Detachment Length Research Articles

Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate

We study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection.

Hydrodynamic characteristics of detachment length and flow mapping in T-junction circular microchannel

This study investigates the droplet formation process in T-junction circular microchannels, emphasizing the influence of wetting properties and contact angles under various operating conditions. A coupled Volume-of-Fluid (VOF)/Level-set multiphase model is employed for Computational Fluid Dynamics (CFD) simulations to accurately capture the microscale phenomena. The effects of contact angles ranging from 125° to 145°, two-phase flow velocities (0.04–0.25 m/s), and interfacial tension (0.035–0.055 N/m) are systematically analyzed. The findings reveal that these parameters significantly impact the detachment length and flow patterns, with four distinct flow regimes identified: dripping, slug, jetting, and annular flow. New dimensionless correlations for slug and detachment lengths are developed and validated through experimental data, offering improved predictive capabilities. The comprehensive flow mapping provided in this study enhances the understanding of multiphase flows in microchannels, offering valuable insights for the optimization of microfluidic device design and practical applications such as extractive desulphurization. These contributions present a novel approach to integrating contact angle effects into microfluidic research, addressing previously overlooked aspects and providing robust guidelines for future studies.

Cavitation analysis of plunging hydrofoils using large eddy simulations

This study employs numerical analysis to investigate the behavior of the National Advisory Committee for Aeronautics (NACA)66 modified (mod) hydrofoil under plunging motion, considering various cavitation numbers. The Large Eddy Simulation (LES) method is utilized to model turbulence. The hydrofoil's plunging motion leads to an increase in lift force and a decrease in drag force. Our research indicates that increasing the speed of the hydrofoil's heaving motion delays the onset of cavitation and enhances the formation of cavity clouds. Furthermore, during the peak oscillatory motion of the hydrofoil in the plunging phase, the detachment length of cavitation bubbles decreases. Additional investigations reveal that cavitation on the hydrofoil's surface accelerates the transition from a laminar to a turbulent boundary layer, strengthening the turbulent boundary layer and postponing the onset of flow separation. This research involves an in-depth investigation of the terms in the vorticity transport equation in cavitation inception, finding a correlation between vapor volume fraction and vorticity dilatation near the hydrofoil surface. This correlation proves crucial to the initial stages of the cavitation inception process.

Evaluation of thermo-fluidic performance of micro pulsating heat pipe with and without evaporator side surface structures

Interfacial behaviour and thermal performance of a 4-loop micro pulsating heat pipe are examined through experiments performed at different filling ratio (30–60 %), working fluid (acetone, ethanol, and methanol), and heat input (0–40 W). During the heat pipe operation, nucleation, growth and merging of bubbles, elongation, and movement of vapor plug, and dry out conditions are noticed upon ramp heating (0–40 W) inside smooth surface evaporator pulsating heat pipe. Experiments show that preparation and boiling inception lead to steady operation of heat pipe. Pulsating heat pipe showed minimum thermal resistance when operated with 40 % filling ratio and acetone as working fluid, which has low viscosity, surface tension and boiling point. Additionally, effect of surface structures (rectangular pillar protrusion and hemispherical dimple cavity) on the evaporator section is tested against base smooth surface micro pulsating heat pipe to understand augmentation of heat transfer. Hemispherical dimple cavities show better nucleation, bubble growth, and vapor plug elongation and thereby reduction in thermal resistance. On the other hand, rectangular pillar protrusions showed clogged bubble, least bubble detachment and vapor plug length in the adiabatic zone which results in higher thermal resistance than even smooth surface.

Characterization of a unique attachment organelle: Single-cell force spectroscopy of Giardia duodenalis trophozoites.

The unicellular parasite Giardia duodenalis is the causative agent of giardiasis, a gastrointestinal disease with global spread. In its trophozoite form, G. duodenalis can adhere to the human intestinal epithelium and a variety of other, artificial surfaces. Its attachment is facilitated by a unique microtubule-based attachment organelle, the so-called ventral disc. The mechanical function of the ventral disc, however, is still debated. Earlier studies postulated that a dynamic negative pressure under the ventral disc, generated by persistently beating flagella, mediates the attachment. Later studies suggested a suction model based on structural changes of the ventral discs, substrate clutching or grasping, or unspecific contact forces. In this study, we aim to contribute to the understanding of G. duodenalis attachment by investigating detachment characteristics and determining adhesion forces of single trophozoites on a smooth glass surface (RMS = 1.1 ± 0.2 nm) by fluidic force microscopy (FluidFM)-based single-cell force spectroscopy (SCFS). Briefly, viable adherent trophozoites were approached with a FluidFM micropipette, immobilized to the micropipette aperture by negative pressure, and detached from the surface by micropipette retraction while retract force curves were recorded. These force curves displayed novel and so far undescribed characteristics for a microorganism, namely, gradual force increase on the pulled trophozoite, with localization of adhesion force shortly before cell detachment length. Respective adhesion forces reached 7.7 ± 4.2 nN at 1 μm s-1 pulling speed. Importantly, this unique force pattern was different from that of other eukaryotic cells such as Candida albicans or oral keratinocytes, considered for comparison in this study. The latter both displayed a force pattern with force peaks of different values or force plateaus (for keratinocytes) indicative of breakage of molecular bonds of cell-anchored classes of adhesion molecules or membrane components. Furthermore, the attachment mode of G. duodenalis trophozoites was mechanically resilient to tensile forces, when the pulling speeds were raised up to 10 μm s-1 and adhesion forces increased to 28.7 ± 10.5 nN. Taken together, comparative SCSF revealed novel and unique retract force curve characteristics for attached G. duodenalis, suggesting a ligand-independent suction mechanism, that differ from those of other well described eukaryotes.

Large eddy simulations of cavitation around a pitching–plunging hydrofoil

In this study, we numerically examine the behavior of the NACA (National Advisory Committee for Aeronautics) 66 hydrofoil under combined oscillatory motion, considering different cavitation numbers. The large eddy simulation method is used for the turbulence modeling. The vertical oscillation (combined oscillation) creates an effective angle of attack, leading to reduced drag force. Our findings indicate that increasing the speed of hydrofoil oscillation leads to a delayed onset and increased production of cavity clouds. Moreover, an increase in the angle of attack during combined oscillatory motion decreases the detachment length of cavitation bubbles. Further investigations show that cavitation on the hydrofoil's surface can accelerate the shift from a laminar to turbulent boundary layer, reinforcing the turbulent boundary layer's strength and thereby delaying the onset of flow separation. Additionally, we accurately examine the terms of the vorticity transport equation in this research. It is evident that the vorticity dilatation term forms near the boundary layers close to the hydrofoil surface and correlates well with the vapor volume fraction. This term plays a vital role in the cavitation inception process.

Augmentation of the stable static travel range of electrostatically actuated slender nano-cantilevers by accounting for the influence of the van der Waals force

The van der Waals (vdW) force, along with the electrostatic force and the first-order fringing field effect, act on the electrostatically actuated nano-cantilever (EANC) when the gap between the deformable electrode and the stationary electrode is less than 20 nanometres. Because of the vdW force, the EANC can undergo a pull-in phenomenon even without the electrostatic force when the nano-cantilever length exceeds its detachment length. The vdW force also results in a significant reduction in static pull-in instability parameters of the slender EANC compared to corresponding parameters obtained when this force is absent. This paper aims to augment the stable static travel range (i.e., the pull-in displacement) of the aforementioned EANC having a length close to its detachment length by varying the beam width. The beam width is assumed to vary in linear and parabolic manners and is controlled using a width variation parameter in each case. The governing equation of the Bernoulli-Euler beam theory and the Galerkin’s technique are utilised to obtain the weighted residual statement (GWRS). The GWRS is utilised to obtain static pull-in instability parameters of referential prismatic and variable-width EANCs. Pull-in instability parameters of variable-width EANCs, for various values of width variation parameters and the initial gap between electrodes, have been obtained. The aforementioned results have been validated with corresponding results obtained by three-dimensional finite element simulations performed using COMSOL Multiphysics®. Compared to the referential prismatic EANC, a significant augmentation in the pull-in displacement of the variable-width EANC has been obtained.

Two‐phase modeling of evaporation characteristics of ethanol droplet under force‐convection environment

AbstractStudies on the evaporation phenomenon of a pure ethanol droplet have been mostly confined to the semianalytical modeling in stagnant ambient. Investigation into this aspect in a convective environment by considering the Navier–Stokes equation is also minimal. Hence, in this study we analyze and investigate the evaporation characteristics of a single‐component spherical‐shaped isolated pure ethanol droplet under force convective air environment by considering both gas‐ and liquid‐phase motions, nonunitary Lewis number in the interface, variable Stefan flow (blowing) effect, and the transient droplet heating. The finite difference method is utilized while solving the governing equations of the spherical polar coordinate system for species, momentum, and energy transfer. The maximum Reynolds number and ambient temperature are kept at 100 and 600 K, respectively. The present work is validated by comparing the normalized surface regression curve of the droplet with the earlier experimental and theoretical results. Using the current simulated data, flow and temperature profiles of both gas and liquid regions are visualized in streamline and isotherm contour plots at various instants of time. It is observed that at a moderate Reynolds number a detached vortex forms at the downstream location of the droplet. However, the detachment length increases with time. The temperature gradients along the droplet surface are observed at the initial stage. Moreover, the heat‐up period occupies about 20% of the total lifetime of the droplet. The droplet life and heat‐up period decrease with an increase in free‐stream velocity. In addition, the saturation temperature increases with ambient temperature.

Effect of transverse magnetic field on wake dynamics and heat transfer through a porous circular cylinder

AbstractA two‐dimensional numerical simulation using the commercial computational fluid dynamics package ANSYS Fluent 15.0 is performed to investigate the effect of a transverse magnetic field on the wake dynamics around a heated porous circular cylinder. The study is conducted considering a Newtonian, incompressible, and electrically conductive fluid with constant properties for the low Reynolds number laminar regime. In the range of Reynolds number (Re = 10–40), recirculating vortices are observed to penetrate (or detach) into (from) the porous cylinder surface depending on the Darcy number, Da (10−6 to 10−2). The effect of the magnetic field parameter (Hartmann number) Ha (0–10) on the detachment and penetration characteristics of a porous cylinder is reported for the first time. A steady separated flow behind the cylinder turns into an attached flow at a critical magnetic field strength. Accordingly, the critical Hartmann number (Hacr) is estimated for the complete suppression of the flow separation behind the porous cylinder. Hacr is found to decrease with an increase in Da and a decrease in Re. The wake behind the cylinder is also found to be detached from the cylinder surface at a particular value of the magnetic field strength termed as the detachment Hartmann number (Had). Had also decreased with an increase in Da and decrease of Re. In addition, the effect of Ha on the separation angle, recirculation length, detachment length, and drag coefficient is also discussed. Furthermore, the effect of the magnetic field on the forced convective heat transfer characteristics is also studied considering various fluids (Prandtl number, Pr = 0.02, 0.71, and 7) past the circular permeable cylinder. At a particular Pr, the heat transfer rate is almost invariant for low permeability, whereas it increases significantly at higher permeability with an applied magnetic field. The rate of heat transfer increases with the Prandtl number for all Hartmann and Darcy numbers. Finally, a correlation is developed to predict the average heat transfer as a function of Re, Pr, Da, and Ha.

Diffusive and capillary instabilities of viscous fluid threads in microchannels

We experimentally investigate the flow behavior of viscous oil threads in a a variety of miscible and immiscible low-molecular weight alcohols in microchannels. A comparative study is conducted between diffusive and capillary regimes using simple functional relationships for the thread characteristics, including diameter and detachment length. We develop a comprehensive classification of immiscible and miscible fluid dynamics in square microfluidic channels and provide a quantitative analysis of the evolution of multiphase flow properties across flow patterns.

Numerical and analytical study of ultimate capacity of steel plate shear walls with partial plate-column connection (SPSW-PC)

This research endeavor intends to use the numerical and analytical approaches to investigate the ultimate shear capacity of steel plate shear walls with partial plate-column connection (SPSW-PC). This study aims to provide an analytical relationship for estimating the ultimate capacity of SPSW-PC. Using plastic analysis and considering the mechanism of plastic hinge formation, a relation has been obtained for estimating the ultimate capacity of SPSW-PCs. Extensive parametric studies have been carried out using a nonlinear finite element method to examine the accuracy of the obtained analytical relationships. The parametric studies include investigating the influence of infill plate thickness and width-to-height ratio as well as the ratio of the plate-column detachment length of SPSW-PCs. To this end, comprehensive verification studies are initially performed by comparing the numerical predictions with several reported experimental results to demonstrate the numerical method's reliability and accuracy. Comparison is made between the hysteresis curves, failure modes, and base shear capacities predicted numerically or obtained/observed experimentally. The results show a sound compromise between the ultimate capacity of the analytical relationship and numerical models of parametric studies. Although removing the connection between the web-plate and columns can be beneficial by decreasing the overall system demand on the vertical boundary members, based on the results and findings of this research study, such detachment can reduce the stiffness and strength capacities of steel shear walls by about 25%, on average.

Factors Determining the Morphology of Peripapillary Retinoschisis.

PurposeWe conducted cross-sectional examinations to determine the frequency of peripapillary retinoschisis (PRS) in eyes with glaucoma and suspected glaucoma and analyzed the pathogenesis of PRS by using spectral-domain optical coherence tomography (SD-OCT).Patients and MethodsIn 1516 cases involving glaucoma and suspected glaucoma, we retrospectively reviewed the disc and macular volume scans obtained by SD-OCT and categorized PRS into two groups based on whether the retinoschisis was closer to the optic nerve over the Bruch’s membrane opening (BMO) (ahead group) or did not go past the BMO (behind group) and then compared the characteristics between both groups.ResultsThe total frequency of PRS was 1.49% (20/1342 eyes) in primary open-angle glaucoma (POAG) eyes and 0.59% (10/1687 eyes) in glaucoma suspects. In the behind group, PRS was mostly detected in the inner layers of the retina (retinal nerve fiber layer: 30.9%, ganglion cell layer: 21.8%, inner plexiform layer: 7.3%). However, in the ahead group, PRS was detected in the outer layers (inner nuclear layer: 10%, outer plexiform layer: 20%, outer nuclear layer: 50%). In addition, the eyes in the ahead group had significantly greater axial lengths and significantly smaller spherical equivalent values. These two differences suggest that the pulling force of the vitreous traction may play an important role in PRS only in the behind group and that the scleral stretching force may play a role in the development of PRS in the ahead group.ConclusionThe frequency of PRS in patients with POAG is higher than that in patients with suspected glaucoma. Both forms of PRS are affected by posterior vitreous detachment and axial length elongation. Careful follow-up is required to assess the development of PRS in glaucoma suspects. The pathogenesis of PRS has been elucidated to some degree by classifying the morphological condition of the PRS and BMO.

Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects

Because of fasttechnological development, electrostatic nanoactuator devices like nanosensors, nanoswitches, and nanoresonators are highly considered by scientific community. Thus, this article presents a new solution technique in solving highly nonlinear integro-differential equation governing electrically actuated nanobeams made of functionally graded material. The modified couple stress theory and Gurtin–Murdoch surface elasticity theory are coupled together to capture the size effects of the nanoscale thin beam in the context of Euler–Bernoulli beam theory. For accurate modelling, all the material properties of the bulk and surface continuums of the FG nanoactuator are varied continuously in thickness direction according to power law. The nonlinearity arising from the electrostatic actuation, fringing field, mid-plane stretching effect, axial residual stress, Casimir dispersion, and van der Waals forces are considered in mathematical formulation. The nonlinear nonclassical equilibrium equation of FG nanobeam-based actuators and associated boundary conditions are exactly derived using Hamilton principle. The new solution methodology is combined from three phases. The first phase applies Galerkin method to get an integro-algebraic equation. The second one employs particle swarm optimization method to approximate the integral terms (i.e. electrostatic force, fringing field, and intermolecular forces) to non-integral cubic algebraic equation. Then, solved the system easily in last phase. The resulting algebraic model provides means for obtaining critical deflection, pull-in voltage, detachment length, minimum gap, and freestanding effects. A reasonable agreement is found between the results obtained from the present method and those in the available literature. A parametric study is performed to investigate the effects of the gradient index, material length scale parameter, surface energy, intermolecular forces, initial gap, and beam length on the pull-in response and freestanding phenomena of fully clamped and cantilever FG nanoactuators.

Experimental investigation of the effects of surfactant on the dynamics of formation process of liquid drops

In the present study, the formation of surfactant-laden viscous drops in ambient air is experimentally investigated using a high-speed digital camera. The mixtures of 90%, 92.5%, and 95% glycerol by weight in water containing various concentrations of sodium dodecyl sulfate are chosen as the drop phase fluid. The focus of this work is to investigate the effects of concentration of surfactant dissolved in solutions with different viscosities, on physical and geometrical parameters related to drop formation process, such as the drop elongation, minimum neck thickness, formation time, and the drop volume. The formation of satellite drops and the influence of surfactant concentration on their size are also studied. The obtained results indicate that increasing the surfactant concentration and the viscosity of drop phase fluid, slows down the necking process and causes the drop detachment length to increase. The entire process of drop formation is divided into two stages, and it was found that adding surfactant to the solutions has inverse effects on the duration of these two stages. It was also shown that surfactant addition contributes to an increase in the size of the satellite drop due to generation of Marangoni stresses on the surface of the drop's neck.

Severity Assessment of Acute Hydrops Due to Recurrent Keratoconus after Penetrating Keratoplasty Using Anterior Segment Optical Coherence Tomography

ABSTRACTPurpose: To compare the clinical characteristics of acute hydrops between eyes with recurrent keratoconus and eyes with treatment-naïve keratoconus.Methods: Six eyes with acute hydrops caused by recurrent keratoconus (recurrent group) and 29 eyes with acute hydrops due to treatment-naïve keratoconus (naïve group) were included. We collected data from anterior-segment optical coherence tomography (AS-OCT), corneal topography and medical records. With AS-OCT, we investigated the location of Descemet’s membrane break, the length and frequency of Descemet’s membrane detachment, and the speed of corneal thinning before acute hydrops.Results: Descemet’s membrane breaks were detectable in 6 cases in the recurrent group (100%) and 7 cases in the naïve group (70%). Distance from the break to the central line was 2–3 mm in the recurrent group, and less than 1 mm in the naïve group (p < .001). Detachment length was significantly greater in the recurrent group than in the naïve group (p = .003). Steep corneal power values tended to increase before acute hydrops in the recurrent group, but the difference between groups was not significant (observation period; 6.03 ± 2.67, 7.36 ± 5.53 years, respectively). Penetrating keratoplasty was required in 5 cases (83%) in the recurrent group, and 8 cases (28%) in the naïve group (p = .02).Conclusions: Acute hydrops due to recurrent keratoconus occurred around graft-host junctions and was more severe than that in eyes with treatment-naïve keratoconus. Severity assessment of Descemet’s membrane detachment using AS-OCT provided clues not only for diagnosis, but also for predicting prognosis.

Analytical prediction of the hydraulic jump detachment length in front of mounted obstacles in supercritical open-channel flows

Detached hydraulic jumps are major features of supercritical open-channel flows interacting with emerging obstacles. Such a flow pattern exhibits strong similarities with shock waves detached in front of bluff bodies in supersonic aerodynamic flows. This paper aims at evaluating the capacities of an analytical model, adapted from supersonic aerodynamics, to predict the hydraulic jump detachment length. The analytical predictions are compared to the measured hydraulic jumps from two experiments: (i) a uniform supercritical open-channel flow that skirts a mounted and emerging obstacle (with a horseshoe vortex) and (ii) a mounted and emerging obstacle moving at constant velocity in water at rest (without a horseshoe vortex). Moreover, numerical calculations of supercritical flow skirting emerging obstacles are undertaken, with a free-slip condition at the bed to remove the horseshoe vortex, while keeping the detached hydraulic jump. The comparison of the detachment lengths of these experimental, analytical, and computed hydraulic jumps reveals that two types of detachment lengths can be defined. The detachment length visible on experiments corresponds to the toe of the hydraulic jump, while the detachment length predicted by the analytical model rather corresponds to the location of flow regime transition from the supercritical to subcritical regime. The present work thus validates the analytical model for predicting the location of flow regime transition (for configurations without a horseshoe vortex) but not for predicting the toe of the hydraulic jump. We finally confirm the strong connections between two distinct phenomena: a hydraulic jump in water flow and a shock wave in gas flow.

Experimental study on sudden contraction and split into the inlets of two parallel rectangular jets

The inlets to parallel rectangular jets are unique and a critical component of its design. A sudden contraction (contraction ratio = 4.2) of a vertically upward entry flow into two inlets has been investigated experimentally. Changes in velocity profile close to the inlets were measured, while the corner vortices, fluid separation and the development of axial and lateral turbulent intensities were observed from the result of particle image velocimetry analysis. The velocity profiles in the fluid adjacent to the inlets are independent of the Reynolds number, generally the same for similar geometries, concave but changes rapidly before finally adapting to the positions of the inlets. The radii of the corner vortices decreased and became elliptical with an increase in Re. Also, the detachment length shrunk by 60% when the Re was doubled. Lateral and axial turbulence increased and more fluid flowed parallel to the wall as Re increased. The trend and magnitude of the lateral to axial velocity agree with those of similar works.

Generalized closed form approximations for pull-in characteristics of fixed-fixed nano beam under the influences of van der Waals and Casimir forces

In this paper, we have presented generalized closed form solutions to estimate the permissible dimensional limits for the basic design parameters as well as the accurate pull-in characteristics of electrostatically actuated fixed-fixed nano beam. The coupled electromechanical problem for the nano beam is formulated using Galerkin's approximation while considering the effects of fringe field, mid-plane stretching and intermolecular forces like van der Waals and Casimir. The resulting integrals and higher order polynomials are solved numerically to determine the closed form expressions for allowable detachment length, minimum feasible gap, and critical pull-in parameters. The derived expressions are compared quantitatively with other reported results which show reasonable agreement. The advantage here is that the derived expressions do not involve any complex mathematical operation unlike in existing literature, and thus the expressions can be readily used for quick and accurate estimation of the design parameters. As the applied voltage exceeds beyond pull-in limit, it can lead to severe structural failure during operation; hence the designers must be aware of the accurate pull-in expressions as derived in this paper. It has been observed that the incorporation of the intermolecular forces together with the fringe effect leads to significant reduction in pull-in voltage whereas the mid-plane stretching parameter shows the opposite effect. It is further envisaged that, the proposed generalized closed form expressions will serve as quick guidelines for reliable and safe design and fabrication of various similar electrostatically actuated nanosystems.

Observation of anterior chamber volume after cataract surgery with swept-source optical coherence tomography.

To investigate the changes in the anterior chamber volume (ACV) with swept-source optical coherence tomography (SS-OCT) after cataract surgery and the factors that influence these ACV changes. This was a prospective cohort study. Fifty-one patients who underwent cataract surgery were enrolled. Their ACV, anterior chamber depth, and angle widths were measured with SS-OCT before and 1day, 1week, and 1month after surgery. The associations between the changes in ACV and posterior vitreous detachment (PVD) and axial length (AXL) were determined. Compared with the preoperative volume, ACV increased significantly at all three time points after surgery (all p < 0.001). ACV was greater at 1week after surgery than at 1day after surgery (p < 0.001). Both AXL and the presence of PVD were significantly associated with the change in ACV at 1day after surgery (p = 0.005). However, neither PVD nor AXL affected the change in ACV between 1day and 1week after surgery. ACV stabilized in the first week after cataract surgery. The absorption of irrigation fluid and balanced salt solution in the vitreous cavity contributed to the change in ACV 1week after surgery. Eyes with longer AXL and PVD tended to show less change in ACV at 1day after surgery.

Generalized closed form solutions for feasible dimension limit and pull-in characteristics of nanocantilever under the Influences of van der Waals and Casimir forces

This paper presents generalized closed form expressions for determining the dimension limit for the basic design parameters as well as the pull-in characteristics of a nanocantilever beam under the influences of van der Waals and Casimir forces. The coupled nonlinear electromechanical problem of electrostatic nanocantilever is formulated in nondimensional form with Galerkin’s approximation considering the effects of these intermolecular forces and fringe field. The resulting integrals and higher order polynomials are solved numerically to derive the closed form expressions for maximum permissible detachment length, minimum feasible gap spacing and critical pull-in limit. The derived expressions are compared and validated as well with several reported literature showing reasonable agreement. The major advantages of the proposed closed form expressions are that, they do not contain any complex mathematical term or operation unlike in reported literature and thus they will serve as convenient tools for the NEMS community in successful design of various electrostatically actuated nanosystems.