We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension a
nd the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the time scale over which the instability develops is given by the volume fraction dependent settling time scale of the grains in the cell. We then show that the mobility inversion and the non-equilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.
We investigate the dynamics of textbf{textit{Lumbriculus variegatus}} in water-saturated sediment beds to understand limbless locomotion in the benthic zone found at the bottom of lakes and oceans. These slender aquatic worms are observed to perform
elongation-contraction and transverse undulatory strokes in both water-saturated sediments and water. Greater drag anisotropy in the sediment medium is observed to boost the burrowing speed of the worm compared to swimming in water with the same stroke using drag-assisted propulsion. We capture the observed speeds by combining the calculated forms based on resistive-force theory of undulatory motion in viscous fluids and a dynamic anchor model of peristaltic motion in the sediments. Peristalsis is found to be effective for burrowing in non-cohesive sediments which fill in rapidly behind the moving body inside the sediment bed. Whereas, the undulatory stroke is found to be effective in water and in shallow sediment layers where anchoring is not possible to achieve peristaltic motion. We show that such dual strokes occur as well in the earthworm textbf{textit{Eisenia fetida}} which inhabit moist sediments that are prone to flooding. Our analysis in terms of the rheology of the medium shows that the dual strokes are exploited by organisms to negotiate sediment beds that may be packed heterogeneously, and can be used by active intruders to move effectively from a fluid through the loose bed surface layer which fluidize easily to the well-consolidated bed below.
Twisting sheets as a strategy to form yarns with nested structure lacks scientific guiding principles but relies on millennia of human experience in making catguts, food packaging, and redeployable fabric wearables. We formulate a tensional twist-fol
ding route to making yarns with prescribed folded, scrolled, and encapsulated architectures by remote boundary loading. By harnessing micro-focus x-ray scanning to noninvasively image the fine internal structure, we show that a twisted sheet follows a surprisingly ordered folding transformation as it self-scrolls to form structured yarns. As a sheet is twisted by a half-turn, we find that the elastic sheet spiral accordion folds with star polygon shapes characterized by Schlafli symbols set by the primary instability. A scalable model incorporating dominant stretching modes with origami kinematics explains not only the observed multilayered structure, torque, and energetics, but also the topological transformation into yarns with prescribed crosssections through recursive folding and twist localization. By using hyperelastic materials, we further demonstrate that a wide range of structures can be readily redeployed, going well beyond other self-assembly methods in current broad use.
We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a
significantly higher drag is observed with increasing speeds. The drag as a function of depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction $mu_e$ encountered over six orders of magnitude of speeds. While a constant $mu_e$ is found when the grain size, rod depth and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze $mu_e$ in terms of the inertial number $I$ and viscous number $J$ to understand the relative importance of inertia and viscous forces, respectively. For sufficiently large fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function $mu_e = mu_o + k J^n$, where $mu_o$ is the effective friction measured in the quasi-static limit, and $k$ and $n$ are material constants. The drag is then analyzed in terms of the effective viscosity $eta_e$ and found to decrease systematically as a function of $J$. We further show that $eta_e$ as a function of $J$ is directly proportional to the fluid viscosity and the $mu_e$ encountered by the rod.
We investigate the effective friction encountered by an intruder moving through a sedimented medium which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction $mu_e$
on a spherical intruder is captured by the inertial number $I$ given by the ratio of the time scale over which the intruder moves and the inertial time scale of the granular medium set by the overburden pressure. Further, $mu_e$ is described by the function $mu_e(I) = mu_s + alpha I^beta$, where $mu_s$ is the static friction, and $alpha$ and $beta$ are material dependent constants which are independent of intruder depth and size. By measuring the mean flow of the granular component around the intruder, we find significant slip between the intruder and the granular medium. The motion of the medium is strongly confined near the intruder compared with a viscous Newtonian fluid and is of the order of the intruder size. The return flow of the medium occurs closer to the intruder as its depth is increased. Further, we study the reversible and irreversible displacement of the medium by not only following the medium as the intruder moves down but also while returning the intruder back up to its original depth. We find that the flow remains largely reversible in the quasi-static regime, as well as when $mu_e$ increases rapidly over the range of $I$ probed.
We show that a freshly sedimented granular bed settles and creeps forward over extended periods of time under an applied hydrodynamic shear stress, which is below the critical value for bedload transport. The rearrangements are found to last over a t
ime scale which is millions of times the sedimentation time scale of a grain in the fluid. Compaction occurs uniformly throughout the bed, but creep is observed to decay exponentially with depth, and decreases over time. The granular volume fraction in the bed is found to increase logarithmically, saturating at the random close packing value $phi_{rcp} approx 0.64$, while the surface roughness is observed to remain essentially unchanged. We demonstrate that an increasingly higher shear stress is required to erode the bed after a sub-critical shear is applied which results in an increase in its volume fraction. Thus, we find that bed armoring occurs due to a deep shear-induced relaxation of the bed towards the volume fraction associated with the glass transition.
We investigate with experiments the twist induced transverse buckling instabilities of an elastic sheet of length $L$, width $W$, and thickness $t$, that is clamped at two opposite ends while held under a tension $T$. Above a critical tension $T_lamb
da$ and critical twist angle $eta_{tr}$, we find that the sheet buckles with a mode number $n geq 1$ transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable, and stiff are identified, by introducing a bendability length $L_B$ and a clamp length $L_{C}(<L_B)$. In the stiff regime ($L>L_B$), we find that mode $n=1$ develops above $eta_{tr} equiv eta_S sim (t/W) T^{-1/2}$, independent of $L$. In the bendable regime $L_{C}<L<L_B$, $n=1$ as well as $n > 1$ occur above $eta_{tr} equiv eta_B sim sqrt{t/L}T^{-1/4}$. Here, we find the wavelength $lambda_B sim sqrt{Lt}T^{-1/4}$, when $n > 1$. These scalings agree with those derived from a covariant form of the Foppl-von Karman equations, however, we find that the $n=1$ mode also occurs over a surprisingly large range of $L$ in the bendable regime. Finally, in the clamp-dominated regime ($L < L_c$), we find that $eta_{tr}$ is higher compared to $eta_B$ due to additional stiffening induced by the clamped boundary conditions.
Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering, aggregati
on at the side walls, and clustering absent in round SP particles. Furthermore, we find that at sufficiently strong excitation SP rods engage in a persistent swirling motion in which the velocity is strongly correlated with particle orientation.
