Reducing wall drag in turbulent pipe and channel flows is an issue of great practical importance. In engineering applications, end-functionalized polymer chains are often employed as agents to reduce drag. These are polymers which are floating in the solvent and attach (either by adsorption or through irreversible chemical binding) at one of their chain ends to the substrate (wall). We propose a PDE model to study this setup in the simple setting where the solvent is a viscous incompressible Navier–Stokes fluid occupying the bulk of a smooth domain Ω⊂ℝ𝑑, and the wall-grafted polymer is in the so-called mushroom regime (inter-polymer spacing on the order of the typical polymer length). The microscopic description of the polymer enters into the macroscopic description of the fluid motion through a dynamical boundary condition on the wall-tangential stress of the fluid, something akin to (but distinct from) a history-dependent slip-length. We establish the global well-posedness of strong solutions in two-spatial dimensions and prove that the inviscid limit to the strong Euler solution holds with a rate. Moreover, the wall-friction factor ⟨𝑓⟩ and the global energy dissipation ⟨𝜀⟩ vanish inversely proportional to the Reynolds number 𝐑𝐞. This scaling corresponds to Poiseuille’s law for the friction factor ⟨𝑓⟩∼1/𝐑𝐞 for laminar flow and thereby quantifies drag reduction in our setting. These results are in stark contrast to those available for physical boundaries without polymer additives modeled by, for example, no-slip conditions, where no such results are generally known even in two-dimensions.
more »
« less
Boundaries control active channel flows
Boundary conditions dictate how fluids, including liquid crystals, flow when pumped through a channel. Can boundary conditions also be used to control internally driven active fluids that generate flows spontaneously? By using numerical simulations and stability analysis we explore how parallel surface anchoring of active agents at the boundaries and substrate drag can be used to rectify coherent flow of an active polar fluid in a 2D channel. Upon increasing activity, a succession of dynamical states is obtained, from laminar flow to vortex arrays to eventual turbulence, that are controlled by the interplay between the hydrodynamic screening length and the extrapolation length quantifying the anchoring strength of the orientational order parameter. We highlight the key role of symmetry in both flow and order and show that coherent laminar flow with net throughput is only possible for weak anchoring and intermediate activity. Our work demonstrates the possibility of controlling the nature and properties of active flows in a channel simply by patterning the confining boundaries.
more »
« less
- Award ID(s):
- 2041459
- NSF-PAR ID:
- 10383428
- Date Published:
- Journal Name:
- Frontiers in Physics
- Volume:
- 10
- ISSN:
- 2296-424X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The effect of slip surfaces on the laminar–turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. In laminar flows, the inclusion of the slip surfaces results in a drag reduction of over 10 %, which is in good agreement with previous studies and the theory of laminar slip flows. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. We show that slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and the likelihood is further decreased as slip length is increased. A more deterministic analysis of the effects of slip surfaces on a transition to turbulence is performed by using nonlinear travelling-wave solutions to the Navier–Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham, J. Fluid Mech. , vol. 782, 2015, pp. 430–454). Additionally, they exhibit distinct flow structures – the P3 and P4 are denoted as core mode and critical-layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin-friction evolution, linear growth rate and phase-space projection of transitional trajectories. The slip surface appears to modify the transition dynamics very little for the core mode, but quite considerably for the critical-layer mode. Most importantly, the slip surface promotes different transition dynamics – an early and bypass-like transition for the core mode and a delayed and H- or K-type-like transition for the critical-layer mode. We explain these distinct transition dynamics based on spatio-temporal and quadrant analyses. It is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while long sustained ejection events are present in the region of the $\unicode[STIX]{x1D6EC}$ -shaped vortex cores close to the critical layer, resulting in a delayed transition. This should motivate flow control strategies to fully exploit these distinct transition dynamics for transition to turbulence.more » « less
-
Active matter consumes local fuels to self-propel. When confined in a closed circular boundary, they can self-organize into a circulatory flow. Such coherence originates from the interactions between the active matter and boundaries, and boundary conditions play an important role on self-organization of active fluid. Herein, we probed how fluid boundaries influenced the self-organization of active fluid. The fluid boundaries were created by confining the active fluid in a compressed water-in-oil droplet. Due to surface tension, the droplet shaped into a cylinder-like geometry. Since water and oil were both fluids, their interface was fluid. We systematically probed how droplet shapes and the amount of oil surrounding the droplet influenced the development of circulation. We found that the formation of circulatory flows depended on the thickness of the oil layer surrounding the droplet, implying that the fluid dynamics between the active fluid within the droplet and the oil outside the droplet were coupled. We used a 3D COMSOL-based simulation successfully reproduced such oil-layer dependence. Finally, we developed two milli-fluidic devices to deform the droplet and alter the oil layer thickness manually to trigger and suppress the intra-droplet circulatory flow in real time.more » « less
-
When fluids flow through straight channels sustained turbulence occurs only at high Reynolds numbers [typically [Formula: see text]]. It is difficult to mix multiple fluids flowing through a straight channel in the low Reynolds number laminar regime [[Formula: see text]] because in the absence of turbulence, mixing between the component fluids occurs primarily via the slow molecular diffusion process. This Letter reports a simple way to significantly enhance the low Reynolds number (in our case [Formula: see text]) passive microfluidic flow mixing in a straight microchannel by introducing asymmetric wetting boundary conditions on the floor of the channel. We show experimentally and numerically that by creating carefully chosen two-dimensional hydrophobic slip patterns on the floor of the channels, we can introduce stretching, folding, and/or recirculation in the flowing fluid volume, the essential elements to achieve mixing in the absence of turbulence. We also show that there are two distinctive pathways to produce homogeneous mixing in microchannels induced by the inhomogeneity of the boundary conditions. It can be achieved either by (1) introducing stretching, folding and twisting of fluid volumes, i.e., via a horse-shoe type transformation map, or (2) by creating chaotic advection, achieved through manipulation of the hydrophobic boundary patterns on the floor of the channels. We have also shown that by superposing stretching and folding with chaotic advection, mixing can be optimized in terms of significantly reducing mixing length, thereby opening up new design opportunities for simple yet efficient passive microfluidic reactors.more » « less
-
The transition from laminar to turbulent flow is of great interest since it is one of the most difficult and unsolved problems in fluids engineering. The transition processes are significantly important because the transition has a huge impact on almost all systems that come in contact with a fluid flow by altering the mixing, transport, and drag properties of fluids even in simple pipe and channel flows. Generally, in most transportation systems, the transition to turbulence causes a significant increase in drag force, energy consumption, and, therefore, operating cost. Thus, understanding the underlying mechanisms of the laminar-to-turbulent transition can be a major benefit in many ways, especially economically. There have been substantial previous studies that focused on testing the stability of laminar flow and finding the critical amplitudes of disturbances necessary to trigger the transition in various wall-bounded systems, including circular pipes and square ducts. However, there is still no fundamental theory of transition to predict the onset of turbulence. In this study, we perform direct numerical simulations (DNS) of the transition flows from laminar to turbulence in a channel flow. Specifically, the effects of different magnitudes of perturbations on the onset of turbulence are investigated. The perturbation magnitudes vary from 0.001 (0.1%) to 0.05 (5%) of a typical turbulent velocity field, and the Reynolds number is from 5,000 to 40,000. Most importantly, the transition behavior in this study was found to be in good agreement with other reported studies performed for fluid flow in pipes and ducts. With the DNS results, a finite amplitude stability curve was obtained. The critical magnitude of perturbation required to cause transition was observed to be inversely proportional to the Reynolds number for the magnitude from 0.01 to 0.05. We also investigated the temporal behavior of the transition process, and it was found that the transition time or the time required to begin the transition process is inversely correlated with the Reynolds number only for the magnitude from 0.02 to 0.05, while different temporal behavior occurs for smaller perturbation magnitudes. In addition to the transition time, the transition dynamics were investigated by observing the time series of wall shear stress. At the onset of transition, the shear stress experiences an overshoot, then decreases toward sustained turbulence. As expected, the average values of the wall shear stress in turbulent flow increase with the Reynolds number. The change in the wall shear stress from laminar to overshoot was, of course, found to increase with the Reynolds number. More interestingly was the observed change in wall shear stress from the overshoot to turbulence. The change in magnitude appears to be almost insensitive to the Reynolds number and the perturbation magnitude. Because the change in wall shear stress is directly proportional to the pumping power, these observations could be extremely useful when determining the required pumping power in certain flow conditions. Furthermore, the stability curve and wall shear stress changes can be considered robust features for future applications, and ultimately interpreted as evidence of progress toward solving the unresolved fluids engineering problem.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fphy.2022.948415
