The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The hepatic stellate cell has surprised and engaged physiologists, pathologists, and hepatologists for over 130 years, yet clear evidence of its role in hepatic injury and fibrosis only emerged following the refinement of methods for its isolation and characterization. The paradigm in liver injury of activation of quiescent vitamin A-rich stellate cells into proliferative, contractile, and fibrogenic myofibroblasts has launched an era of astonishing progress in understanding the mechanistic basis of hepatic fibrosis progression and regression. But this simple paradigm has now yielded to a remarkably broad appreciation of the cell's functions not only in liver injury, but also in hepatic development, regeneration, xenobiotic responses, intermediary metabolism, and immunoregulation. Among the most exciting prospects is that stellate cells are essential for hepatic progenitor cell amplification and differentiation. Equally intriguing is the remarkable plasticity of stellate cells, not only in their variable intermediate filament phenotype, but also in their functions. Stellate cells can be viewed as the nexus in a complex sinusoidal milieu that requires tightly regulated autocrine and paracrine cross-talk, rapid responses to evolving extracellular matrix content, and exquisite responsiveness to the metabolic needs imposed by liver growth and repair. Moreover, roles vital to systemic homeostasis include their storage and mobilization of retinoids, their emerging capacity for antigen presentation and induction of tolerance, as well as their emerging relationship to bone marrow-derived cells. As interest in this cell type intensifies, more surprises and mysteries are sure to unfold that will ultimately benefit our understanding of liver physiology and the diagnosis and treatment of liver disease.

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Hepatic Stellate Cells: Protean, Multifunctional, and Enigmatic Cells of the Liver

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

https://hal.archives-ouvertes.fr/hal-00118375/document

A constitutive law for dense granular flows

This review encompasses the most important advances in liver functions and hepatotoxicity and analyzes which mechanisms can be studied in vitro. In a complex architecture of nested, zonated lobules, the liver consists of approximately 80 % hepatocytes and 20 % non-parenchymal cells, the latter being involved in a secondary phase that may dramatically aggravate the initial damage. Hepatotoxicity, as well as hepatic metabolism, is controlled by a set of nuclear receptors (including PXR, CAR, HNF-4α, FXR, LXR, SHP, VDR and PPAR) and signaling pathways. When isolating liver cells, some pathways are activated, e.g., the RAS/MEK/ERK pathway, whereas others are silenced (e.g. HNF-4α), resulting in up- and downregulation of hundreds of genes. An understanding of these changes is crucial for a correct interpretation of in vitro data. The possibilities and limitations of the most useful liver in vitro systems are summarized, including three-dimensional culture techniques, co-cultures with non-parenchymal cells, hepatospheres, precision cut liver slices and the isolated perfused liver. Also discussed is how closely hepatoma, stem cell and iPS cell-derived hepatocyte-like-cells resemble real hepatocytes. Finally, a summary is given of the state of the art of liver in vitro and mathematical modeling systems that are currently used in the pharmaceutical industry with an emphasis on drug metabolism, prediction of clearance, drug interaction, transporter studies and hepatotoxicity. One key message is that despite our enthusiasm for in vitro systems, we must never lose sight of the in vivo situation. Although hepatocytes have been isolated for decades, the hunt for relevant alternative systems has only just begun.

/pdf/recent-advances-in-2d-and-3d-in-vitro-systems-using-primary-46n7hrqknx.pdf

Recent advances in 2D and 3D in vitro systems using primary hepatocytes, alternative hepatocyte sources and non-parenchymal liver cells and their use in investigating mechanisms of hepatotoxicity, cell signaling and ADME.

We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.

Flows of Dense Granular Media

https://www.gastrojournal.org/article/S0016-5085(02)15915-4/pdf

Telomerase reconstitution immortalizes human fetal hepatocytes without disrupting their differentiation potential

This study deals with the viscous incompressible flow over a stretching sheet. The velocity of the sheet is a quadratic polynomial of the distance from the slit and the sheet is subjected to a linear mass flux. A closed form solution is obtained under some restrictions on the linear mass flux. Stream line patterns are plotted and the effect of mass flux on the flow is also studied.

A note on the flow over a stretching sheet

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume \upsilon f, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2 \Gamma) or a three-parameter (3\Gamma) gamma distribution. The free parameter m in both the 2\Gamma and 3\Gamma models is identified as the "regularity factor." The regularity factoris the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of \upsilon f. Simulations carried outusing a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural in homogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)]for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system,D, is found necessary for the hard-disk and hard-sphere systems. Thus,for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.

Voronoi cell volume distribution and configurational entropy of hard-spheres

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-7836.2005.01508.x

Transplantation of endothelial cells corrects the phenotype in hemophilia A mice.

The stability of the interface between a gel of thickness HR and a Newtonian fluid of thickness R subjected to a linear shear flow is studied in the limit where inertial effects are negligible. The shear stress for the gel contains an elastic part that depends on the local displacement field and a viscous component that depends on the velocity field. The shear flow at the surface tends to destabilize the surface fluctuations, and the critical strain rate γc, which is the minimum strain rate required for unstable fluctuations, is determined as a function of the dimensionless quantities H, ηr = (ηg/ηf), and T = (Γ/ER). Here ηg and ηf are the gel and fluid viscosities, E is the gel elasticity, Γ is the surface tension of the gel — fluid interface and the strain rate γ is scaled by (E/ηf). In the limit H ↦∞, we find that γc decreases proportional to H-1 independent of ηr and T. But at finite H, γc is strongly dependent on ηr and T. For ηr ≥1, the interface is stable for all values of the strain rate for $H \sqrt{\eta_{\rm r}}$. For ηr = 1 and H ↦1, we find that γc ∝(H - 1)1/2 for T=0 and γc ∝(H - 1)3/4T1/4 for T ≠0. For ηr > 1, the analysis indicates that $\gamma_{\rm c} \propto(H-\sqrt{\eta_{\rm r}})^{-1}$ independent of T for $H \to \sqrt{\eta_{\rm r}}$. For ηr < 1, the onset of instability depends strongly on the parameter T. For T = 0, the critical strain rate is finite in the limit H ↦0, while for T ≠0 the critical strain rate diverges at a finite value of H. This minimum H decreases proportional to ηr for large T. The instability is caused by the energy transfer from the mean flow to the fluctuations due to the work done by the mean flow at the interface.

https://hal.archives-ouvertes.fr/jpa-00248015/document

Vinay Kumaran

Papers

Telomerase reconstitution immortalizes human fetal hepatocytes without disrupting their differentiation potential

A note on the flow over a stretching sheet

Voronoi cell volume distribution and configurational entropy of hard-spheres

Transplantation of endothelial cells corrects the phenotype in hemophilia A mice.

Flow induced instability of the interface between a fluid and a gel at low Reynolds number