Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Universal and non-universal features in coarse-grained models of flow in disordered solids.

Abstract: We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as −1/2 in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.

Layered droplet microstructures in sheared emulsions: finite-size effects.

Abstract: We investigate the influence of confinement on the steady state microstructure of emulsions sheared between parallel plates, in a regime where the average droplet dimension is comparable to the gap width between the confining walls. Utilizing droplet velocimetry, we find that the droplets can organize into discrete layers under the influence of shear. The number of layers decreases from two (at relatively higher shear rates) to one (at lower shear rates), as the drops grow slightly larger due to coalescence. We argue that the layering and overall composition profile may be controlled by the interplay of droplet collisions (which can cause separation of droplet centers in the velocity gradient direction), droplet migration toward the centerline (due to wall effects), and droplet packing constraints. We also study the effects of mixture composition on droplet microstructure, and summarize these results in the form of a morphology diagram in the parameter space of mass fraction and shear rate. We find that formation of strings of the suspended phase (reported earlier by our group in flow-visualization studies on confined emulsions) is observed over a broad composition window. We also find a stable (nontransient) morphology wherein the droplets are arranged in highly ordered pearl-necklace chain structures.

Acoustic Streaming and Its Applications

Abstract: Broadly speaking, acoustic streaming is generated by a nonlinear acoustic wave with a finite amplitude propagating in a viscid fluid. The fluid volume elements of molecules, d V , are forced to oscillate at the same frequency as the incident acoustic wave. Due to the nature of the nonlinearity of the acoustic wave, the second-order effect of the wave propagation produces a time-independent flow velocity (DC flow) in addition to a regular oscillatory motion (AC motion). Consequently, the fluid moves in a certain direction, which depends on the geometry of the system and its boundary conditions, as well as the parameters of the incident acoustic wave. The small scale acoustic streaming in a fluid is called “microstreaming”. When it is associated with acoustic cavitation, which refers to activities of microbubbles in a general sense, it is often called “cavitation microstreaming”. For biomedical applications, microstreaming usually takes place in a boundary layer at proximity of a solid boundary, which could be the membrane of a cell or walls of a container. To satisfy the non-slip boundary condition, the flow motion at a solid boundary should be zero. The magnitude of the DC acoustic streaming velocity, as well as the oscillatory flow velocity near the boundary, drop drastically; consequently, the acoustic streaming velocity generates a DC velocity gradient and the oscillatory flow velocity gradient produces an AC velocity gradient; they both will produce shear stress. The former is a DC shear stress and the latter is AC shear stress. It was observed the DC shear stress plays the dominant role, which may enhance the permeability of molecules passing through the cell membrane. This phenomenon is called “sonoporation”. Sonoporation has shown a great potential for the targeted delivery of DNA, drugs, and macromolecules into a cell. Acoustic streaming has also been used in fluid mixing, boundary cooling, and many other applications. The goal of this work is to give a brief review of the basic mathematical theory for acoustic microstreaming related to the aforementioned applications. The emphasis will be on its applications in biotechnology.