Gabriel Juarez

Motility of small nematodes in wet granular media

The motility of the worm nematode Caenorhabditis elegans is investigated in shallow, wet granular media as a function of particle size dispersity and area density (). Surprisingly, we find that the nematodes propulsion speed is enhanced by the presence of particles in a fluid and is nearly independent of area density. The undulation speed, often used to differentiate locomotion gaits, is significantly affected by the bulk material properties of wet mono- and polydisperse granular media for ≥0.55. This difference is characterized by a change in the nematodes waveform from swimming to crawling in dense polydisperse media only. This change highlights the organisms adaptability to subtle differences in local structure and response between monodisperse and polydisperse media.

Mixing by cutting and shuffling

Dynamical systems theory has proven to be a successful approach to understanding mixing, with stretching and folding being the hallmark of chaotic mixing. Here we consider the mixing of a granular material in the context of a different mixing mechanism —cutting and shuffling— as a complementary viewpoint to that of traditional chaotic dynamics. Cutting and shuffling has a theoretical foundation in a relatively new area of mathematics called piecewise isometries (PWIs) with properties that are fundamentally different from the stretching and folding mechanism of chaotic advection. To demonstrate the effect of the cutting and shuffling combined with stretching and folding, we consider the mixing of granular materials of two different colors in a half-filled spherical tumbler that is rotated alternately about orthogonal axes. Mixing experiments using 1 mm particles in a 14 cm diameter tumbler are compared to PWI maps. The experiments are readily related to the PWI theory using continuum model simulations. By comparing experimental, simulation, and theoretical results, we demonstrate that mixing in a three-dimensional granular system can be viewed as mixing by traditional chaotic dynamics (stretching and folding) built on an underlying framework, or skeleton, of mixing due to cutting and shuffling. We further demonstrate that pure cutting and shuffling can generate a well-mixed system, depending on the angles through which the tumbler is rotated. We also explore the generation of interfacial area between the two colors of material resulting from both stretching in the flowing layer and cutting due to switching the axis of rotation.

Transition to centrifuging granular flow in rotating tumblers: a modified Froude number

Centrifuging of granular material in a partially filled rotating circular tumbler occurs when particles are flung outward to form a ring of particles at the periphery of the tumbler rotating as a solid body. The critical rotation speed for centrifuging was studied experimentally in a quasi-two-dimensional tumbler as a function of particle diameter, tumbler fill fraction and interstitial fluid. A qualitative numerical study using the discrete element method was also conducted to obtain a better understanding of the impact of friction on the transition. Experimental results show that the critical rotational speed for dry systems is not affected by the particle diameter unless the fill fraction is above 75%, where endwall friction begins to play a significant role. The critical speed is proportional to (1−)(−1/4), where represents the tumbler fill fraction. The angle of repose, which represents inter-particle friction, also affects the transition to centrifuging. Finally, the interstitial fluid, or rather the density difference between the particles and the interstitial fluid, affects the measured critical speed. Correction terms for the critical rotational speed are proposed to more accurately characterize the transition to centrifuging for granular flow in rotating tumblers, resulting in a modified Froude number.

Splash control of drop impacts with geometric targets

Drop impacts on solid and liquid surfaces exhibit complex dynamics due to the competition of inertial, viscous, and capillary forces. After impact, a liquid lamella develops and expands radially, and under certain conditions, the outer rim breaks up into an irregular arrangement of filaments and secondary droplets. We show experimentally that the lamella expansion and subsequent breakup of the outer rim can be controlled by length scales that are of comparable dimension to the impacting drop diameter. Under identical impact parameters (i.e., fluid properties and impact velocity) we observe unique splashing dynamics by varying the target cross-sectional geometry. These behaviors include (i) geometrically shaped lamellae and (ii) a transition in splashing stability, from regular to irregular splashing. We propose that regular splashes are controlled by the azimuthal perturbations imposed by the target cross-sectional geometry and that irregular splashes are governed by the fastest-growing unstable Plateau-Rayleigh mode.

Extensional rheology of DNA suspensions in microfluidic devices

Newtonian liquids that contain even small amounts (∼ppm) of flexible polymers can exhibit viscoelastic behavior in extensional flows. Here, the effects of the presence of DNA molecules in viscous fluids on the dynamics of filament thinning and drop breakup are investigated experimentally in a cross-slot microchannel. Both bulk flow and single molecule experiments are presented. Suspensions of DNA molecules of different molecular weights (MW) are used, namely λ-DNA (MW = 3 × 107) and T4 DNA (MW = 1 × 108). Results of both dilute (c/c* = 0.5) and semi-dilute (c/c* = 1) suspensions are compared to those of a viscous, Newtonian liquid. Results show that the dynamics of the high MW, semi-dilute suspension of T4 DNA are similar to viscoelastic fluids such as slow, exponential decay of the fluid thread and beads-on-a-string morphology. The exponential decay rate of the filament thickness is used to measure the steady extensional viscosity of all fluids. We find that the semi-dilute T4 DNA suspension exhibits extensional strain rate thinning extensional viscosity, while for all other fluids the extensional viscosity is independent of strain rate. Direct visualization of fluorescently labeled λ-DNA molecules using high-speed imaging shows that the strong flow in the thinning fluid threads provide sufficient forces to stretch the majority of DNA molecules away from their equilibrium coiled state. The distribution of molecular stretch lengths, however, is very heterogeneous due to molecular individualism and initial conditions.

Regular and irregular splashing of drops on geometric targets

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