Active control of dispersion within a channel with flow and pulsating walls

Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

“…We remark that there are two subtle differences compared with the previous studies [45,46,42]. First, the previous studies made not only the ansatz of the expansion of T , but also the expansion of T .…”

“…By utilizing the first-order approximation of the cross-sectional averaged concentration, we present a nonnegative asymptotic expansion of the scalar field at long times which captures the transverse variations. We document situations in which a time varying cell problem produces a more accurate approximation than the parametric (adiabatic) approach employed recently [45,46,42]. In section 4, we demonstrate that a class of flows with finite correlation time will induce a deterministic effective diffusivity at long times.…”

“…After that, based on the Aris' moment method, a number of studies reported on the enhanced diffusivity induced by the single-frequency pulsating flow [15,25,63,47,38], the single frequency Couette-Poiseuille [10,49,12,11] and the multi-frequency flow [61,62,29]. Alternative approaches, using center manifold theory, [45,46,42,43] or homogenization methods [27,28] not only predict the effective diffusivity but also gives the direct expression for the full concentration field at long times.…”

“…Here, with the center manifold theory, we present a systematic procedure to construct an approximation to capture the traverse variation of the scalar field. Second, several interesting articles [45,46,42] implemented center manifold theory for such unsteady problems employing certain slowly varying assumptions to simplify the calculation. Such assumptions restrict the applicability of the effective dynamics.…”

Changing flows balance nutrient absorption and bacterial growth along the gut

“…Gut motility [11][12][13][14] further affects nutrient absorption, while motility patterns vary, with peristalsis prevalent during starvation [11][12][13][14][15][16][17][18][19] and the 'checkerboard-like' segmentation pattern during digestion after food intake [11][12][13][14]. From a physics perspective gut motility drives fluid flows [15,16] and thus impacts the dispersion and transport of solutes [20][21][22][23]. Gut motility may therefore well control nutrient absorption and bacterial densities [17] with all processes being highly intertwined.…”