The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Fluid shear stress inhibits TNF-α activation of JNK but not ERK1/2 or p38 in human umbilical vein endothelial cells: Inhibitory crosstalk among MAPK family members

Atherosclerosis preferentially occurs in areas of turbulent flow and low fluid shear stress, whereas laminar flow and high shear stress are atheroprotective. Inflammatory cytokines, such as tumor necrosis factor-α (TNF-α) and IL-1 stimulate expression of endothelial cell (EC) genes that may promote atherosclerosis. TNF-α and IL-1 regulate gene expression in ECs, in part, by stimulating mitogen-activated protein kinases (MAPK), which phosphorylate transcription factors. We hypothesized that steady laminar flow inhibits cytokine-mediated activation of MAPK in EC. To test this hypothesis, we determined the effects of flow (shear stress = 12 dynes/cm2) on TNF-α and IL-1-stimulated activity of three MAPK in human umbilical vein ECs (HUVEC): extracellular signal-regulated kinase (ERK1/2), p38, and c-Jun N-terminal kinase (JNK). Flow alone stimulated ERK1/2 and p38 activity but decreased JNK activity compared with static controls. TNF-α or IL-1 alone activated ERK1/2, p38, and JNK maximally at 15 min in HUVEC. Preexposing HUVEC for 10 min to flow inhibited TNF-α and IL-1 activation of JNK by 46% and 49%, respectively, but had no significant effect on ERK1/2 or p38 activation. Incubation of HUVEC with PD98059, which inhibits flow-mediated ERK1/2 activation, prevented flow from inhibiting cytokine activation of JNK. Phorbol 12-myristate 13-acetate, which strongly activates ERK1/2, also inhibited TNF-α activation of JNK. These findings indicate that fluid shear stress inhibits TNF-α-mediated signaling events in HUVEC via the activation of the ERK1/2 signaling pathway. Inhibition of TNF-α signal transduction represents a mechanism by which steady laminar flow may exert atheroprotective effects on the endothelium.

Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation. These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.