Fluid transport by a single active filament in a three-dimensional two-phase flow

TL;DR

This work addresses how a single active filament can drive fluid transport in a 3D two-phase mucociliary-like system. It couples a slender elastic filament to a Shan-Chen two-phase lattice Boltzmann solver via immersed boundary methods, with beating implemented by a time-varying basal angle and bending stiffness. Key findings show that net forward transport arises from a spatially asymmetric beat; transport is optimized by moderate PCL thickness $L_{ m PCL}$, viscosity ratio $r_ u$, and high bending stiffness $r_B$, due to the interplay of drag-elastic balance and viscous diffusion of momentum, and the flow-rate–beat relationship can be quantified through tip amplitude and beating asymmetry. The results provide mechanistic insight into mucociliary clearance and a framework for exploring disease states and ciliated devices, with future work aimed at incorporating non-Newtonian mucus rheology and ciliary metachrony.

Abstract

Micro-scale cilia play a vital role in mucociliary clearance (MCC) in the human respiratory airways. In this numerical study, we examine fluid transport driven by the active beating of a single filament immersed in a three-dimensional two-phase flow. The cilium is modeled as an elastic filament actuated by a time-varying basal angle. The two-phase flow is resolved using the Shan-Chen model in a lattice Boltzmann solver, while the two-way coupling between the filament and the fluid is treated by the immersed boundary method. Pathological conditions such as cystic fibrosis and chronic obstructive pulmonary disease are associated with drastic alterations of MCC properties, including changes in periciliary layer (PCL) thickness and the viscosity ratio between the PCL and the mucus layer (ML). Here, we systematically investigate the effects of these parameters, along with filament bending stiffness, on the beating pattern and fluid transport. Within the parameter ranges investigated, a moderate PCL thickness and viscosity ratio, together with high bending stiffness, tend to yield higher net flow rate and transport efficiency. The underlying hydrodynamic mechanisms are characterized through analyses of the beating pattern, filament dynamics, energy partition, and flow-field evolution. Two competing mechanisms are identified: the drag-elastic force balance and the viscous diffusion of momentum. Furthermore, quantitative relationships are established between flow rate and beating pattern, expressed in terms of tip amplitude and beating asymmetry.

Figures (17)

• Figure 1: (a) Schematic of a filament in the computational domain (not in scale), where the filament beats in the plane $y=0.5L$. (b) Schematic of a beating filament actuated by its basal angle ($\theta(t)$).
• Figure 2: (a) Schematic of a filament in an uniform flow (not in scale). (b) Time histories of the $x$-position of the filament tip ($x_{\mathrm{tip}}^*$).
• Figure 3: Time histories of (a) the $x$-position of the filament tip ($x_{\mathrm{tip}}^*$) and (b) the flow rate ($Q^*$) in one beating period for different grid sizes $\Delta h^*$ and time steps $\Delta t^*$ (PCL thickness $L_\mathrm{PCL}^*=0.9$, viscosity ratio $r_\nu = 50$, bending stiffness ratio $r_B = 10$).
• Figure 4: (a) Superimposed instantaneous filament shapes in one beating period. The red dashed line represents the tip trajectory of the filament. The red arrow indicates the direction of tip movement during the power stroke. The grey dashed line represents the initial interface between the PCL and the ML. (b) Fluid displacement in the $x$-direction ($d_x^*$) as a function of $z^*$ in one beating period ($L_\mathrm{PCL}^*=0.8$, $r_\nu = 10$, $r_B = 70$).
• Figure 5: Time histories of (a) the flow rate ($Q^*$), (b) the $x$-component of the fluid force ($F^{\mathrm{IB} *}_x$) and its decomposition into contributions from the PCL and ML, (c) the $x$-position of the filament tip ($x_{\mathrm{tip}}^*$) and basal angle ($\theta (t)$), (d) the $z$-position of the filament tip ($z_{\mathrm{tip}}^*$), (e) the kinetic energy ($E_{\mathrm{ks}}^*$), and (f) the elastic strain energy ($E_{\mathrm{es}}^*$) of the filament ($L_\mathrm{PCL}^*=0.8$, $r_\nu = 10$, $r_B = 70$). The vertical dotted lines correspond to the instants $t^*=$ 0.07, 0.18 and 0.93.