This paper focuses on the theoretical treatment of the laminar, incompressible, and time-dependent flow of a viscous fluid in a porous channel with orthogonally moving walls. Assuming uniform injection or suction at the porous walls, two cases are considered for which the opposing walls undergo either uniform or nonuniform motions. For the first case, we follow Dauenhauer and Majdalani ͓Phys. Fluids 15, 1485 ͑2003͔͒ by taking the wall expansion ratio ␣ to be time invariant and then proceed to reduce the Navier-Stokes equations into a fourth order ordinary differential equation with four boundary conditions. Using the homotopy analysis method ͑HAM͒, an optimized analytical procedure is developed that enables us to obtain highly accurate series approximations for each of the multiple solutions associated with this problem. By exploring wide ranges of the control parameters, our procedure allows us to identify dual or triple solutions that correspond to those reported by Zaturska et al. ͓Fluid Dyn. Res. 4, 151 ͑1988͔͒. Specifically, two new profiles are captured that are complementary to the type I solutions explored by Dauenhauer and Majdalani. In comparison to the type I motion, the so-called types II and III profiles involve steeper flow turning streamline curvatures and internal flow recirculation. The second and more general case that we consider allows the wall expansion ratio to vary with time. Under this assumption, the Navier-Stokes equations are transformed into an exact nonlinear partial differential equation that is solved analytically using the HAM procedure. In the process, both algebraic and exponential models are considered to describe the evolution of ␣͑t͒ from an initial ␣ 0 to a final state ␣ 1. In either case, we find the time-dependent solutions to decay very rapidly to the extent of recovering the steady state behavior associated with the use of a constant wall expansion ratio. We then conclude that the time-dependent variation of the wall expansion ratio plays a secondary role that may be justifiably ignored.

PCE has reached 25.5% in less than one decade since the first report of all-solid-state PSCs in 2012. [5][6][7] Although remarkable progress has been made in device efficiency, there is still a huge gap toward the theoretical Shockley-Queisser limit efficiency (30.5%). [8] Besides the PCE, the long-term stability of PSCs is of great significance for commercial applications, but it could be affected by the interfacial degradation induced by various stresses. [3,4] In a typical planar n-i-p PSC structure, the perovskite absorber is sandwiched between an electron transport layer (ETL) and hole transport layer (HTL). The interfaces between perovskite and carrier transport layers have been considered crucial for the further improvement of efficiency and stability of PSCs. [9,10] On the one hand, the interfacial defects and imperfect band alignments would result in substantial nonradiative recombination losses and thus compromised PCE. [11,12] On the other hand, the degradation of PSCs derived from both perovskite/HTL interfaces and ETL/perovskite interfaces severely threatens the stability of PSCs. [13][14][15][16] Plenty of research has concentrated on stabilizing perovskite/ HTL interfaces via post-fabrication treatment and HTL modification. [17] However, the concentration of defects accumulating at the buried interface is even higher than that at the top interface, [18] which makes the buried interface equally significant as the top interface. Unfortunately, little attention has been paid to it, which is partly because of the difficulties in fabricating and investigating the buried interface. [19] Moreover, the perovskite film near the ETL interface bears the strongest illumination stress under operational condition. Especially under UV exposure, the photovoltaic (PV) performance of PSCs could drop dramatically with the halogen oxidation and Pb reduction because of the vulnerability of perovskite to UV light. [20,21] This process is further accelerated by the desorption of UV-activated oxygen from ETLs, which also exposes deep-level interfacial defects and thus affecting the charge collection. [22][23][24] Although various strategies have been adopted to modify the ETLs to reduce defects, [25][26][27][28][29] there is little research effort on the interaction between the modified ETLs and perovskite films. Recently, Dong and co-workers reported a perovskite/ ETL interface enhancement strategy where formamidinium iodide incorporated SnO 2 reacts with PbI 2 -excess perovskiteThe buried interface between the perovskite and the electron transport layer (ETL) plays a vital role for the further improvement of power conversion efficiency (PCE) and stability of perovskite solar cells (PSCs). However, it is challenging to efficiently optimize this interface as it is buried in the bottom of the perovskite film. Herein, a buried interface strengthening strategy for constructing efficient and stable PSCs by using CsI-SnO 2 complex as an ETL is reported. The CsI modification facilitates the growth of the perovskite film and eff...

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