Pulsatile parallel flow of air and a viscoelastic fluid with multiple characteristic times. An application to mucus in the trachea and the frequency of cough.

We study the dynamics of a binary fluid, where the two fluids are flowing parallel to each other in a cylindrical geometry, and driven by a pulsatile pressure gradient. One of the fluids is a low viscosity Newtonian fluid, the other one is viscoelastic. In order to be able to apply the model to different biofluids, we consider that the viscoelastic fluid has several characteristic times. We characterize the dynamics of the fluids as generalized Darcy's laws, with linear response functions to pulsatile pressure gradients, whose parameters are coupled for both fluids through the fluid-fluid boundary conditions. We apply our results to the dynamics of mucus and air in the trachea and find that the frequency that allows for a larger movement of the mucus, coincides with the experimental frequency of cough. This allows us to propose a plausible explanation for the frequency of cough in healthy individuals, a mechanical process to expel noxious substances from the respiratory system.

Pinning and avalanches in hydrophobic microchannels.

Rare events appear in a wide variety of phenomena such as rainfall, floods, earthquakes, and risk. We demonstrate that the stochastic behavior induced by the natural roughening present in standard microchannels is so important that the dynamics for the advancement of a water front displacing air has plenty of rare events. We observe that for low pressure differences the hydrophobic interactions of the water front with the walls of the microchannel put the front close to the pinning point. This causes a burstlike dynamics, characterized by series of pinning and avalanches, that leads to an extreme-value Gumbel distribution for the velocity fluctuations and a nonclassical time exponent for the advancement of the mean front position as low as 0.38.

A plausible explanation for heart rates in mammals.

We consider a simple model to give a plausible mechanical explanation of what are the actual resting heart rates of mammals optimized for. We study what is the optimal frequency for a viscoelastic fluid circulating in a pulsatile way through a network of tubes and conclude that the heart rate is not optimized to transport blood through the whole net. Rather, actual resting heart rates of mammals happen at frequencies that optimize flow in vessels of radii that correspond to large arteries, which bring oxygenated blood rapidly far away from the heart, towards head and limbs. Our results for the optimal frequencies, obtained using observed radii of femoral arteries in mammals, agree best with the heart rates observed. We find a theoretical allometric relation between optimal flow frequency and radius: nu approximately R(-1). This one, agrees with the exponent obtained when plotting observed heart rates versus radii of both, femoral arteries and carotids in mammals of different sizes, from mice to horses.

Pattern formation and morphology evolution in Langmuir monolayers.

We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace's equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.

Fluctuations in Saffman-Taylor fingers with quenched disorder.

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

Lateral instability in normal viscous fingers.

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime.

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.