Molecular and mechanical insights into gecko seta adhesion: multiscale simulations combining molecular dynamics and the finite element method

• Yash Jain,
• Saeed Norouzi,
• Tobias Materzok,
• Stanislav N. Gorb and
• Florian Müller-Plathe

Beilstein J. Nanotechnol. 2025, 16, 2055–2076, doi:10.3762/bjnano.16.141

• University, Am Botanischen Garten 1–9, D-24118 Kiel, Germany 10.3762/bjnano.16.141 Abstract Gecko adhesion, enabled by micro- and nanoscale structures known as setae and spatulae, has prompted extensive research. We present a concurrent multiscale computational model of a seta that integrates molecular

• . The model reproduces key aspects of spatula behavior during adhesion and detachment, showing that spatula–substrate contact evolves through a combination of bending, sliding, and peeling, depending on the spatula’s initial orientation. Our results further demonstrate that lateral sliding can delay

• microscopy (AFM) experiments. Our investigation into how gecko keratin interacts with hydrophilic and hydrophobic substrates [12] supported the importance of the water-mediating effect [10] and elucidated mechanistic differences depending on surface chemistry. A particle-based mesoscale model of a single

The cement of the tube-dwelling polychaete Sabellaria alveolata: a complex composite adhesive material

• Emilie Duthoo,
• Aurélie Lambert,
• Pierre Becker,
• Carla Pugliese,
• Jean-Marc Baele,
• Arnaud Delfairière,
• Matthew J. Harrington and
• Patrick Flammang

Beilstein J. Nanotechnol. 2025, 16, 1998–2014, doi:10.3762/bjnano.16.138

• of inspiration for developing biomimetic adhesives. However, a thorough understanding of their composition and operating mechanism is essential for advancing such applications. Sabellariid tubeworms are model organisms in bioadhesion research, and their adhesive system has been characterized in

• several studies. However, some aspects of cement formation are still poorly understood and several differences have been pointed out between the two main model species. This study aims to investigate the adhesive system of Sabellaria alveolata by identifying new potential adhesive proteins, as well as

• underwater adhesive materials for various applications, particularly in the industrial and biomedical fields [3][4]. Polychaetes of the family Sabellariidae are one of the model organisms that have been studied extensively for their adhesion and have fascinated researchers since the 18th century [5]. Two

Mechanical property measurements enabled by short-term Fourier-transform of atomic force microscopy thermal deflection analysis

• Thomas Mathias,
• Roland Bennewitz and
• Philip Egberts

Beilstein J. Nanotechnol. 2025, 16, 1952–1962, doi:10.3762/bjnano.16.136

• dynamic mechanics models relating the contact stiffness of the tip/cantilever pressing into a surface with the oscillation frequency of the cantilever and show that they did not accurately model the experiment. Several material combinations of tip and sample were examined; tip size and cantilever

• stiffness demonstrate that existing models cannot capture the physics of this problem. While concrete solutions to use analytical models to interpret CR-AFM data have not been found, a possible solution may include revisiting the analytical model to capture a potentially more complex system than the current

• model, improved matching the cantilever/sample stiffness to obtain a larger variation in contact stiffness with frequency, or investigating the use of higher-order modes that may achieve this improved match. Keywords: atomic force microscopy; contact resonance; highly oriented pyrolytic graphite (HOPG

PEGylated lipids in lipid nanoparticle delivery dynamics and therapeutic innovation

• Peiyang Gao

Beilstein J. Nanotechnol. 2025, 16, 1914–1930, doi:10.3762/bjnano.16.133

• outperformed single-ligand LNPs with folate or Herceptin only [42]. In vivo validation was performed using a zebrafish larvae xenograft model, in which MCF7 breast cancer cells were implanted into the larvae at 48 h post-fertilization. The LNPs were labeled for tracking and then administered via intravenous

• the same mouse model, strong protein expressions were observed after injection of 10 µg mRNA per dose. Additionally, in vitro studies using human whole blood also revealed that pSar-LNPs triggered lower levels of the proinflammatory cytokines IL-1β, IL-6, and IL-8, compared to PEG-LNPs [81]. Recent

Targeting the vector of arboviruses Aedes aegypti with nanoemulsions based on essential oils: a review with focus on larvicidal and repellent properties

• Laryssa Ferreira do Nascimento Silva,
• Douglas Dourado,
• Thayse Silva Medeiros,
• Mariana Alice Gonzaga Gabú,
• Maria Cecilia Queiroga dos Santos,
• Daiane Rodrigues dos Santos,
• Mylena Lemos dos Santos,
• Gabriel Bezerra Faierstein,
• Rosângela Maria Rodrigues Barbosa and
• Fabio Rocha Formiga

Beilstein J. Nanotechnol. 2025, 16, 1894–1913, doi:10.3762/bjnano.16.132

• produced an LC50 of 192.5 µg/mL at 48 hours. Furthermore, acute oral toxicity tests in Danio rerio (zebrafish), a non-target model organism, showed no adverse effects. Although the study did not compare the nanoemulsion to the corresponding free essential oil, it highlights the potential of this

Programmable soliton dynamics in all-Josephson-junction logic cells and networks

• Vsevolod I. Ruzhickiy,
• Anastasia A. Maksimovskaya,
• Sergey V. Bakurskiy,
• Andrey E. Schegolev,
• Maxim V. Tereshonok,
• Mikhail Yu. Kupriyanov,
• Nikolay V. Klenov and
• Igor I. Soloviev

Beilstein J. Nanotechnol. 2025, 16, 1883–1893, doi:10.3762/bjnano.16.131

• , high-speed, and scalable computing. In these systems, the propagation of information is associated with the movement of a current wave/topological soliton, which is clearly visible in the model by a 2π jump of the so-called Josephson phase, φ. In contrast to conventional rapid single flux quantum (RSFQ

• for the flexible configuration of advanced logic and neuromorphic circuits. Results Model description To model the dynamics of kinetic solitons [43], we employ the resistively and capacitively shunted junction (RCSJ) model [1], where the total current I across a Josephson junction is the sum of the

• current flowing from the node k to the node j(h). Each current is described by the RCSJ model (Equation 2): With this approach, the current across the inductance is defined by the expression where l = L/LJ is inductance normalized to the Josephson inductance . After substituting the expressions for the

Self-assembly and adhesive properties of Pollicipes pollicipes barnacle cement protein cp19k: influence of pH and ionic strength

• Shrutika Sawant,
• Anne Marie Power and
• J. Gerard Wall

Beilstein J. Nanotechnol. 2025, 16, 1863–1872, doi:10.3762/bjnano.16.129

• timescale of fibrillogenesis likely preventing premature adhesive curing within the gland prior to secretion. Overall, our findings support a model in which cp19k undergoes pH- and salt concentration-dependent self-assembly into fibrils in the cement gland, with implications for the mechanism and timing of

On the road to sustainability – application of metallic nanoparticles obtained by green synthesis in dentistry: a scoping review

• Lorena Pinheiro Vasconcelos Silva,
• Joice Catiane Soares Martins,
• Israel Luís Carvalho Diniz,
• Júlio Abreu Miranda,
• Danilo Rodrigues de Souza,
• Éverton do Nascimento Alencar,
• Moan Jéfter Fernandes Costa and
• Pedro Henrique Sette-de-Souza

Beilstein J. Nanotechnol. 2025, 16, 1851–1862, doi:10.3762/bjnano.16.128

• scoping review. Acknowledgements To improve the clarity and fluency of the English writing, we used the assistance of ChatGPT-4.1, a large language model developed by OpenAI. As non-native English speakers, this tool supported us in refining the textual coherence of the manuscript. Nonetheless, all

Phytol-loaded soybean oil nanoemulsion as a promising alternative against Leishmania amazonensis

• Victória Louise Pinto Freire,
• Mariana Farias Alves-Silva,
• Johny W. de Freitas Oliveira,
• Matheus de Freitas Fernandes-Pedrosa,
• Alianda Maira Cornélio,
• Marcelo de Souza-Silva,
• Thayse Silva Medeiros and
• Arnóbio Antônio da Silva Junior

Beilstein J. Nanotechnol. 2025, 16, 1826–1836, doi:10.3762/bjnano.16.126

• promastigotes represents a limitation, this model was used as a proof-of-concept, with promising evidence of the potential of PHYT-NE. Future studies in macrophage models infected with intracellular amastigotes will be essential to confirm the observed efficacy and validate the potential of PHYT-NE as a safe

• , Brazil); soybean oil (Sigma-Aldrich, Brazil); Tween® 80 (Sigma-Aldrich, Brazil); purified water (obtained from a reverse osmosis purification equipment, model OS50 LX, Gehaka, Brazil) were used for nanoemulsion preparation. Mammalian cells were cultured in DMEM, High Glucose (Life Technologies, Cat

• temperature (24 ± 2 °C). Colloidal and physicochemical stability For accelerated stability analysis, 1 mL aliquots of the nanoemulsion were transferred to Eppendorf tubes and subjected to three centrifugation cycles at 960 and 8600g for 15 min, each using a mini centrifuge (Fisherbrand®, model Gusto, Illinois

Further insights into the thermodynamics of linear carbon chains for temperatures ranging from 13 to 300 K

• Alexandre Rocha Paschoal,
• Thiago Alves de Moura,
• Juan S. Rodríguez-Hernández,
• Carlos William de Araujo Paschoal,
• Yoong Ahm Kim,
• Morinobu Endo and
• Paulo T. Araujo

Beilstein J. Nanotechnol. 2025, 16, 1818–1825, doi:10.3762/bjnano.16.125

• nanotubes (LCC@DWCNT and LCC@MWCNT, respectively) behave as Debye’s materials for temperatures as high as 293 K with an estimate that such materials could still withstand such characteristics for even higher temperatures (≈700 K). Using the Debye model, thermodynamic observables (internal energy

• unchanged. Our measurements were performed in both isolated and small bundles of LCC@MWCNT, which allowed us to demonstrate that small bundles or isolated environments do not seem to influence the vibrational and thermodynamic properties measured. Keywords: carbon nanotubes; Debye model; Grüneisen

• whose thermal properties can be described by the Debye model [30]. The reason is that the responses of materials to changing temperatures usually come from two contributions: (1) the lattice thermal expansion (LTE), associated with e–ph interactions; and (2) anharmonic effects, associated with ph–ph

Electrical, photocatalytic, and sensory properties of graphene oxide and polyimide implanted with low- and medium-energy silver ions

• Josef Novák,
• Eva Štěpanovská,
• Petr Malinský,
• Vlastimil Mazánek,
• Jan Luxa,
• Ulrich Kentsch and
• Zdeněk Sofer

Beilstein J. Nanotechnol. 2025, 16, 1794–1811, doi:10.3762/bjnano.16.123

• and Ag ion interstitials. The discrepancy between the SRIM-simulated and RBS-measured Ag depth profiles can be attributed to several factors. SRIM simulations are based on an idealized model that assumes a homogeneous, amorphous target with constant density and does not account for structural or

Exploring the potential of polymers: advancements in oral nanocarrier technology

• Rousilândia de Araujo Silva,
• Igor Eduardo Silva Arruda,
• Luise Lopes Chaves,
• Mônica Felts de La Roca Soares and
• Jose Lamartine Soares Sobrinho

Beilstein J. Nanotechnol. 2025, 16, 1751–1793, doi:10.3762/bjnano.16.122

• synthesis. This technique is frequently employed due to its simplicity and efficiency. In a rat model of diabetes, orally administered insulin-loaded NPs exhibited a hypoglycemic effect lasting 5 h, compared to 3 h for subcutaneously administered insulin. The PEG-coated NPs demonstrated greater potency

Advances of aptamers in esophageal cancer diagnosis, treatment and drug delivery

• Yang Fei,
• Hui Xu,
• Chunwei Zhang,
• Jingjing Wang and
• Yong Jin

Beilstein J. Nanotechnol. 2025, 16, 1734–1750, doi:10.3762/bjnano.16.121

• diagnostic outcomes. The establishment of a multiprotein model [49] confirms this conjecture. There are already gold nanoparticle aptamer biosensors and fluorescent aptamer sensors that show great potential in esophageal cancer diagnosis (Table 1). 3.1 Gold nanoparticle–aptamer sensors Scholars reviewed

• specific target has not been extracted and identified. Qiao et al. [114] screened the SYL-6 aptamer with the strongest binding ability to ESCC cells by Cell-SELEX, identified and verified PHB2 as the molecular target for SYL-6-specific binding. The results of mouse model showed that SYL-6-Dox had almost

Multifunctional anionic nanoemulsion with linseed oil and lecithin: a preliminary approach for dry eye disease

• Niédja Fittipaldi Vasconcelos,
• Almerinda Agrelli,
• Rayane Cristine Santos da Silva,
• Carina Lucena Mendes-Marques,
• Isabel Renata de Souza Arruda,
• Priscilla Stela Santana de Oliveira,
• Mércia Liane de Oliveira and
• Giovanna Machado

Beilstein J. Nanotechnol. 2025, 16, 1711–1733, doi:10.3762/bjnano.16.120

• phase. The supernatant was washed three times with 10% (w/v) citric acid and then concentrated via rotary evaporation. A 2 µL aliquot of the supernatant was injected in split injection mode (1:10 in ethyl acetate) into a gas chromatograph with flame ionization detection (GC-FID) model 7290 A (Agilent

• determined by electrophoretic mobility using the same instrument at 25 °C. Calculations were based on the Smoluchowski model. All measurements were performed in triplicate and expressed as mean ± standard deviation. pH Value The pH value of the pre-formulation and nanoformulations was measured using a

Beyond the bilayer: multilayered hygroscopic actuation in pine cone scales

• Kim Ulrich,
• Max David Mylo,
• Tom Masselter,
• Fabian Scheckenbach,
• Sophia Fischerbauer,
• Martin Nopens,
• Silja Flenner,
• Imke Greving,
• Linnea Hesse and
• Thomas Speck

Beilstein J. Nanotechnol. 2025, 16, 1695–1710, doi:10.3762/bjnano.16.119

• our samples inside the chamber, as well as a side view of the samples, were recorded externally every 10 min using a single-board computer (Raspberry Pi 4 Model B, Raspberry Pi Foundation, Cambridge, UK) connected to a temperature and humidity sensor (DHT22, Sertronics GmbH, Berlin, Germany) and a

• cross sections were taken from positions 2.5, 5.5, 7.5, and 11.5 mm more apical. These five cross-sectional positions were then used as control points with the same longitudinal spacing between them to extrude the volume model. Since the sclerenchyma fibers branch along the longitudinal axis of a scale

• X- and Y-directions (spanning the cross section of each model), the mean value of the two measured values was used, while the Z-value (from the basal to the apical end of the models) was derived directly. The same coefficients were used in all simulations. A linear elastic material model was applied

Ambient pressure XPS at MAX IV

• Mattia Scardamaglia,
• Ulrike Küst,
• Alexander Klyushin,
• Rosemary Jones,
• Jan Knudsen,
• Robert Temperton,
• Andrey Shavorskiy and
• Esko Kokkonen

Beilstein J. Nanotechnol. 2025, 16, 1677–1694, doi:10.3762/bjnano.16.118

• operando. With IRRAS, vibrational information is available, which greatly complements the electronic information obtained by photoelectron spectroscopy. This combination enables a more complete picture of surface reaction mechanisms. The examples discussed here focus on “model catalysts”, that is, systems

• where the active phase is well defined and often prepared on single crystals. While studies on industrial catalysts are limited by charging effects (insulating oxide-supported samples) and higher pressure requirements, model systems remain invaluable for fundamental insights. We now turn to specific

• here. Instead, we focus on a study by Vesselli and co-workers that directly addresses catalytic activity in a biomimetic SAC system [20][21]. In their work, a cobalt single-atom biomimetic model catalyst is based on a self-assembled monolayer of Co-porphyrins grown on an almost free-standing graphene

Energy spectrum and quantum phase transition of the coupled single spin and an infinitely coordinated Ising chain

• Seidali Seidov,
• Natalia Pugach and
• Anatolie Sidorenko

Beilstein J. Nanotechnol. 2025, 16, 1668–1676, doi:10.3762/bjnano.16.117

• .16.117 Abstract In this work we consider a spin model composed of a single spin and connected to an infinitely coordinated Ising chain. Theoretical models of this type arise from various fields of theoretical physics, such as theory of open systems, quantum control, and quantum computations. In the

• thermodynamic limit of an infinite chain, we map the chain Hamiltonian to the Hamiltonian of the Lipkin–Meshkov–Glik model, and the system as a whole is described by a generalized Rabi Hamiltonian. Next, the effective Hamiltonian is obtained using the Foulton–Gouterman transformation. In the thermodynamic limit

• we obtain the spectrum of the whole system and study the properties of the ground-state quantum phase transition. Keywords: Ising chain; Lipkin–Meshkov–Glick model; quantum phase transitions; Introduction In the present manuscript, we consider a single spin connected to an infinitely coordinated

Prospects of nanotechnology and natural products for cancer and immunotherapy

• Jan Filipe Andrade Santos,
• Marcela Bernardes Brasileiro,
• Pamela Danielle Cavalcante Barreto,
• Ligiane Aranha Rocha and
• José Adão Carvalho Nascimento Júnior

Beilstein J. Nanotechnol. 2025, 16, 1644–1667, doi:10.3762/bjnano.16.116

• nanoparticles were obtained by precipitation and freeze-drying and were analyzed by HPLC and DLS. Additionally, the in vivo studies performed in a mice model with breast cancer tumor (4T1 cell) showed that the drug exhibits a level of biosafety while reaching 44% tumor inhibition [75]. Polysaccharide

Venom-loaded cationic-functionalized poly(lactic acid) nanoparticles for serum production against Tityus serrulatus scorpion

• Philippe de Castro Mesquita,
• Karla Samara Rocha Soares,
• Manoela Torres-Rêgo,
• Emanuell dos Santos-Silva,
• Mariana Farias Alves-Silva,
• Alianda Maira Cornélio,
• Matheus de Freitas Fernandes-Pedrosa and
• Arnóbio Antônio da Silva-Júnior

Beilstein J. Nanotechnol. 2025, 16, 1633–1643, doi:10.3762/bjnano.16.115

• : zero order, first order, Korsmeyer–Peppas, and parabolic diffusion (Table 2). The zero order, first order, and Korsmeyer–Peppas models exhibiting determination coefficient (r2) values demonstrate that the release mechanism cannot be explained by these models. The parabolic diffusion model better fitted

• , based on the analysis of the determination coefficient (r²), obtained from the application of four mathematical models to experimental data, the model that explains the release profile of the venom-loaded PLA nanoparticles has been identified, and a more accurate adjustment was observed for the

• parabolic diffusion model. This mathematical model suggests that the release mechanism of venom-loaded PLA nanoparticles was controlled by diffusion dependent on the protein-loading level [18]. These results corroborate with previous studies that used nanoparticles for venom protein delivery [42][43

Bioinspired polypropylene-based functionally graded materials and metamaterials modeling the mistletoe–host interface

• Lina M. Rojas González,
• Naeim Ghavidelnia,
• Christoph Eberl and
• Max D. Mylo

Beilstein J. Nanotechnol. 2025, 16, 1592–1606, doi:10.3762/bjnano.16.113

• ]. Biological materials and their highly modified structure–function relationship are designed to enable organisms to survive and/or adapt to the environmental conditions in which they live [24][25]. The European mistletoe (Viscum album) is an excellent model of a long-lasting connection between two material

• . Additionally, we will examine how this structuring can be employed to model local failure behavior through material distribution. Furthermore, we will investigate the transferability of the FGM framework to mechanical metamaterials, with the aim of expanding their geometry-based properties through graded

• and material gradients, finite element (FE) simulations were performed using small deformation implicit modeling. The linear solver of the ANSYS static structural module was used for the FE simulations. Due to the low thickness of the metamaterial structures, the plane stress 2D model (PLANE 183

Few-photon microwave fields for superconducting transmon-based qudit control

• Irina A. Solovykh,
• Andrey V. Pashchenko,
• Natalya A. Maleeva,
• Nikolay V. Klenov,
• Olga V. Tikhonova and
• Igor I. Soloviev

Beilstein J. Nanotechnol. 2025, 16, 1580–1591, doi:10.3762/bjnano.16.112

• transmon (a slightly nonlinear oscillator) is quite close to the equidistant one; however, a number of widely used theoretical models describing its evolution in an external electromagnetic field (the Jaynes–Cummings model) do not take into account the high-lying energy levels of the artificial atom, nor

• non-classical field and a transmon-based qudit with several, even high-lying, levels being taken into account. We develop methods of rapid quantum control of the designed transmon-based qudit and its state population dynamics. The structure of the article is as follows: First, the model of the system

• under study is described in more detail, followed by a theoretical description of the Fock-based control of the qudit states and a discussion of possible practical implementations. Results Model description The system under consideration consists of a high-quality superconducting resonator (the quality

Photocatalytic degradation of ofloxacin in water assisted by TiO₂ nanowires on carbon cloth: contributions of H₂O₂ addition and substrate absorbability

• Iram Hussain,
• Lisha Zhang,
• Zhizhen Ye and
• Jin-Ming Wu

Beilstein J. Nanotechnol. 2025, 16, 1567–1579, doi:10.3762/bjnano.16.111

• investigation, we extend the application to drug pollution treatments with OFL as a model molecule. Since H2O2 produces reactive oxygen species (ROS), which promote the oxidation and degradation of OFL, H2O2 was introduced into the system to increase the photocatalytic efficiency, and the impacts of its

• irradiance meter (Model UV-A, Beijing Normal University). The solution was maintained in darkness, and the UV light was activated following the establishment of a dark adsorption–desorption equilibrium for three hours. The degradation experiments were repeated in triplicate to ensure statistical reliability

• -first-order kinetic model, as determined by Equation 3: The concentration of OFL was assessed using high-performance liquid chromatography with a C18 column maintained at 30 °C. The UV–vis detector was calibrated to a wavelength of 292 nm. The mobile phase consisted of a 15:85 ratio of methanol to 0.8

Modeling magnetic properties of cobalt nanofilms used as a component of spin hybrid superconductor–ferromagnetic structures

• Aleksey Fedotov,
• Olesya Severyukhina,
• Anastasia Salomatina and
• Anatolie Sidorenko

Beilstein J. Nanotechnol. 2025, 16, 1557–1566, doi:10.3762/bjnano.16.110

• ., Dolgoprudny, 141701, Russia 10.3762/bjnano.16.110 Abstract The paper presents a mathematical model for studying the magnetic behavior of atoms, which takes into account spin and interatomic interactions. Two problems were solved by means of mathematical modeling. At the first stage, the problem of modeling a

• previously obtained data confirmed the adequacy of the applied mathematical model. The second stage of numerical studies was devoted to the analysis of the magnetic behavior of cobalt nanofilms of different thicknesses. It was shown that the film thickness has a significant influence on the magnetic

• materials science. These properties depend not only on the composition, but also on factors such as film thickness, which in turn affects their application in microelectronics, spintronics, and other high-tech fields. The aim of this article is to model the magnetic properties of cobalt nanofilms of

Dendrimer-modified carbon nanotubes for the removal and recovery of heavy metal ions from water

• Thao Quynh Ngan Tran,
• Huu Trung Nguyen,
• Subodh Kumar and
• Xuan Thang Cao

Beilstein J. Nanotechnol. 2025, 16, 1522–1532, doi:10.3762/bjnano.16.107

• ions (Pb2+ and Cd2+) from aqueous solutions with enhanced recyclability than less dendrimerized CNTs. Kinetic studies have revealed that the adsorption process followed a pseudo-second order kinetic model, and the rate-limiting step was mainly chemisorption. This study has not only excluded the

• models: pseudo-first order and pseudo-second order. These models have been described by their respective equations (Supporting Information File 1, Equations S1 and S2). For the pseudo-first order kinetic model, a linear plot of ln(qe − qt) as a function of time (t) was drawn at different initial

• concentrations of metal ions (Figure 4a and Supporting Information File 1, Table S1). The correlation coefficients were calculated to be relatively low. In contrast, the pseudo-second order kinetic model represented by the plot of t/qt against time (t) demonstrated a much better fit with higher correlation

Laser processing in liquids: insights into nanocolloid generation and thin film integration for energy, photonic, and sensing applications

• Akshana Parameswaran Sreekala,
• Pooja Raveendran Nair,
• Jithin Kundalam Kadavath,
• Bindu Krishnan,
• David Avellaneda Avellaneda,
• M. R. Anantharaman and
• Sadasivan Shaji

Beilstein J. Nanotechnol. 2025, 16, 1428–1498, doi:10.3762/bjnano.16.104

• model, which was experimentally validated. In 2010, as research on pulsed laser irradiation progressed, Koshizaki’s group explored the potential of non-focused laser beams with moderate fluence, lower than the ablation threshold, to irradiate colloidal NPs [42][48][49][64][65][66][67]. Their findings

• used to deposit photoresist films for microelectronic manufacturing, where understanding the interaction between liquid flow and mass transfer during the process became crucial as device sizes decreased. A one-dimensional model of spin coating was developed to describe film thinning due to both

• thicknesses ranging from micrometers to nanometers. A mathematical model was derived to explain the dominant mechanisms in film formation, considering factors such as evaporation and shear stress, and extending the analysis to non-Newtonian fluids [102]. Despite its widespread use, the process faces