Variation of the maximum velocity along the umbilical vein supports the Reynolds pulsometer model.

OBJECTIVE: To challenge, with a modern sonographic approach and a numerical model, the Reynolds's concept which suggests that the vascular structure of the umbilical cord could act as a pulsometer facilitating the venous return to the foetus. METHOD: Forty-five patients between 20 and 28 weeks of gestation were included in the study. The blood maximum velocity in the umbilical vein, measured at both foetal and placental ends, was assessed. Several sonographic parameters of the cord, including the diameter of the umbilical vein at both extremities, cord cross-sectional area and Wharton's jelly section surface were measured. We compare our data with those of a numerical model. RESULTS: A difference in maximum velocity between the two extremities of the umbilical vein (ΔUVVmax) was noted. The maximum velocity was significantly higher at the foetal umbilical end (14.12 +/-3.18 cm/s) than at the placental end (11.93 +/-2.55 cm/s; p < 0.0001). The mean difference is 2.2 +/- 2.3 cm/s. No difference in the umbilical vein diameter was measured at both cord ends (umbilical 4.85 +/-0.9 mm, placental 4.86 +/-0.87 mm, p < 0.0001). There is no significant relationship between ΔUVVmax and the cord cross-sectional area or Wharton's jelly index. CONCLUSION: Modifications of the spatial velocity profile together with the pulsometer model could explain the maximum velocity changes that is measured in the umbilical vein along the cord. This numerical model consolidates the sonographic observations.

Importance of wave-number dependence of Biot numbers in one-sided models of evaporative Marangoni instability: Horizontal layer and spherical droplet.

A one-sided model of the thermal Marangoni instability owing to evaporation into an inert gas is developed. Two configurations are studied in parallel: a horizontal liquid layer and a spherical droplet. With the dynamic gas properties being admittedly negligible, one-sided approaches typically hinge upon quantifying heat and mass transfer through the gas phase by means of transfer coefficients (like in the Newton's cooling law), which in dimensionless terms eventually corresponds to using Biot numbers. Quite a typical arrangement encountered in the literature is a constant Biot number, the same for perturbations of different wavelengths and maybe even the same as for the reference state. In the present work, we underscore the relevance of accounting for its wave-number dependence, which is especially the case in the evaporative context with relatively large values of the resulting effective Biot number. We illustrate the effect in the framework of the Marangoni instability thresholds. As a concrete example, we consider HFE-7100 (a standard refrigerant) for the liquid and air for the inert gas.

Bénard instabilities in a binary-liquid layer evaporating into an inert gas.

A linear stability analysis is performed for a horizontal layer of a binary liquid of which solely the solute evaporates into an inert gas, the latter being assumed to be insoluble in the liquid. In particular, a water-ethanol system in contact with air is considered, with the evaporation of water being neglected (which can be justified for a certain humidity of the air). External constraints on the system are introduced by imposing fixed "ambient" mass fraction and temperature values at a certain effective distance above the free liquid-gas interface. The temperature is the same as at the bottom of the liquid layer, where, besides, a fixed mass fraction of the solute is presumed to be maintained. Proceeding from a (quasi-)stationary reference solution, neutral (monotonic) stability curves are calculated in terms of solutal/thermal Marangoni/Rayleigh numbers as functions of the wavenumber for different values of the ratio of the gas and liquid layer thicknesses. The results are also presented in terms of the critical values of the liquid layer thickness as a function of the thickness of the gas layer. The solutal and thermal Rayleigh and Marangoni effects are compared to one another. For a water-ethanol mixture of 10wt.% ethanol, it appears that the solutal Marangoni effect is by far the most important instability mechanism. Furthermore, its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber. On the other hand, it is also shown that, if taken into account, water evaporation has only minor quantitative consequences upon the results for this predominant, solutal Marangoni mechanism.