Mathematical Modeling of Synovial Joints with Chemical Reaction

Vijayakumar, R.; Ratchagar, Nirmala P.

doi:10.1088/1742-6596/1724/1/012051

Cited by 8 publications

(14 citation statements)

References 7 publications

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“…. Because liquids are in-compressible so the mass conservation equation is continuous and viscous stresses are twice the local rate of linear deformation times the dynamic viscosity [17][18][19][20] .…”

Section: Kinematicsmentioning

confidence: 99%

“…Also, S M x and S M y are source terms include contribution due to body forces only and P is pressure [17][18][19][20] . We consider S M x = S M y = 0 with linear deformation rate and neglect the variation of pressure normal to very thin film of lubrication [17][18][19][20] . We know that, n is power law index with n = 1 for Newtonian fluids.…”

Section: Kinematicsmentioning

confidence: 99%

“…Where K and α are permeability of porous medium and slip parameter respectively [17][18][19][20] . The boundary of porous medium with a free viscous fluid is the continuity of pressure and the normal mass flux which give rise to wipe up the tangential velocity of the synovial fluid [17][18][19][20] . Such boundary condition was proposed by Beavers and Joseph (BJ) in 1967 as a empirical formula 18,19,21 .…”

Section: Kinematicsmentioning

confidence: 99%

“…The hyaluronic acid (HA) molecules in synovial fluid linked by convection diffusion phenomena is simple mass balance between changes in concentration C of solutes [20][21][22][23] ,…”

Section: Kinematicsmentioning

confidence: 99%

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Significance of Brinkman and Stokes System Conjuncture in Human Knee Joint

Al-Atawi

HASNAIN²,

Saqib

et al. 2022

Preprint

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Stokes’s equation in the fluid domain and Brinkman’s equation in the porous media are combined in the current study which is designated by the Stokes-Brinkman coupling. The current paper gives a theoretical analysis of the Stokes-Brinkman coupling. It has been shown that such a model is a good match for the knee joint. A flow model has been investigated in order to get a better understanding of the convective diffusion of the viscous flow along the articular surfaces between the joints. The Beavers and Joseph slip conditions which are a specific boundary condition for the synovial fluid are used to solve the governing system of partial differential equations for the synovial fluid and the results are provided here. Through the development of an analytical solution and numerical simulation (using the finite volume approach) it is hoped that the mechanisms of nutritional transport into the synovial joint will be better understood. According to the data the average concentration has a negative connection with both the axial distance and the duration spent in the experiment. Many graphs have been utilized to gain understanding into the problem’s various characteristics including velocity and concentration, among others. Hyaluronate (HA) is considered to be present in porous cartilage surfaces and the viscosity of synovial fluid fluctuates in response to the amount of HA present.

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Section: Kinematicsmentioning

confidence: 99%

Section: Kinematicsmentioning

confidence: 99%

Section: Kinematicsmentioning

confidence: 99%

“…The hyaluronic acid (HA) molecules in synovial fluid linked by convection diffusion phenomena is simple mass balance between changes in concentration C of solutes [20][21][22][23] ,…”

Section: Kinematicsmentioning

confidence: 99%

See 2 more Smart Citations

Significance of Brinkman and Stokes System Conjuncture in Human Knee Joint

Al-Atawi

HASNAIN²,

Saqib

et al. 2022

Preprint

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“…Romanishina et al [17] assumed the SF as a two-phase fluid with solid and liquid phases. VijayaKumar and Ratchagar [18] modeled lubricating SF between parallel plates in the presence of a reaction.…”

Section: Introductionmentioning

confidence: 99%

A Model of Synovial Fluid with a Hyaluronic Acid Source: A Numerical Challenge

Ozan

Labrosse

Uguz

2021

Fluids

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Initially motivated by the analysis of the flow dynamics of the synovial fluid, taken as non-Newtonian, this paper also reports on a numerical challenge which occurred unexpectedly while solving the momentum equation of the model. The configuration consists of two infinitely long horizontal parallel flat plates where the top plate is sheared at constant speed and the bottom plate is fixed. The synovial fluid shows a shear-thinning rheology, and furthermore it thickens with the hyaluronic acid (HA) concentration, i.e., it is also chemically-thickening. Accordingly, a modified Cross model is employed to express the shear rate and concentration-dependent viscosity, whose parameter values are determined from experimental data. Another significance of the study is the investigation of the effect of an external stimulus on the flow dynamics via a HA source term. The resulting flow exhibits peculiar features resulting from extremely large and small, but positive, numerical quantities, such as the viscosity and the shear rates. This requires constructing a parametrized zero-machine level solver, up to 300 accurate digits or so, for capturing the correct length scales of the flow physics. As a conclusion, the physical model, although simple, but original, leads to interesting results whose numerical determination turns out to be successful only once the real cause of the numerical trap is identified.

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