A continuum model of blood flow

Popel, Aleksander S.; Regirer, S. A.; Usick, P.I.

doi:10.3233/bir-1974-11605

Cited by 84 publications

(37 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The other modification of the micropolar theory postulates a linear dependence of the gradient of particles' chemical potential, Z, on their rotational velocity [127][128][129]:…”

Section: Micropolar and Micromorphic Modelsmentioning

confidence: 99%

Segregation of Flowing Blood: Mathematical Description

Tokarev

Panasenko

Ataullakhanov

2011

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract. Blood rheology is completely determined by its major corpuscles which are erythrocytes, or red blood cells (RBCs). That is why understanding and correct mathematical description of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and non-uniform radial distribution affect the passage of blood through the vessels. Hence, they have to be taken into account while modelling the blood dynamics. Other important blood corpuscles are platelets, which are crucial for blood clotting. RBCs strongly affect the platelet transport in blood expelling them to the vessel walls and increasing their dispersion, which has to be considered in models of clotting. In this article we give a brief review of basic modern approaches in mathematical description of these phenomena, discuss their applicability to real flow conditions and propose further pathways for developing the theory of blood flow.

show abstract

“…The other modification of the micropolar theory postulates a linear dependence of the gradient of particles' chemical potential, Z, on their rotational velocity [127][128][129]:…”

Section: Micropolar and Micromorphic Modelsmentioning

confidence: 99%

Segregation of Flowing Blood: Mathematical Description

Tokarev

Panasenko

Ataullakhanov

2011

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…Such a motion of the uid can be interpreted as a motion in a cross section x 3 = const of the three-dimensional domain × (−∞; +∞) when u 3 = 0 and the axes of rotation of particles are parallel to the x 3 -axis. Under these assumptions Equations (1) and (2) are becoming much simpler. We have u = (u 1 ; u 2 ; 0), !…”

Section: Introductionmentioning

confidence: 99%

“…As experiments show the solutions of this model represent ows of many uids (like, e.g. blood, see References [2,3]) more precisely than solutions of the Navier-Stokes model. The di erence between these two models becomes larger for ows in narrow channels.…”

Section: Introductionmentioning

confidence: 99%

Global attractor for heat convection problem in a micropolar fluid

Tarasińska

2006

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…e.g. [6,7]), particularly when the domain of flow was small. It corresponds with our conjecture that the smaller is the domain of flow, the stronger is the influence of the internal structure.…”

Section: Introductionmentioning

confidence: 99%

Ladder estimates for micropolar fluid equations and regularity of global attractor

Szopa

2010

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

Communicated by M. LachowiczThis paper is devoted to obtain ladder inequalities for 2D micropolar fluid equations on a periodic domain Q = (0,L) 2 . The ladder inequalities are differential inequalities that connect the evolution of L 2 norms of derivatives of order N with the evolution of the L 2 norms of derivatives of other (usually lower) order. Moreover, we find (with slight assumption on external fields) long-time upper bounds on the L 2 norms of derivatives of every order, which implies that a global attractor is made up from C ∞ functions.

show abstract

A continuum model of blood flow

Cited by 84 publications

References 0 publications

Segregation of Flowing Blood: Mathematical Description

Segregation of Flowing Blood: Mathematical Description

Global attractor for heat convection problem in a micropolar fluid

Ladder estimates for micropolar fluid equations and regularity of global attractor

Contact Info

Product

Resources

About