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.

Intramembrane charge movements and excitation– contraction coupling expressed by two-domain fragments of the Ca2+ channel

To investigate the molecular basis of the voltage sensor that triggers excitation–contraction (EC) coupling, the four-domain pore subunit of the dihydropyridine receptor (DHPR) was cut in the cytoplasmic linker between domains II and III. cDNAs for the I-II domain (α1S 1–670) and the III-IV domain (α1S 701-1873) were expressed in dysgenic α1S-null myotubes. Coexpression of the two fragments resulted in complete recovery of DHPR intramembrane charge movement and voltage-evoked Ca2+ transients. When fragments were expressed separately, EC coupling was not recovered. However, charge movement was detected in the I-II domain expressed alone. Compared with I-II and III-IV together, the charge movement in the I-II domain accounted for about half of the total charge (Qmax = 3 ± 0.23 vs. 5.4 ± 0.76 fC/pF, respectively), and the half-activation potential for charge movement was significantly more negative (V1/2 = 0.2 ± 3.5 vs. 22 ± 3.4 mV, respectively). Thus, interactions between the four internal domains of the pore subunit in the assembled DHPR profoundly affect the voltage dependence of intramembrane charge movement. We also tested a two-domain I-II construct of the neuronal α1A Ca2+ channel. The neuronal I-II domain recovered charge movements like those of the skeletal I-II domain but could not assist the skeletal III-IV domain in the recovery of EC coupling. The results demonstrate that a functional voltage sensor capable of triggering EC coupling in skeletal myotubes can be recovered by the expression of complementary fragments of the DHPR pore subunit. Furthermore, the intrinsic voltage-sensing properties of the α1A I-II domain suggest that this hemi-Ca2+ channel could be relevant to neuronal function.