Seth Lichter

The critical Weber number for vortex and jet formation for drops impinging on a liquid pool

When a liquid drop impacts on a pool, the drop will either coalesce into the host liquid, with the creation of a vortex ring below the surface and little splashing above, or will splash, producing a cavity in the host liquid that collapses inward, producing an upward jet of fluid. It is found that there is a critical Weber number, Wec=U(ρD/T)1/2≂8, below which vortex rings are formed and above which a jet is produced for drops falling into the identical fluid. Here, U is the drop speed at impact, D is the drop diameter, and ρ and T are density and surface tension, respectively. The Weber number criterion is compared with experiments using water and mercury.

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman-Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.

Molecular mechanisms of liquid slip

It is now well-established that the liquid adjacent to a solid need not be stationary – it can slip. How this slip occurs is unclear. We present molecular-dynamics (MD) simulation data and results from an analytical model which support two mechanisms of slip. At low levels of forcing, the potential field generated by the solid creates a ground state which the liquid atoms preferentially occupy. Liquid atoms hop through this energy landscape from one equilibrium site to another according to Arrhenius dynamics. Visual evidence of the trajectories of individual atoms on the solid surface supports the view of localized hopping, independent of the dynamics outside a local neighbourhood. We call this defect slip. At higher levels of forcing, the entire layer slips together, obviating the need for localized defects and resulting in the instantaneous motion of all atoms adjacent to the solid. The appearance of global slip leads to an increase in the number of slipping atoms and consequently an increase in the slip length. Both types of slip observed in the MD simulations are described by a dynamical model in which each liquid atom experiences a force from its neighbouring liquid atoms and the solid atoms of the boundary, is sheared by the overlying liquid, and damped by the solid. In agreement with the MD observations, this model predicts that above a critical value of forcing, localized slipping occurs in which atoms are driven from low-energy sites, but only if there is a downstream site which has been vacated. Also as observed, above a second critical value, all the liquid atoms adjacent to the wall slip. Finally, the dynamical equation predicts that at extremely large values of forcing, the slip length approaches a constant value, in agreement with the MD simulation results.

Subharmonic resonance of nonlinear cross-waves

The evolution equation governing wavemaker-generated cross-waves near a cutoff frequency in an infinitely deep, infinitely long channel is shown to be the nonlinear Schrodinger equation with a homogeneous boundary condition at the wavemaker. With the inclusion of an empirically determined damping coefficient, numerical results for growth rate, slow modulation period, and wave amplitude show good agreement with previous experiments. The results also describe observations of trapped and propagating solutions.

Identification of cross‐wave regimes in the vicinity of a cut‐off frequency

Experiments were performed in a long rectangular water tank equipped with a plane wavemaker. Cross waves were generated in the vicinity of the cutoff frequency of the fifth mode. Four different wave regimes were identified as a function of forcing frequency and amplitude. Long‐time modulation of the wave field was observed to be either quasiperiodic or chaotic. Under certain experimental conditions, envelope solitons were generated nearly periodically at the wavemaker. Propagation velocity of these solitons is also presented.

Dipole formation in the transient planar wall jet

An initially quiescent quarter‐plane of fluid is set into motion by the action of a wall jet, i.e., a jet parallel and adjacent to a wall. The circumstances for which the jet separates from the wall and forms a dipole at the upstream head of the jet are studied numerically. The streamfunction‐vorticity formulation is used to track the time evolution of vorticity over a range of Reynolds numbers, 50≤Re≤1000, based on jet velocity and width. By implementing both a no‐slip and a slip boundary condition and comparing the results for the time evolution of vorticity, it is found that the boundary condition has a negligible effect on dipole development. By contrast, the relative magnitude of positive ω+ and negative ω− vorticity present in the inlet jet flow controls whether dipole formation occurs. In particular, dipole formation requires a sufficiently large magnitude of negative vorticity ω−/ω+≳0.65. The results refine a conjecture by Yushina (‘‘Evolution of the near‐wall jet,’’ in General Circulations of the...

Experiments on nonlinear cross waves

Surface water waves are generated by a paddle‐type wavemaker operating at one end of a long tank. In addition to a progressing wave field at the forcing frequency, a subharmonic cross wave is generated in the neighborhood of the wavemaker. At lower forcing amplitudes there is a Benjamin–Feir instability of the progressing wave. At large forcing amplitudes, the fundamental decays rapidly along the channel. The cross wave dominates the near field and is strongly modulated on a slow time scale. During each modulation period a soliton propagates away from the wavemaker. The near‐field standing cross wave undergoes a transformation into a progressing wave in the far field.

Modulated, Frequency-locked, and Chaotic Cross-waves

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations ― a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation

Viscous Cross-waves: An Analytical Treatment

Viscous effects on the excitation of cross‐waves in a semi‐infinite box of finite depth and width are considered. A formalism using matched asymptotic expansions and an improved method of computing the solvability condition is used to derive the relative contributions of the free‐surface, sidewall, bottom, and wavemaker viscous boundary layers. This analysis yields an expression for the damping coefficient previously incorporated on heuristic grounds. In addition, three new contributions are found: a viscous detuning of the resonant frequency, a slow spatial variation in the coupling to the progressive wave, and a viscous correction to the wavemaker boundary condition. The wavemaker boundary condition breaks the symmetry of the linear neutral stability curve at leading order for many geometries of experimental interest.

Effect of Molecular-Scale Features on the Polymer Coil Size of Model Viscosity Index Improvers

Temperature-induced changes in coil size have been proposed as a mechanism underlying the functionality of viscosity index improving polymers. Here, molecular dynamics simulations are used to characterize the effect of temperature on the coil size of model additive polymers. The simulations reproduce experimental observations, where only some polymers increase in size with increasing temperature. The results also reveal that the presence of oxygen atoms in the polymer structure is a key factor in determining whether the polymer expands or contracts. This new simulation approach provides a general methodology for investigating temperature-induced coil size changes in polymeric lubricant additives.