesh Mehter International Journal of Zoology Studies 2 (5), 175-181 , 2017 2017
APPLIED MATHEMATICAL MODELS OF TWO PHASE HUMAN PULMONARY BLOOD FLOW IN VENULES WITH SPECIAL REFERENCE TO LUNG CANCER DPS Dheerendra Kumar, Virendra Upadhyay, Surya Kant Chaturvedi, P. N. Pandey International Journal of Current Research 9 (10), 58601-58606 , 2017 2017
Priliminary survey of bird fauna in Karwi Tehsil, District Chitrakoot, U.P., India AD Surya Kant Chaturvedi1, Srishti Nigam International Journal of Science and Research (IJSR) ISSN (Online): 2319 … , 2017 2017
Status of Noise Pollution on Certain Traffic Places in Allahabad City, U.P., India SS Surya Kant Chaturvedi International Journal of Scientific Engineering and Research 5 (4), 39-42 , 2017 2017
A mathematical study of two phase coronary blood flow in coronary arteries with special reference to angina V Upadhyay, S Mishra, SK Chaturvedi, AK Agrawal, PN Pandey IJAR 3 (2), 242-247 , 2017 2017
A study on non-newtonian mathematical modeling of two phase human pulmonary blood flow in venules during lung cancer PNP Dheerendra Kumar, Virendra Upadhyay, Surya Kant Chaturvedi International Journal of Applied Research 3 (9), 04-12 , 2017 2017
Status of Noise Pollution on Certain Traffic Places in Allahabad City, UP India SK Chaturvedi, S Singh Int. J. Sci. Eng. Res 5, 2015-2018 , 2017 2017 Citations: 3
MOST CITED SCHOLAR PUBLICATIONS
Fluoride content in drinking water and ground water quality in rural area of tahsil Mau, district Chitrakoot AK Tiwari, RP Dikshit, IP Tripathi, SK Chaturvedi Indian Journal of Environmental Protection 23, 1045-1050 , 2003 2003 Citations: 26
A mathematical model on effect of stenosis in two phase blood flow in arteries remote from the heart V Upadhyay, SK Chaturvedi, A Upadhyay Journal of International Academy of Physical Sciences 16 (3), 247-257 , 2012 2012 Citations: 11
Study of man-monkey conflict and its management in Chitrakoot, Madhya Pradesh, India SK Chaturvedi, MK Mishra International Journal of Global Science Research 1 (2), 107-110 , 2014 2014 Citations: 10
Mathematical study and simulation on Stenosed Carotid Arteries with the help of a two‐phase blood flow model P Maurya, V Upadhyay, SK Chaturvedi, D Kumar The Canadian Journal of Chemical Engineering 101 (10), 5468-5481 , 2023 2023 Citations: 6
Analysis of Anthropogenic impact on Paiswani River - A Spatial Approach AK Tiwari, SK Chaturvedi Indian Journal of Environmental Protection 32 (12), 977-987 , 2012 2012 Citations: 6
Preliminary Investigations of Ground Water Quality in Rural Areas of Karwi, Chitrakoot SK Dixit, AK Tiwari, SK Chaturvedi Research Journal on Science and Technology 7 (3), 176 , 2015 2015 Citations: 5
Analysis of Two Phase Blood Flow in Human Pulmonary Artery during Lung Cancer by Mathematical Modeling PNP Dheerendra Kumar, Surya Kant Chaturvedi, V. Upadhyay American International Journal of Research in Science, Technology … , 2017 2017 Citations: 4
Status and distribution of Indian flying fox (Pteropus giganteus) in district Chitrakoot, Uttar Pradesh, India SK Chaturvedi, S Singh Int. J. Zool. Stu 3, 126-128 , 2018 2018 Citations: 3
Status of Noise Pollution on Certain Traffic Places in Allahabad City, UP India SK Chaturvedi, S Singh Int. J. Sci. Eng. Res 5, 2015-2018 , 2017 2017 Citations: 3
Preliminary Survey of Bird Fauna in Karwi Tehsil, District Chitrakoot, UP, India SK Chaturvedi, S Nigam, A Dwivedi Inter J Sci Res 6 (8), 1585-90 , 2015 2015 Citations: 3
Acoustic & morphology based identification of microchiropteran species in Chitrakoot district, Uttar Pradesh, India SK Chaturvedi, S Singh, AK Tiwari International Journal of Zoology 3 (1), 352-357 , 2018 2018 Citations: 2
Selection of sleeping sites by Hanuman Langurs in Chitrakoot forest range of Madhya Pradesh, India M Mishra, SK Chaturvedi, MK Upadhayay Forest 1, 59 , 2012 2012 Citations: 2
Use of Ficus religiosa and Ficus benghalensis as habitat and food resources by peri-urban forest dwelling fauna in Chitrakoot SK Chaturvedi International Journal of Zoology Studies , 2025 2025 Citations: 1
A Mathematical Analysis and Simulation of the FL Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue V Upadhyay, P Maurya, SK Chaturvedi, V Chaurasiya, D Kumar Symmetry 16 (6), 728 , 2024 2024 Citations: 1
First record of Mango blossom midge Procystiphora mangiferae (Felt, 1927) from Satna, Madhya Pradesh RC Tripathi, SK Chaturvedi, G Bhaskar International Journal of Entomology Research 5 (Issue 3; 2020), 87-89 , 2020 2020 Citations: 1
Eco-ethological study on Semnopithecus entellus in Chitrakoot (Satna), Madhya Pradesh MK Mishra, SK Chaturvedi International Journal of Advance Research, Ideas, and Innovations in … , 2017 2017 Citations: 1
Mathematical modeling of two phase human pulmonary blood flow in arterioles: Lung cancer SKC Dheerendra Kumar, Virendra Upadhyay International Journal of Applied Research 2 (11), 184-190 , 2016 2016 Citations: 1
A mathematical model on stenosed artery with its application in arterial diseases P Maurya, V Upadhyay, D Kumar, SK Chaturvedi The European Physical Journal Plus 140 (10), 1028 , 2025 2025
A Mathematical Analysis and Simulation of the FL Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue. Symmetry 2024, 16 … V Upadhyay, P Maurya, SK Chaturvedi, V Chaurasiya, D Kumar 2024
WATER QUALITY ANALYSIS OF PAISWANI RIVER USING GIS–A CASE STUDY AK Tiwari, A Awasthi, SK Chaturvedi European Journal of Biomedical 11 (5), 267-275 , 2024 2024