## 1 Introduction  
Airway surface liquid (ASL) covers the respiratory epithelia that is mainly comprised of two distinct layers: mucus layer (ML)--a non-homogenous, non-Newtonian, viscoelastic fluid [1]; and periciliary liquid layer (PCL)--treated as a watery lubricating (nearly Newtonian) fluid layer with much less viscosity [2]. Transport of the ASL is of vital importance to keep the respiratory system clear from inhaled particulate matters deposited on the ML. Such clearance mechanism is facilitated by periodic ciliary actions, with the ASL being swept forward during the effective stroke and backward during the recovery stroke [3]. Ineffective and poor mucus clearance is a major factor for lung health. There are generally two main reasons for muco-ciliary dysfunction in the respiratory system: airway mucosal diseases (such as cystic fibrosis (CF), chronic obstructive pulmonary disease (COPD), asthma, etc.) and ciliary abnormalities. Mucosal diseases occur in patients as a result of the conversion from healthy to pathologic mucus, where the mucus hydration and its biochemical constituents change by multiple mechanisms, leading to higher viscosity and elasticity of the mucus (see [PERSON] and [PERSON] [4], and the references therein). Defects in ciliary structure and function can cause abnormal ciliary beating. Primary ciliary dyskinesia (PCD) is known as the most significant disorder causing ciliary abnormalities [5]. There is fairly a limited number of numerical studies in the literature with the focus of modelling of diseased lungs. [PERSON] and [PERSON] [6] emulated diseased environments in their 2D simulations by varying the viscoelastic properties and the thickness of the ML. Their findings revealed that the effects of the mucus elasticity depends very much on the ML thickness. Specifically, for the diseased states (thinner PCL), the higher elasticity led to a decrease in the mucus transport, whereas an opposite trend was observed for the healthy states. [PERSON] et al. [7] attempted to simulate the high viscous effect of pathologic mucus in CF three-dimensionally by taking into account the highly shear-thinning nature of mucus and thus the non-Newtonian effects on the muco-ciliary clearance. Based on the mucus samples collected from patients with and without CF disorder, they concluded that shear-thinning effects can be of the same order as the viscoelastic effects for the mucus transport. [PERSON] et al. [8] studied ASL flow physics two-dimensionally in the presence of cilia beating under various ciliary abnormalities, such as ciliary beat pattern, length of cilia, immotile cilia, beating amplitude, and uncoordinated beating of cilia. According to the results obtained, each of the above ciliary abnormalities could greatly reduce the process of mucus clearance, except for uncoordinated beating. The ultimate goal of this paper is to obtain a clear understanding of how the epithelial cilia-driven fluid flows perform under various ciliary abnormalities in respiratory diseases. Such abnormalities, whether inherited (genetic disorder) or acquired, are directly linked to lung infection and chronic respiratory diseases in humans. Table 1 summarises the most common lung disorders along with their damaging effects on the ciliary function. More details on various types of ciliary abnormalities, such as PCD, CF, asthma, and COPD, can be found in [5; 9; 10]. We therefore performed a parametric analysis to investigate the effects of ciliary abnormalities, like low beating frequency, short length, abnormal beating pattern, and reduced ciliary density, as well as epithelium patchiness due to missing cilia on the PCL transport as an extension to previous work reported in Reference [23]. To achieve this, the three-dimensional equations of fluid motion are solved using the IB method coupled with finite-difference projection method. Some theoretical studies have concluded that the PCL remains stationary during the process of clearance [24; 25; 26; 27; 28; 29]. However,