Modelling and simulation of coupled fluid transport and time-dependent fracture in fibre-reinforced hydrogel composites

Abstract. In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no finite time or aperiodically time-dependent version of the KAM theorem, the Nekhoroshev theorem, by its very nature, is a finite time result, but for a "very long" (i.e. exponentially long with respect to the size of the perturbation) time interval and provides a rigorous quantification of "nearly invariant tori" over this very long timescale. We discuss an aperiodically time-dependent version of the Nekhoroshev theorem due to Giorgilli and Zehnder (1992) (recently refined by Bounemoura, 2013 and Fortunati and Wiggins, 2013) which is directly relevant to fluid transport problems. We give a detailed discussion of issues associated with the applicability of the KAM and Nekhoroshev theorems in specific flows. Finally, we consider a specific example of an aperiodically time-dependent flow where we show that the results of the Nekhoroshev theorem hold.

Download Full-text

Muscarinic stimulation of gallbladder epithelium. II. Fluid transport, cell volume, and ion permeabilities

AJP Cell Physiology ◽

10.1152/ajpcell.1993.265.6.c1613 ◽

1993 ◽

Vol 265 (6) ◽

pp. C1613-C1619 ◽

Cited By ~ 1

Author(s):

G. A. Altenberg ◽

M. Subramanyam ◽

L. Reuss

Keyword(s):

Cell Volume ◽

Fluid Transport ◽

Apical Membrane ◽

Basolateral Membrane ◽

Time Dependent ◽

Water Volume ◽

K Channels ◽

Membrane Conductances ◽

Muscarinic Stimulation ◽

Stimulation Of

Activation of muscarinic receptors in the fluid-absorptive epithelium of the Necturus gallbladder elevates cytosolic Ca2+ concentration, transiently hyperpolarizes the cell membrane voltages, and decreases the apparent fractional resistance of the apical membrane [G. A. Altenberg, M. Subramanyam, J. S. Bergmann, K. M. Johnson, and L. Reuss. Am. J. Physiol. 265 (Cell Physiol. 34): C1604-C1612, 1993]. In these studies, we show that at the peak of the hyperpolarization both apical and basolateral membrane resistances (Ra and Rb, respectively) decreased, but in 2-3 min Ra returned to control values while Rb rose to a level approximately 60% higher than control. The acetylcholine (ACh)-induced decrease in Ra is caused by activation of apical membrane maxi K+ channels secondary to elevation of cytosolic Ca2+ concentration. The increase in Rb is due to decreases in K+ and Cl- conductances. ACh had no effects on cell KCl content or water volume, although K+ conductance transiently increased. These results can be explained by the changes in basolateral membrane conductances. ACh did not alter fluid absorption. In conclusion, ACh has complex time-dependent effects on K+ and Cl- electrodiffusive permeabilities without measurable changes in cell volume or in the rate of transepithelial fluid transport.

Download Full-text