Film Width Research Articles

Modeling of Spin Transport in Hybrid Magnetic Tunnel Junctions for Magnetic Recording Applications

We have demonstrated modeling of phonon and defect-induced spin relaxation length (LS) in Fe3O4 and organic semiconductor (OSC) Alq3. LS of Alq3 decreases with enhanced disorder and film thickness at a low film width regime. Exponential change of LS at low width regime is found for Alq3 which is, however, absent for Fe3O4 indicating comparable spin-dependent scattering and LS in Fe3O4. LS also decreases with spin-flip probability both for Alq3 and Fe3O4. Voltage-dependent tunnel magnetoresistance (TMR) response in Fe3O4/Alq3/Co and La0.7Sr0.3MnO3 (LSMO)/Alq3/Co hybrid magnetic tunnel junction (MTJ) devices has been attributed to modified spin filter effect across magnetic/OSC junction at high bias regime. TMR reduction with Alq3 thickness for Fe3O4 device has been attributed to spin relaxation at the organic spacer layer. A low bias peak from differential TMR indicates spin-polarized injection for both MTJ devices. Enhanced in-plane spin transfer torque for both MTJ is associated with modified spin filtering at magnetic/OSC junctions. Lower TMR signal for LSMO device indicates reduced tunneling and enhanced carrier injection across the OSC, which is also supported by the band structure profile. The TMR response observed from simulation results matches well with previously reported experimental results. Higher TMR response for Fe3O4 device indicates the possibility of device employment in room temperature magnetic recording applications.

Excitation by shot circuited coaxial transducer of magnetostatic modes in rectangular yttrium iron garnet film

The purpose of this work is the study of design of new short-circuited coaxial transducer with thin linear jumper, that circuites on both sides of the grounded coaxial cylinder, located above the rectangular iron-yttrium garnet (YIG) film, in homogeneous constant magnetic field with rectangular film along its length or width. The thin linear jumper is directed parallel to the width of the YIG film. Methods. In the CST Microwave Studio environment, an electrodynamic analysis of the model was carried out using the finite element method. To study the efficiency of modes excitation in a ferrite film at different distances between the coaxial transducer and the surface of the YIG film, the frequency dependencies of the inverse losses S11 of the model were calculated. Results. 1. The identification of modes in a homogeneous static magnetic field H, directed parallel to the plane of a rectangular YIG film along its width (y-axis) was carried out. 2. The identification of modes in a homogeneous static magnetic field H directed parallel to the plane of the rectangular YIG film along its length (z-axis) was carried out. 3. A comparison of modes spectra was made at H, directed parallel to the plane of the YIG film along its width (y axis) and length (z axis). Conclusion. In this paper short-circuited transducer with a thin linear jumper, circuited on both sides of the grounded coaxial cylinder, is investigated. By the electrodynamic method distributions of high-frequency magnetic field of the excited magnetostatic modes were calculated and their identification was carried out for two directions of homogeneous static magnetic field: along width and along length of rectangular YIG film. The dependence of number of excited modes on the distance between a short-circuited transducer and rectangular YIG was also studied. A comparison of modes spectra is carried out at H, directed parallel to the plane of the YIG film along its width and length. With this rotation of H vector, the band of effectively excitable modes shifts from 4.6...4.9 GHz to 4.5...4.75 GHz. However, the excitation of these modes in the case of the vector H, directed along the width of YIG film (z-axis), is much more effective in the band 4.65...4.9 GHz than in the case when this vector is directed along the length of YIG film (z-axis). At the same time, excitation of these modes in the case of the vector H, directed along the length of YIG film (z axis) is much more effective in the band 4.4...4.6 GHz.

Entropy and Bejan Number Influence on the Liquid Film Flow of Viscoelastic Hybrid Nanofluids in a Porous Space in Terms of Heat Transfer.

The aim of this study is to determine the influence of the various parameters on the flow of thin film motion on an inclined extending surface. Maxwell fluid is used as a base fluid, and magnesium oxide (MgO) and titanium dioxide (TiO2) are used as nanocomponents. The width of the thin film is considered variable and varied according to the stability of the proposed model. The magnetic field is used in the vertical track to the flow field. The entropy generation and Bejan number are examined under the influence of various embedded parameters. The outputs of the liquid film motion, thermal profile, and concentration field are also shown with the help of their respective graphs based on the collected data. The solution of the model involves key features such as entropy generation, Bejan number, drag force, and heat transfer rate. Brinkman number, magnetic parameter, radiation parameter, thickness parameter β, and unsteadiness parameter S are also deliberated graphically. The percentage improvement for the enhancement of heat transfer has been calculated and compared for both the nanofluid and hybrid nanofluids. The results are validated through comparison with the existing literature.

Manipulating liquid metal flow for creating standalone structures with micro-and nano-scale features in a single step

Standalone structures with periodic surface undulations or ripples can be spontaneously created upon flowing a liquid metal, e.g. Ga, over a metallic film, e.g. Pt, Au, etc, through a complex ‘wetting-reaction’-driven process. Due to the ability of 3-dimensional patterning at the small length scale in a single step, the liquid metal ‘ripple’ flow is a promising non-conventional patterning technique. Herein, we examine the effect of a few process parameters, such as distance away from the liquid reservoir, size of the liquid reservoir, and the geometry, thickness, and width of substrate metal film, on the nature of the ripple flow to produce finer patterns with feature sizes of ≤ 2 μm. The height and the pitch of the pattern decrease with distance from the liquid reservoir and decrease in the reservoir volume. Furthermore, a decrease in the thickness and width of the substrate film also leads to a decrease in the height and pitch of the ripples. Finally, the application of an external electric field also controls the ripple patterns. By optimizing various parameters, standalone ripple structures of Ga with the height and pitch of ≤ 500 nm are created. As potential applications, the ripple patterns with micro-and nano-scopic features are demonstrated to produce a diffraction grating and a die for micro-stamping.

Film casting of polycarbonate/multi-walled carbon nanotubes composites using ultrasound-assisted twin-screw extruder: experiment and simulation

Abstract A one-step ultrasonic film casting process to manufacture nanocomposite films was developed, in which polycarbonate (PC) was mixed with multi-walled carbon nanotubes (CNT) and cast into films in one process. Numerical and experimental investigations of necking phenomenon were carried out for film casting of PC/CNT composites. Experimental results revealed that the necking along film line decreased with imposition of ultrasound and increasing CNT content, indicating that incorporation of CNT and imposition of ultrasound restrained the elongational flow behavior of melt, resulting in film of a larger width. Isothermal and nonisothermal numerical simulations of the process were performed. In isothermal simulations, the polymer melt was assumed to be maintained at the die temperature. In nonisothermal simulations, the temperature change along the film line was determined from heat transfer calculations with the WLF temperature-dependent viscosity. The simulated and experimental results on normalized film width, defined as a ratio of cast film width to die width, as a function of the distance from the die at various extension ratios were compared. The comparison indicated that changes in film width and thickness along the stretching direction in the nonisothermal process were in better agreement with experimental results than that in the isothermal process. Both experimental and simulated results showed a decrease of film width with take-up speed. Due to the presence of edge effect, the film width in experiment was lower than the simulated one. With incorporation of CNT, a better agreement between experimental and simulated results was obtained, due to a reduced edge effect in the film.

Carbon nanotube-based, serially connected terahertz sensor with enhanced thermal and optical efficiencies

ABSTRACT Owing to their high thermal and optical performances, carbon nanotube (CNT) films are used in various photo-thermo-electric (PTE) applications, such as terahertz (THz) sensing and energy harvesting. To improve the performance of PTE devices, a device structure should be designed based on a deep understanding of the thermal and optical responses of the CNT film. However, the optical properties of CNT films in the THz frequency region remain unclear because of the difficulties associated with device processing and measurements. Herein, we report our findings on the thermal and optical characteristics of CNT films. The shape of the CNT film that maximizes the product of the thermal and optical factors (optimal structure of the PTE sensor) depends on the frequency of the irradiating electromagnetic wave. The optimal film thickness and width values for THz irradiation range from 300–600 nm and 50–70 µm, respectively. Subsequently, we fabricated a serially connected, multi-element PTE sensor with an optimal device structure and enhanced the detection sensitivity by approximately 13 times compared with a single-element PTE sensor. In addition, we demonstrated the first THz spectroscopy application using a PTE sensor. The findings of this study, thermal/optical factor enhancement, and micro-sized CNT film processing technology can be used to improve the performance of all CNT-based photothermal devices, including PTE sensors and thermoelectric generators.

Design of a three-nozzle for air spraying based on jet interference effect and numerical study of spraying process

Due to the problems of many round-trip time and low spraying efficiency when using single-nozzle, a three-nozzle structure is studied in this paper. The spraying process is numerically simulated by the method of computational fluid dynamics. The discrete phase model is used to predict the trajectory of droplets. The interference flow field is formed due to the entrainment of jet. Paint droplets are transported to the target under the action of gas flow field. The geometry of three-nozzle has a significant influence on the characteristics of the interference flow field. The influence of different distance (L) and axis angle (θ) between two adjacent paint holes on the interference gas flow field and coating thickness distribution are analyzed by changing the structure of three-nozzle. Numerical simulation results show that small L and θ result in strong interference effect, while the paint is mainly concentrated in the central region of the target, which is easy to cause overspray. With the gradual increase of L and θ, the strength of interference gradually decreases and the paint gradually spreads to both sides. However, the strength of interference would become very small when L and θ get too large, which is easy to cause an uneven coating film. According to the numerical simulation results, the best spraying effect can be obtained when L = 40 mm and θ = 30°. Compared with single-nozzle and double-nozzle, the effective coating film width of three-nozzle has increased by 414.3% and 176.9%, respectively, which improves the spraying efficiency.Article HighlightsFor the problem of low efficiency of single nozzle, this paper studies a three-nozzle based on jet interference effect.The coating film thickness distribution model is established based on numerical simulation, which avoids expensive and time-consuming experiments.Compared with single-nozzle and double-nozzle, the effective film width of three-nozzle has increased by 414.3% and 176.9%, respectively, which improved the spraying efficiency

Сapillatry effects manifested in the process of draining a liquid film that evaporated into a gas cross flow

The aim of the work is to determine the regularities of changes in the width of the flowing liquid film evaporating into a gas cross flow resulting from thermocapillary and concentration-capillary effects (Marangoni effect).
 The research was carried out experimentally employing an installation with a heated (working) surface, on which a liquid film (water or aqueous glycerol solution) was flowing. A flow of air was fed into the space between the working surface and the enclosing wall located at a distance from it, evenly in height and perpendicularly to the film movement. The film width was measured along the height of the working surface and the obtained dependencies were presented as graphs for different parameters of the flowing process.
 In all experiments, the graphs have an initial section with a sharp decrease in the film width, below which its change occurs smoothly. The degree of reduction in the film width depending on the parameters of the flowing process can reach 80%. In laminar mode, the reduction of the film width is more uniform than in turbulent mode, when some rise of the curves beyond the initial section is observed and can be explained by intensive mixing of the liquid. As the initial liquid flow increases, the degree of reduction in the film width decreases. Significant influence on the change in the film width is exerted by the temperature of the working surface during the flow of water: with increasing temperature, the film width decreases. At values of this temperature greater than 100℃, the rise of the curves is observed, possibly associated with the transition to volumetric evaporation.
 When the glycerol solution is flowing, the temperature of the working surface less influences the change in film width, although its decrease along the height of the working surface is greater than for water. The process parameters such as initial liquid temperature, initial solution concentration, and velocity and air temperature have relatively little effect on the change in film width. To correct the area of the film evaporation surface, determined by technological calculation, the width of the average evaporation surface is introduced under capillary effects. Its value increases with the initial liquid flow. For water, this dependence is characterized by a jump-like decrease in the film width in the transition from laminar to turbulent flow mode. This effect is absent on the dependence for glycerol solution, which can be explained by its higher viscosity. As the temperature of the working surface increases, the width of the average evaporation surface of the film decreases, some decrease being also observed with an increase in air velocity. Empirical equations for estimation of the correction factor were obtained. Capillary effects in this case are expressed by decrease in the width of the film at the height of its runoff, which leads to the need to correct the area of the film evaporation surface determined by technological calculation.

Modelling film and rivulet flows on microstructured surfaces using CFD methods

A new procedure to identify effective contact angles used in the description of the packing surface wetting is proposed. Both non-perforated and perforated surfaces are modelled. The flow of a water and triethyleneglycol (TEG) mixture over inclined, non-corrugated packing sheets was used as a model case. Different microstructures were investigated in a combined experimental and numerical study to determine the effective contact angles best reproducing the experimental film or rivulet widths. The outcome is a simple yet robust approach for modelling the liquid flow on structured packings.

Towards a new MHD non-homogeneous convective nanofluid flow model for simulating a rotating inclined thin layer of sodium alginate-based Iron oxide exposed to incident solar energy

In today's era, energy resources are among the essential objectives for the economic advancement of any developed country. Alternatively, fossil fuels that meet a large percentage of the world's energy needs are becoming increasingly rare and their quantity is dwindling. Solar systems which convert solar radiation into useable heat or electricity now play a vital part in the production of renewable energies. Solar energy, despite its somewhat higher operating costs, is a better alternative energy type when considering environmental safety and substantial uncertainty about future energy provisions. Due to the demand for solar radiation in nowadays era, the features of solar radiation towards the heat transfer of three-dimensional magnetohydrodynamic generalized and sodium alginate-based iron oxide Fe3O4- SA nanofluid flows past a spinning disk are investigated in this article. Furthermore, the Brownian motion and thermophoresis phenomena, and Arrhenius activation energy are taken into account. The obtained equations are altered from partial differential equations into ordinary differential equations with the help of reasonable similarity transformations. The transformed system is solved thereafter semi-analytically by the homotopy analysis method. The convergence area of the applied technique is displayed with the help of figures and tables. Here, we have found that the variation in sodium alginate-based iron oxide nanofluid due to film width is greater as compared to generalized nanofluid. The greater magnetic parameter has reduced the velocity profiles. Also, the generalized nanofluid has gained extraordinary velocity as compared to Fe3O4- SA nanofluid. On the other hand, the greater thermophoresis parameter has augmented the temperature profile while the opposing impact is observed for the concentration profile. Additionally, the generalized nanofluid has gained the greater variation in temperature profile as compared to Fe3O4- SA nanofluid, while no difference is found for concentration profile. The augmented absorption parameter, irradiance parameter, and thermal Biot number have amplified the temperature profile. In addition, the temperature profile of the generalized nanofluid increases significantly as compared to Fe3O4- SA nanofluid.

Experimental study of wavy-annular flow in a rectangular microchannel using LIF method

This article aims at studying gas-liquid flow in a rectangular microchannel with a high aspect ratio (200 × 2045 μm). Liquid and gas phases were 95% ethanol and nitrogen mixture. Experimental flow characteristics are obtained using high-speed visualization and laser-induced fluorescence (LIF) methods. Using the LIF method for wavy-annular flow, the average film thickness, liquid film distribution, and liquid film width were measured. The dependences of the liquid film width and the average film thickness on gas superficial velocity are presented in graphical form and analyzed. An increase in gas superficial velocity causes growth of the liquid film width and thickness of the liquid film, which indicates the process of liquid transfer from the menisci area to the liquid film. For different liquid velocities and the same gas superficial velocities, close values of averaged liquid film thickness were observed for flow with 2D waves and 3D waves on liquid film.

Free surface lubrication of rotating cylinders by impacting Newtonian liquid jet

AbstractFree surface lubrication of rotating cylinders by Newtonian liquid jets was investigated at different impingement positions, jet‐ and circumferential velocities. The interaction between impinging round laminar jet and rotating surface was characterised by high‐speed imaging. Compared to flat surface impingement, the liquid deposition mechanism is more complex and often accompanied by phenomena such as splashing, jet deflection and formation of radial surface stripes. Liquid splashing initially develops in direct deposition regime due to hydraulic jump‐induced droplet shedding, transitioning to lamella instability splash at higher Reynolds numbers. The critical Reynolds number for splash onset is of same order of magnitude as for flat surface impingement and fairly constant at low relative jet impingement angles, but increases exponentially when angle approaches 90°. Liquid film width and thickness were both determined proportional to the square root of the jet/surface velocity ratio, with respective power law models in good agreement with measured values.

Prediction of optoelectronic features and efficiency for CuMX2 (M=Ga, In; X=S, Se) semiconductors using mbj+U approximation

The optoelectronic properties of a selected group of Cu-III-VI2 chalcopyrites-based materials are deeply investigated by using the modified Becke-Johnson (mBJ) potential, combined with DFT + U approach. The obtained results are further used to calculate these materials’ theoretical efficiency limit for solar cell applications. The bandgap findings indicate a reliable ±0.2 eV agreement. After evaluating the electronic and optical properties, the spectroscopic limited maximum efficiency (SLME) model was used as a metric for the screening. Besides the bandgap value considered in the Shockley–Queisser model, the SLME requires that the absorption spectra, the radiative recombination losses, and the absorber layer thickness must be considered to adequately calculate the efficiency of considered cells. Our findings unveil that some candidates, such as CuInS2, where an SLME of 30.25% is achieved at a film width of 500 nm can be classified in the category of materials with higher power conversion efficiency.

Preparation and Performance of Thermochromic and Self-Repairing Dual Function Paint Film with Lac Resin Microcapsules and Fluorane Microcapsules.

Microcapsules with lac resin as the core material and urea-formaldehyde resin as the wall material were prepared by in situ polymerization, and then the lac resin microcapsules and fluorane microcapsules were added into a water-based primer or topcoat, respectively, to prepare water-based coatings with dual functions of thermochromic and self-repair. The effects of different methods of adding microcapsules on the optical properties, mechanical properties, self-repairing properties, and the aging resistance of water-based paint film were investigated, so as to prepare water-based paint film with the best discoloration and self-repairing functions. The results showed that the paint film with 10.0% fluorane microcapsules in the topcoat and 5.0% lac resin microcapsules in the primer had better comprehensive properties, and the paint film changed from yellow to colorless at 32 °C, with a color difference of 68.9, hardness of 3H, adhesion grade of 0, impact resistance of 13.0 kg∙cm, and elongation at break of 20.0%. The resistance of the paint film to NaCl, ethanol, and detergent was grade 2, with slight discontinuous marks, and the resistance to red ink was grade 3, with slight marks. The lac resin microcapsules have good aging resistance, which can enhance the aging resistance of the paint film with fluorane microcapsules. The gap width of the paint film was repaired by 2.1 µm, the self-repairing rate was 12.3%, and the paint film with lac resin microcapsules had a better crack inhibition effect. The results have provided a reference for multifunctional wood coatings.

Influence of oil deposition on the measurement accuracy of a calorimetric flow sensor

The calorimetric flow sensor is easily contaminated by dust and oil vapor particles present in the flow for some harsh scenarios, and its measurement accuracy is thus affected. This paper deals with the impact evaluation of oil deposition on the calorimetric flow sensor's measurement accuracy by simulation and experiment. An oil vapor deposition experiment was proposed to present the process and distribution of oil deposition and quantitatively measure the sensor output variation after contamination. In detail, a 3D simulation model is firstly established to investigate the influences of the parameters such as the thickness, width, and location of the oil film. Accordingly, a manual oil deposition experiment by smearing oil with a fine fiber is implemented to study the effect of the oil film on the measurement and to verify the simulation results. The experiment and simulation results consistently demonstrate that the oil deposited on the heater of the sensor has the most significant influence on the measurement, followed by the oil upstream of the heater. The measurement error exceeds 40% when there is only 7 or 8 μm thick oil film on the heater.

The Polymer Film Casting Process – An Overview

Abstract Cast film extrusion allows producing technical polymer films for packaging and coating applications. Different kinds of defects may be observed. For packaging applications, the challenge is to obtain very thin films in stable conditions at the highest throughput. For coating applications, the challenge is to master the film width reduction (called neck-in) and the induced non-uniform film thickness (called dog-bone defect). Well instrumented experiments point out the influence of the polymer and of the processing conditions on the occurrence of these defects. Numerical models of increasing complexity allow capturing the main experimental features and this makes possible to propose technological solutions to delay or even to suppress defects occurrence.

Analysis of an innovative water-cooling solution for photovoltaic-thermal systems

The research is focused on realizing a comparative analysis regarding the parameters of an active water-cooling solution for improving the efficiency of monocrystalline silicon photovoltaic (PV) panels. The efficiency of the photovoltaic panels is dependent on the climatic conditions, varying especially with the change of the intensity of the solar radiation and of the operating temperature. The cooling of the photovoltaic panels is a viable solution for both fixed and variable positions of the system. Numerical modelling was carried out on a photovoltaic panel integrated into the façade of a buildings. The water-cooling solution consist in using a water film heat exchanger attached on the backside of the PV panel. The parameters of the heat agent analysed were the temperature, velocity and width of the water film. The optimal water film heat exchanger solution was obtained for a thickness of 3 mm of water film, a velocity of 0.01 m/s and an operating temperature of 20 °C. In this case, the thermal power extracted by the film exchanger reaches values of 140.8 W, with an overall heat exchange coefficient of 48.6 W/m2.K. During the study, the global heat transfer coefficient and the raise off efficiency is determined for each case.

Superconducting Order Parameter Nucleation and Critical Currents in the Presence of Weak Stray Fields in Superconductor/Insulator/Ferromagnet Hybrids

The stray fields produced by ferromagnetic layers in Superconductor/Insulator/Ferromagnet (S/I/F) heterostructures may strongly influence their superconducting properties. Suitable magnetic configurations can be exploited to manipulate the main parameters of the hybrids. Here, the nucleation of the superconducting phase in an external magnetic field that periodically oscillates along the film width is studied on the base of the numerical solution of the linearized system of Usadel equations. In addition, the effect of the magnetic configuration of the F-layer on the temperature dependence of the critical current density, Jc(T), is investigated in the framework of the Ginzburg–Landau phenomenological theory on the base of the oscillating model of a stray field. By following this approach, the Jc(T) dependence of a Nb/SiO2/PdNi trilayer is reproduced for different magnetic configurations of the PdNi layer.

Study on film effects during isothermal drying of square capillary tube using Lattice Boltzmann method

The drying phenomena of an initially filled perfectly wetting liquid in a square internal cross-sectional tube are studied. The conditions are such that the liquid films develop along the tube internal corners under the effect of capillary forces until the bulk meniscus recedes in the tube. In this work, the Shan-Chen Lattice Boltzmann method (SC-LBM) is implemented to elucidate the complex multiphase phenomena involved in the isothermal drying of the square capillary tube. The SC-LBM is validated with Stefan-Maxwell diffusion relation and the simulated drying kinetics are in very good agreement with the commonly observed drying phenomena, which are the constant rate period (CRP) followed by the falling rate period (FRP). The computed capillarity along the liquid-gas interface at the internal corners of the tube results in the formation of extended corner films and surface films. Further, the pinning and the depinning phenomena as well as the variations of the corner film width are studied in detail. Based on the roughness factor of the tube, the characteristics of drying kinetics are studied and compared with the smooth square capillary tube.

Optimization and Analysis of Plastic Film Consumption for Wrapping Round Baled Silage Using Combined 3D Method Considering Effects of Bale Dimensions

HighlightsSolved the problem of optimal design, in the sense of minimal film usage, of round bale diameter and height.Necessary and sufficient optimality conditions derived in the form of easy-to-solve cubic equations.Bales of a maximum volume achievable with an actual wrapper and of optimal dimensions ensure minimal film usage.Up to 10% savings in film usage if bale dimensions are optimally designed and wrapping parameters properly selected.Abstract. The combined 3D method is used for wrapping cylindrical bales of agricultural materials based on biaxial rotation of the film applicators. The demand for minimization of plastic film consumption keeps increasing, with the goal to save the environment, reduce plastic costs, and minimize wrapping time. Consequently, methods have been reported to solve the problem of optimal wrapping parameters for the conventional wrapping method. In this article, a model-based problem of such a design based on round bale dimensions (diameter and height) that minimizes film consumption for the combined 3D method is mathematically formulated and analyzed. The film consumption per unit of bale volume is used as a measure of film usage. Generally, it is difficult to find the optimal bale dimensions that minimize the original film usage index, due to the discontinuity of the index. Thus, near-optimal parameters, being as important as optimal parameters for engineering applications, are looked for. The problem of selecting near-optimal bale dimensions was constructed by minimizing the continuous lower bound of the original film usage index. The necessary and sufficient optimality conditions for near-optimal bale dimensions were established in the form of standard cubic equations, which can easily be solved using both analytical and numerical methods. Based on the optimality conditions, analytical and numerical analyses were performed of the influence of film width, pre-assumed bale volume, and numbers of bottom and upper film layers on the near-optimal bale dimensions and film usage. The results indicated that the near-optimal bale diameter and height, hereinafter called optimal, monotonically increase, while the optimal film consumption monotonically decreases, with increasing pre-assumed bale volume. Therefore, it is recommended to use bales of a maximum volume achievable with an actual wrapper and of optimal dimensions, i.e., diameter and height. The film width also influences the optimal bale dimensions and film usage: the wider the film, the smaller the minimal film usage. To confirm the effect of near-optimal bale design on film usage, the errors of the near-optimality were examined for four to sixteen film layers. The results of the numerical experiments demonstrated that for four to sixteen layers of film, there are compositions of the bottom and upper film layers for which the relative near-optimality errors do not exceed 0.01% whenever the optimal bale dimensions are used. Simultaneously, inappropriate selection of wrapping parameters may result in increased film usage, measured by mean relative errors of 1% to 9.5%, which means up to 10% film cost savings when the bale dimensions are optimally designed according to the proposed approach, and the wrapping parameters are appropriately selected. Keywords: 3D bale wrapping, Mathematical model, Minimal film consumption, Round bales, Stretch film usage.