April 2025
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Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the flow-induced deformation of the conduit due to slow viscous flow within. Elucidating the two-way coupling between oscillatory flow and deformation of a three-dimensional (3D) rectangular channel is crucial for designing lab- and organ-on-a-chip microsystems and eventually understanding flow-structure instabilities that can enhance mixing and transport. We determine the axial variations of the primary flow, pressure, and deformation for Newtonian fluids in the canonical geometry of a slender (long) and shallow (wide) 3D rectangular channel with a deformable top wall under the assumption of weak compliance and without restriction on the oscillation frequency (i.e., on the Womersley number). Unlike rigid conduits, the pressure distribution is not linear with the axial coordinate. To validate this prediction, we design a PDMS-based experimental platform with a speaker-based flow-generation apparatus and a pressure acquisition system with multiple ports along the axial length of the channel. The experimental measurements show good agreement with the predicted pressure profiles across a wide range of the key dimensionless quantities: the Womersley number, the compliance number, and the elastoviscous number. Finally, we explore how the nonlinear flow -- deformation coupling leads to self-induced streaming (rectification of the oscillatory flow). Following Zhang and Rallabandi (J. Fluid Mech., 996, 2024, A16), we develop a theory for the cycle-averaged pressure based on the primary problem's solution, and we validate the predictions for the axial distribution of the streaming pressure against high-precision experimental measurements.
![Comparison of conventional and photothermal de‐icing techniques. a) Ice adhesion strength reported in the past literature for various surface designs, along with the corresponding working mechanisms shown above. For a summary of all data, please see Table S1 (Supporting Information).[9–14,23] Error bars for each data are not shown for clarity. Schematics showing typical passive de‐icing approaches: b) electro‐thermal approach,[15,26] c) air‐induced shear,[²⁷] d) low pressure driven self‐lodging,[²⁸] e) gravity driven ice shedding.[²⁴] f) Comparison in ice adhesion strength between non‐photothermal and photothermal approaches. Photothermal‐assisted interfacial ice melting and its advantage in ice shedding from g) small‐scale[³²] to h) large‐scale applications. Schematics not to scale. d) Adapted under the terms of the CCBY Creative Commons Attribution 4.0 International license.[²⁸] Copyright 2023, The Authors, published by Springer Nature. f) Adapted with permission.[³¹] Copyright 2023, Springer Nature. h) Adapted with permission.[³³] Copyright 2022, Wiley‐VCH GmbH.](https://www.researchgate.net/publication/387336164/figure/fig1/AS:11431281310795859@1739976584889/Comparison-of-conventional-and-photothermal-de-icing-techniques-a-Ice-adhesion-strength_Q320.jpg)
![Mechanisms governing the three typical photothermal effects. a) Plasmonic localized heating.[³⁵] b) Non‐radiative relaxation.[³⁵] c) Thermal vibration in molecules.[³⁵] a1‐c1) Adapted with permission.[³⁵] Copyright 2019, the Royal Society of Chemistry. a2) Adapted with permission.[³⁹] Copyright 2019, Elsevier; Copyright 2014, Springer. b2) Adapted with permission.[⁴¹] Copyright 2017, Wiley‐VCH GmbH. c2) Adapted with permission.[³⁸] Copyright 2020, Springer. The color band on top denotes the wavelength of excitation where each photothermal heating mode is dominant. Schematics not to scale.](https://www.researchgate.net/publication/387336164/figure/fig2/AS:11431281310758193@1739976585094/Mechanisms-governing-the-three-typical-photothermal-effects-a-Plasmonic-localized_Q320.jpg)
![De‐icing performance based on plasmonic localized heating. a) TEM and SEM images of typical nanoparticles that exhibit plasmonic localized heating. Reproduced with permission.[45,50,53] Copyright 2016, American Chemical Society; Copyright 2022, Elsevier; Copyright 2022, Wiley‐VCH GmbH; Copyright 2021, Cell Press. b) The variation of spectra as a function of nanorod aspect ratio of nanorods. Adapted with permission.[⁵⁷] Copyright 2014, Springer Nature. c) UV‐visible absorbance spectra of Ag nanocubes and Au nanocages. The Au nanocages are prepared by adding different volumes of 0.1 mM HauCl4 solution: from left to right on the x‐axis, 0, 0.3, 0.5, 1.0, 1.5, 2.0, 4.0, and 5.5 mL. Adapted with permission.[⁵⁸] Copyright 2014, Springer. d) Month eye‐inspired design for sunlight trapping. Adapted with permission.[⁵⁰] Copyright 2021, Elsevier. e) Cactus‐inspired design for sunlight trapping and the f) overall spectral absorptance across the UV, visible, and infrared wavelengths on the surface of a superhydrophobic selective solar absorber (SHSSA), superhydrophobic black absorber (SHB), and selective solar absorber (SSA). Adapted with permission.[⁵⁹] Copyright 2021, Cell Press. g) Temperature rise of different photothermal designs under different substrate temperature and sunlight illuminations. Data obtained from literature sources.[33,48–51,53,59,60] For a Summary of the data, please see Table S2 (Supporting Information). h) Photograph of a sessile water droplet residing on a surface which is at ultralow cryogenic temperatures down to ‐60 °C before freezing on a TiN‐particle decorated superhydrophobic surface. Reproduced with permission.[⁵⁹] Copyright 2021, Cell Press. i) Complete de‐icing achieved on an FBC/TiN nanoparticle‐coated surface under sun illumination. Reproduced with permission.[⁶⁰] Copyright 2022, Elsevier.](https://www.researchgate.net/publication/387336164/figure/fig3/AS:11431281310758195@1739976585305/De-icing-performance-based-on-plasmonic-localized-heating-a-TEM-and-SEM-images-of_Q320.jpg)
![De‐icing performance of materials undergoing non‐radiative relaxation. a) SEM images of representative semiconductor particles and composites. Reproduced with permission.[41,61] Copyright 2017, Wiley‐VCH GmbH; Copyright 2023, American Chemical Society; Copyright 2022, Elsevier; Copyright 2021, Elsevier. b) The band structure and the correspondent optical absorption curves of a pristine semiconductor, doping‐induced shallow‐level and deep‐level states, and doping‐induced bandgap narrowing. Adapted with permission.[⁶⁷] Copyright 2015, the Royal Society of Chemistry. c) Schematics of electro‐hole generation and relaxation enabled by the conventional bulk Ti2O3 with a comparatively high bandgap and Ti2O3 nanoparticles with a narrow bandgap (0.1 eV), and d) the correspondent reflectance spectra of these two materials as well as commercial TiO2 and graphite. Reproduced with permission.[⁴¹] Copyright 2017, Wiley‐VCH GmbH. e) Light trapping effect due to the hierarchical structure, together with the non‐radiative relation effect of Fe3O4 nanoparticles, resulting in efficient surface heating. Reproduced with permission.[⁶¹] Copyright 2022, Elsevier. f) Photothermal design using hierarchical structure as well as varied surface compositions Reproduced with permission.[⁶⁴] Copyright 2021, National Academy of Sciences. g) Temperature rise of non‐radiative relaxation designs under different substrate temperature and sunlight illuminations in literature. Data obtained from literature sources.[21,61,64] For a Summary of the data, please see Table S3 (Supporting Information). PDMS is the abbreviation of Polydimethylsiloxane. h) The efficiency in photothermal trap of cermet (MT1300 mirotherm®, Alanod GmbH) coating leads to a substantial rise in surface temperature under a subzero ambient temperature, which promotes the melting and complete shedding of frozen droplets and i) snow after 5 min of illumination. Adapted under the terms of the CC‐BY Creative Commons Attribution 4.0 International license.[²¹] Copyright 2022, The Authors, some rights reserved, exclusive licensee AAAS. j) The efficient de‐icing performance manifested on a double‐layer solar thermal coating composed of SiO2 nanospheres and CuFeMnO4 semiconductor. Reproduced with permission.[⁶¹] Copyright 2021, Elsevier.](https://www.researchgate.net/publication/387336164/figure/fig4/AS:11431281310786827@1739976585569/De-icing-performance-of-materials-undergoing-non-radiative-relaxation-a-SEM-images-of_Q320.jpg)
![De‐icing performance of materials undergoing thermal vibration in molecules. a) SEM images of representative carbon‐based particles and composites. Reproduced with permission.[70,72,74] Copyright 2022, Elsevier; Copyright 2018, Wiley‐VCH GmbH; Copyright 2017, Wiley‐VCH GmbH; Copyright 2019, American Chemical Society. b) The structures formed by carbon nanospheres exhibit the enhanced light trapping ability, while the underlying porous PDMS layer shows the capability to insulate conduction losses into the substrate, both of which govern the interface temperature rise. Reproduced with permission.[⁷³] Copyright 2023, Elsevier. c) Hierarchical rGO structures showing the increased light trapping. Adapted with permission.[⁷⁶] Copyright 2020, Royal Society of Chemistry. d) Temperature variation of different samples with various rGO contents under one‐sun illumination for 400 s. EPG, SPG, and HPG refers to emulsion templated PDMS/rGO, sugar templated PDMS/rGO, and hierarchical structured PDMS/rGO, respectively. Reproduced with permission.[⁷⁶] Copyright 2020, Royal Society of Chemistry. e) Temperature rise of molecular thermal vibration designs under different ambient temperatures and sunlight illuminations. Data obtained from literature sources.[48,71,73,75–79,82] For a Summary of the data, please see Table S4 (Supporting Information). f) Time‐lapse images of frozen droplet sliding on the hierarchical structured PDMS/rGO coating, at −35 °C ambient temperature under one‐sun illumination. Reproduced with permission.[⁷⁶] Copyright 2020, Royal Society of Chemistry. g) Long‐term solar thermal deicing performance under rime and glaze icing conditions. Reproduced with permission.[⁷⁶] Copyright 2020, Royal Society of Chemistry.](https://www.researchgate.net/publication/387336164/figure/fig5/AS:11431281310728701@1739976585859/De-icing-performance-of-materials-undergoing-thermal-vibration-in-molecules-a-SEM_Q320.jpg)
![Asymmetric oxidation of a GUV encapsulating a photosensitizer (PS) and modes of membrane rupture observed in experiments. A) Morphological modifications of a GUV encapsulating PS undergoing photosensitized oxidation. The inset shows the distribution of lipid oxidation products in the lipid bilayer. Initially the vesicle membrane maintains a symmetric configuration of unoxidized lipids (LH). i) In the contact independent reaction pathway, lipids oxidize symmetrically across the membrane to produce LOOH (with a cylindrical shape) with an addition of ─OOH (blue circle). ii) In the contact dependent reaction pathway, LH and LOOH further oxidize to form truncated lipids (with a conical shape) bearing a polar group at the truncated tail (orange circle: an aldehyde (─CHO) or a carboxyl (─COOH)). Asymmetric oxidation leads to asymmetric distribution of oxidized lipid products in inner (IL) and outer (OL) leaflets. B–D) Modes of membrane rupture for GUVs (encapsulated PS concentration c = 20 mM), showing B) no‐curling, C) curling, and D) pore. In the no‐curling mode (B) of vesicle explosion, the sprouting of tubules‐like structures around the rim with no accumulation is observed. Meanwhile, in the curling mode (C) of vesicle explosion, a bright spot showing lipid accumulation around the pore rim grows as the explosion progresses. In other cases, a transient pore forms and reseals (D) without vesicle explosion. Here, t = 0 is defined as the moment when membrane rupture is observed. In (B–D), the fluorescent signal could be a mixed signal from the lipid label and HPTS. Additionally, we note that HPTS is not expected to be absorbed inside the membrane layer due to the polar nature and high solubility of HPTS in aqueous solutions.[34,35] Scale bars are 10 µm.](https://www.researchgate.net/publication/383085478/figure/fig2/AS:11431281284068997@1729086571379/Asymmetric-oxidation-of-a-GUV-encapsulating-a-photosensitizer-PS-and-modes-of-membrane_Q320.jpg)
![Vesicle rupture and explosion statistics. A) Fraction of vesicles responding in different modes during the light illumination. No vesicle survives at higher PS concentration differences (Δc=$\Delta c=$ 10, 15, and 20 mM). Error bars represent the standard error of a proportion,[⁴⁴] with negative errors truncated to zero. B) Probability density of vesicle collapse time, Tcol${T}_{\mathrm{col}}$, at different Δc$\Delta c$. C) Vesicle exposure time, Texp${T}_{\exp}$, for PS concentration differences Δc=$\Delta c=$ 10, 15, and 20 mM. The box‐plot represents the distribution of Texp${T}_{\exp}$ based on first quartile, median (red line), and third quartile.[⁴⁵] The whiskers extend to the minimum and maximum values of Texp${T}_{\exp}$ excluding outliers. For a given Δc$\Delta c$, the median values of Texp${T}_{\exp}$ increases across the modes of no‐curling, curling, and transient pores, respectively. D) Non‐monotonic evolution of Gaussian‐weighted moving average Tcol${T}_{\mathrm{col}}$ with Texp${T}_{\exp}$. The zoomed‐in inset shows an initial decrease of Tcol${T}_{\mathrm{col}}$ with the increasing Texp${T}_{\exp}$.](https://www.researchgate.net/publication/383085478/figure/fig3/AS:11431281284068998@1729086571549/Vesicle-rupture-and-explosion-statistics-A-Fraction-of-vesicles-responding-in-different_Q320.jpg)
