Each one of the three industrial revolutions that have taken place so far present common characteristics which distinguish them from common, evolutional changes of the industrial sector. The main requirement for each one to take place has always been the accumulation of various innovations in industrial production. This is followed by up-dating infrastructure and the evolution of societies around a consequently transformed economy sector, producing new products, enhanced opportunities, as well as a reorganised production model. Eventually, the required resources and cost for production are reduced, product quality improves, niche products are developed. Finally, the real sector of economy reaches a new developed level of operation (Popkova et al., 2019).

Any industrial revolution that follows the previous three will also evolve in a similar way. In fact, the concept of the Fourth Industrial Revolution, which was introduced in 2011 (Slusarczyk, 2018), and published as a strategic plan for industrial development by two German Ministries in 2012 (Platform Industrie 4.0, 2012), required the accumulation of innovations in the sector of Internet of Things and Robotics, transition to fully automatised production lines, the development of new infrastructure able to support ultra-fast internet connections, the design and development of high-end robotic equipment, niche and cheap materials, significant decrease of the human factor in production, followed by an increased demand for highly specialised know-how (Popkova et al., 2019).

Even though “Industry 4.0” is not due soon, since the concept was introduced, most competitive industrial manufacturers around the world have been trying to secure sustainable, high quality, low cost technological developments. Using the continuously evolving and developing benefits that cyber-physical systems, the internet of things and artificial intelligence have to offer, the total computerisation of manufacturing and fabrication has been set as an aim (Müller et al., 2018). While these pillars of “Industry 4.0” would take care of the conversion of experimental data into digital format, to establish the smart factories of the future, processes themselves need to enter a new era. New manufacturing technologies will need to arise in order to replace traditional production lines with more flexible ones able to support the evolved industrial needs of this next transition.

Among these technologies, additive manufacturing processes have significantly contributed to the rapid transformation of the industrial landscape during the last decade (Ford and Despeisse, 2016). Much research has been focused on this new approach for fabrication, pointing out, not only the advantages but, also, the disadvantages derived from applying such methods and techniques. In particular, “low-volume/high-value” industrial sectors, such as the aerospace, marine and energy industries, are expected to benefit from this kind of approaches. This is mainly because manufacturing of larger volumes of customised products could be achieved in that manner. There could be a reduction of industrial and economic waste, which would decrease the cost of operation and reduce environmental impact. One such technology is electroforming.

Electroforming was first introduced as a technical process by the Prussian engineer and physicist, Moritz Hermann von Jacobi, in 1838. Since then, the process has been used in a wide range of applications; from fabrication of micro-components for medical and electronics sectors to the construction of large parts for aerospace industries, thereby impacting our daily life.

An appropriate definition would be, “electroforming is the production or reproduction of articles by electrodeposition upon a mandrel or mould that is subsequently separated from the deposit” (International, 2003) to be used as a standalone product. An electrochemical process requires at least two electrodes, an anode, and a cathode, to be immersed in an electrolytic solution, an electrolyte which contains the metal ions to be plated, and a power supply (DC) which enables current to flow through the system. The anode consists of the metal that is to be deposited on the mandrel while, the mandrel itself plays the role of the cathode and current collector. Due to voltage difference between the two electrodes, current passes between the anode and the cathode, leading to the conversion of metallic ions into atoms on the cathode’s surface.

From the mechanical engineer’s point of view, this is synonymous with an additive process because the atoms are being built up, layer by layer, until the desirable thickness of the electroformed part is achieved. As opposed to many academic studies in electrochemistry, the process is run using two electrodes in a galvanostatic fashion. The aspects which separate this process from normal electroplating is the fact that the formed part has to be separated from the substrate, which requires the form to have sufficient mechanical strength (John et al., 1999) as well as low internal stress (Kume et al., 2016) (Stein, 1996). These two requirements impose stringent limits on shape complexity, electrolyte choice and applied current density.

Even though nickel electroforms present exceptional mechanical properties and low to zero internal stresses (Committee B-8 Staff, 1962; Popereka, 1970; Uriondo et al., 2015; Davies and Jenkins, 2014; Jianhua et al., 2016; Zhu et al., 2006; Zhu et al., 2008; Li et al., 2019; Khazi and Mescheder, 2019) rendering electroforming a promising manufacturing process for “heavy” industries, our current knowledge base is derived predominantly from empirical data since scientific research has been limited. As it has been reported already (Roy and Andreou, 2020), although there is a huge volume of empirical data, more in-depth scientific analysis, amenable to predictive modelling, is needed. Most importantly, for volume manufacturing, systematic experimental and modelling investigations in the laboratory, and thereafter scaling-up to industrial conditions, are required. Such an approach would provide credible information which is currently not available.

Based on such information, certifiable models and new methodologies for controlling the thickness of an electroform, its uniformity and shape evolution could be developed. The authors have already discussed the state-of-the-art studies of modelling the electroforming process in a previous review paper (Andreou and Roy, 2021). However, it is important to briefly present here some of the most influential works—to the authors’ opinion—on modelling other metal electrodeposition processes, which have reported findings that are proven to be a potent starting point for the studies focusing on modelling the electroforming process itself.

In the 1980s Matlosz et al. investigated the secondary current distribution (SCD) in a Hull cell comparing the finite and boundary element methods for model development (Matlosz et al., 1987). Making the point that previous studies had mainly studied the primary current distribution (PCD) in deposition cells, they developed models and experimentally verified them to describe the SCD kinetics during copper deposition, ignoring the effects of mass transport phenomena. By assuming Butler-Volmer kinetics and studying both the Tafel and linear approximations, they reported a good agreement between the two computational methods and suggested that current density in a Hull cell can be described by a set of a Wagner number for Tafel kinetics, a Wagner number for linear kinetics and the anodic and cathodic Tafel slopes.

During the same decade the RDE was also used for secondary and tertiary current distribution (TCD) studies focusing on the co-deposition of nickel alloys (Ying et al., 1988) (Hessami and Tobias, 1989). By assuming Butler-Volmer kinetics to build their models, these studies investigated how process parameters like applied current densities, ion concentration and cathode surface pH affect the final product. To mention only some of their interesting suggestions, Ying et al. (Ying et al., 1988) succeeded in predicting their copper-nickel deposit composition as a function of the applied current, the process current efficiency and the polarisation data describing the experimental co-deposition process. Interestingly, they pointed out the difficulty in gathering data about hydrogen evolution during nickel deposition, arguing that the various reactions occurring in the process would not allow for accurate measurements. Consequently, they suggested that approximate predictions would only be possible through a “data force fitting” approach.

Hessami and Tobias (Hessami and Tobias, 1989) also investigated how agitation rate, electrolyte pH and hydrogen evolution affect deposit composition and process efficiency during the anomalous codeposition of nickel-iron alloys. Increasing agitation was reported to be in favour of iron deposition, linking that behaviour to higher hydrogen evolution at low potentials which reduces current efficiency. Another noticeable aspect is that increasing pH led to high nickel content at higher potentials and high iron content at low potentials. Through their observations and predictions, the authors confirmed once more the complex behaviour of anomalous co-deposition systems. Most importantly, however, and even though they reported good agreement between those observations and predictions, they established and pointed out the need for in-depth, systematic experimental studies before anomalous co-deposition processes could be sufficiently decoded.

Moving on to the next couple of decades, models were deployed to give answers to pressing electrodeposition-related questions considering various aspects of reactor and process optimisation. Aiming to overcome the Hull cell’s incapability during studies of processes dominated by a mass transport-limited step, Madore et al. (Madore et al., 1992a) developed a model in order to investigate primary and current distributions in a rotating cylinder Hull (RCH) geometry that they, themselves, had proposed months earlier (Madore et al., 1992b). Using the boundary element method (BEM) for their calculations and the Tafel approximation to describe the system’s kinetics, they calculated these distributions and established through experimental validation that their proposed cell could be successfully used for the study of various deposition processes, including alloy deposition.

On a different use of electrodeposition modelling, Krause et al. (Krause et al., 1997) took up the task of settling the argument between earlier models of Matlosz (Matlosz, 1993) and others’ (Romankiw, 1987; Grande and Talbot, 1993; Ramasubramanian et al., 1996) on the importance of NiOH + and FeOH + presence during nickel-iron co-deposition. To do so, Krause and his team proposed a reaction mechanism which involves Ni + 2 and Fe + 2 as the electroactive species instead and conducted NiFe deposition experiments in a sulphate bath, using the RDE setup, to validate their predictions. Indeed, they succeeded in obtaining similar results with all the previously suggested models, proving that the presence of NiOH + and FeOH + species could be totally ignored. However, they highlighted the fact that none of the models could definitively be considered dominant over the others due to the tendency of transport models to include adjustable parameters which can be sensitive to variations in electrode preparation procedures, the electrodes’ working conditions or even the slightest differences in experimental approaches among different research groups.

In most recent years PCD, SCD and TCD studies are still a matter of interest for scientists and engineers worldwide. As new modelling tools become (commercially) available, new studies not only validate and update earlier modelling approaches, but also enrich already established models by incorporating complex phenomena with greater confidence. Using COMSOL Multiphysics® (formerly FEMLAB®), Low et al. (Low et al., 2007) modelled the copper electrodeposition from an acid sulphate electrolytic solution in an RCH cell with an offset anode developed by RotaHull® in early 2000s. Using the Tafel approximation to describe the system’s kinetics, assuming Nernstian behaviour for the diffusion layer, and taking into account even complex turbulent flow-related phenomena, they validated a novel setup and suggested, through simulations, the PCD’s dependence on the system’s geometrical characteristics, as well as a non-uniform current profile on the cathode’s surface. Furthermore, SCD simulated the real-life process more accurately under out-of-equilibrium conditions since it accounted for charge transfer, and it was observed to be valid far below the limiting current density. As a final step, TCD studies were run to determine the concentration, local current and overpotential profiles on the deposition surface and were used to describe their correlation.

Following an identical approach, Pérez and Nava (Pérez and Nava, 2014) investigated PCD, SCD and TCD in a rotating cylinder electrode (RCE) using four-plate, six-plate, and concentric cylinders as counter electrodes, under turbulent flow conditions. Their simulations were validated through copper deposition experiments. Their work provided an important insight into the behaviour of systems that use different counter electrodes and could potentially lead to more cost-effective and technically efficient cell systems.

Modelling of electrodeposition processes has also been useful to the study of industrial setups, especially ones with complex geometries and thus, complex electrode-electrolyte interactions. Such a case is the one of zinc electrowinning cells which Bouzek et al. (Bouzek et al., 1995) modelled in 1995. To simulate the case of an industrial electrowinning reactor the authors developed a model which was solving the Laplace’s equation for calculation of the potential and current distributions, the Tafel approximation to account for hydrogen and oxygen evolution and the Nernst equation to compute the equilibrium potentials needed for the analysis. Current efficiency was determined around an average of 85% due to impurities. Current distributions for the anodes and cathodes were also successfully computed. The model was validated for positioning of the cathodes’ active width between the anodes, since only the cathode position was varied experimentally. For other electrode arrangements the model was over-predicting the current density values. To account for such differences caused by the movement of a single cathode, an extended model consisting of three cathodes and two anodes was developed. Even then, however, inconsistencies between the experiments and simulations were observed. This model behaviour was attributed possibly to dendritic growth at the edges or, other, similar mass transport effects. At the same time, differences in predicted current densities between the regular and extended model revealed complex electrode interactions, with current travelling not only between a cathode and its neighbouring anode but also the second nearest one. As a general observation, moving the cathodes sideways was found to have much more effect on current distribution than positioning them at an angle with reference to the anodes. Also, the use of insulating edge strips at the cathodes’ edges led to significant non-uniformity in current distribution. To conclude, this work proposed a systematic approach for conducting geometry sensitivity studies, proving that careful reactor design could play an important role towards process optimisation.

Following a similar approach, Henquín and Bisang (Henquín and Bisang, 2009) studied current distribution in bipolar electrochemical reactors. Modelling the primary and secondary current distributions, they established that the latter is critically determined by a current leakage and an open bipolar stack, where the electrolyte is not constrained between the electrodes. Additionally, two different current paths were revealed, the expected one when current travels through the bipolar electrodes and a bypass when current travels around the electrodes rendering their overpotentials irrelevant to the process.

Last but not least, great attention has been paid recently in modelling the flow during electrodeposition under agitation. Modern modelling software has provided researchers with the ability to simulate fluid dynamics in reactor cells, incorporating into their models complex flow equations, minimising at the same time the need for overpowering assumptions and simplifications. Even though electrodeposition hydrodynamics have been the subject of modelling for many years now (Tribollet and Newman, 1983), computational fluid dynamics (CFD) analysis has been gaining significant ground during the last couple decades. Rivero et al. (Rivero et al., 2010) solved the Reynolds-averaged Navier-Stokes (RANS) equations to model a mass transport-controlled copper recovery process under turbulent conditions. They chose to study the process in an RCE and a six-plate counter electrode setup, establishing, among others, that dendritic formations can lead to an increase in micro-turbulence, as well as the fact that hydrogen evolution can be avoided under conditions of potentiostatic control for longer electrolysis when, eventually, mass transport takes control.

A similar methodology was also deployed more recently by Pérez et al. (Pérez et al., 2020) for modelling a laboratory-scale, filter-press flow cell for nickel electrodeposition. This time the authors aimed for reactor optimisation by conducting CFD studies to neutralise jet flow and edge effects on current density. They carefully considered the effects of hydrogen evolution during nickel deposition and observed that it takes place below − 0.4  V . Consequently, they established that their SCD and TCD studies, conducted within a ( − 0.4  V ) − ( − 0.7  V ) potential window, should indeed account for hydrogen evolution. Their proposed cell design was experimentally validated, suggesting that electrolyte manifolds followed by polymer meshes can significantly decrease edge effects on flow and current density. A “flow calming zone” was also introduced and established to be an effective addition to the reactor design.

Nevertheless, since most of the above discussed studies were conducted in the laboratory-scale, it is important to highlight the need for cautious adaptation of their findings to the inherent characteristics of large-scale additive manufacturing, including nickel electroforming for aerospace applications. To provide just a couple of examples, in these cases, it should be kept in mind that geometry sensitivity studies cannot be focused on simulating current distribution and/or mass transport phenomena for close electrode positions, as it is usually the case in laboratory-scale studies. Aerospace industry protocols determine the closest position that two electrodes could be placed at therefore, any effort to simulate real close electrode positions would not be of any use to industry.

However, it would be very useful, for example, to determine whether the anode position with reference to the cathode is “irrelevant” to the model. On another, rather dividing aspect, the need, or not, of modelling hydrogen evolution and tertiary current distribution should be considered cautiously. For one, even though specific processes (e.g., copper deposition) might easily result being affected by hydrogen evolution, this may not be the case for electroforming. In industry, nickel electroforming at currents between 5–20 ASD, using 100 L tanks under agitation, may be adequately described by SCD. In simulating such a process, therefore, the inherent characteristics of the system need to be considered to allow for comprehensive and informed modelling.

Approaching the issue from such a perspective and utilising the power of numerical analysis and the increasingly available computational resources, modelling the scale-up of an electroforming process could be used for making well-educated decisions on the limitations of an industrial-scale electroforming process. This would enable one to visualise the process conditions needed to obtain a particular electroform. A second consideration for such modelling is the availability of commercial software which can be implemented for an industrial process, and the limitations of such modelling tools.

In that effort, finite element methods (FEM) have been dominating the modelling studies of the electroforming process (Behagh et al., 2015) (Belov et al., 2016). The main reason is that it is the most efficient computational approach in sufficiently describing the boundary conditions and satisfactorily solving nonlinear electrochemical problems. A slightly different approach using BEM has also been used (Nouraei and Roy, 2007), where electrode shape changes, induced during a process, had to be taken into account. On one hand, finite element methods generally solve the current-potential equation throughout the electrolyte and the boundaries (i.e., cathode and anode), which may be slightly less efficient for the purposes of electrodeposition, electro-dissolution and electroforming where electrochemical reactions occur mainly at the boundaries. BEM, on the other hand, concentrates on evolving shape and associated changes in current and potential arising from these processes (Nouraei and Roy, 2007) (Elsyca, 2021). However, as computing power increases, computing efficiency is less of a problem, and hence FEM can be used to reasonably large-scale systems.

When it comes to scale-up modelling of processes with industrial interest, modellers should be able to comprehensively determine the way in which a model’s input parameters, geometric characteristics, and assumed physics, might be affected as the scale of a simulation increases. The inclusion of too many fitting parameters confounds engineering information, such as if size and shape of reactors (in the simplest case these are plating tanks) should be changed, current density should be increased or decreased or whether pulsating currents should be chosen (Wolfgang and Hansal, 2012), or how electrolyte–which influences electrode kinetics–should be chosen. In other words, the geometric and analytical limits of all models should be thoroughly researched and based on experimentally determined parameters, as far as possible, before any scaling up process is attempted. Nevertheless, such a research approach is missing nowadays, leaving important, scale-related, questions unanswered.

In an effort to shed light onto such a modelling methodology, which examines and elucidates the approach to resolving some of those uncertainties, this work consists of two parts. The first part includes geometry optimisation and model sensitivity studies of a 3-D electrodeposition model simulating the electroforming process on a laboratory-scale rotating disk electrode (RDE). This section involves the thorough examination of computational aspects of the model. The second part is focused on scaling-up to an industrial-scale process and compared against the RDE model. While an RDE-type system is seldom used in industry, the simplicity of the geometry allows one to explore issues arising due to scale up. In addition, for both the RDE as well as the industrial-scale system, experiments related to parameter determination and validation are reported here.

Geometry optimisation and model sensitivity studies were once more conducted for comparison purposes between the two scales. The key differences, challenges, and limitations during sizing upwards are reported here. For geometry optimisation studies, the relative position of the anode, with reference to the cathode position, and the cell size were varied for both the laboratory-scale and industrial-scale models. Additionally, the model sensitivity studies were focused on how the input parameters, process physics, mesh spacing, and computation times might be affected by the setup’s sizing-up.

COMSOL Multiphysics® was chosen for the studies presented in this paper. The software has been popular with electrochemists (Mahapatro and Suggu, 2018) (Heydari et al., 2020) and uses FEM for calculations. The authors have discussed the potential and limitations of the software in an earlier review (Andreou and Roy, 2021). In particular, it needs to be mentioned that our model used the “Electrodeposition” interface in COMSOL Multiphysics®. The system was set to work under galvanostatic mode (as is done in industry), the current at the cathode was determined, and the deposit thickness was calculated at each time step. This thickness was used to move boundary for the formed electrode as it evolved with time, and again the local currents were computed. The electrode reactions chosen were of Butler-Volmer type, with nickel and its ions being the only electroactive species. The physical dimensions of the reactor were used to fix reactor geometry. It is important to mention that COMSOL Multiphysics® can be installed in super-computers [e.g., Archie-West in Scotland (ARCHIE-WeSt, 2021)] as easily as in an average PC therefore it offers the possibility of studying scaled-up models of very large parts. This paper is based on results obtained using COMSOL Multiphysics® on a professional desktop.

The laboratory-scale reactor was a 0.2  L double-wall electrolytic cell. The recessed RDE consisted of a 2  M , industrial grade, Ni ( SO 3 NH 2 ) 2 electrolytic solution, a 304 stainless-steel disk electrode ( D  =   0.12  dm ), and a nickel anode made out of industrial grade nickel pellets mounted on a titanium rod. The nickel sulphamate electrolyte is used for electroforming due to the deposits having good ductility, heat-resistance properties, high current-resistance properties and is related to low intrinsic stress (Baudrand, 1996). Since very low stress is required for aerospace applications, additives are not used, and these inherent characteristics of nickel sulphamate electrolytes are an advantage. The anode area was twice as that of the cathode to avoid anode passivation (Roy and Andreou, 2020). The disk electrode was rotating at 1,500 rpm. The electrolytic solution was heated by a water bath circulating water at 50 ℃ through the cell’s jacket. Current was applied by a 1  A power supply through copper crocodile clips and deposits of 0.2 × 10 − 3  m (nominal) were deposited for verification of model computations. The RDE setup’s schematic is provided in Supplementary Figure S1 of this publication.

The 18  L tank reactor is made of polypropylene (PP) due to the material’s good mechanical properties at temperatures up to 80   ℃ and chemical resistance to dilute acids (Hindle, 2021). The system uses a SIEBEC MC15 pump and filter system to achieve sufficient electrolyte circulation. The M15 magnetic drive pump allowed for a maximum flow rate of 1.5   m 3 / h and particles between 0.5 up to 150  μm were filtered using an on-line filter. A SIEBEC polypropylene 1 / 4 ' ' eductor nozzle was used to circulate the electrolyte within the tank. The electrolyte was heated by a 0.5  kW BRAUDE Polaris cylindrical non-corrodable heater. A BRAUDE Tankmaster MP temperature and level controller was used for continuous monitoring and controlling of the solution.

The anode basket and mandrels used in the process were immersed in the electrolyte by mounting them on 12  mm copper busbars of > 99 % purity. Current was applied by a 20  A , 18  V RS PRO Switching DC Power Supply using 30  A , steel, BU-65–0 Farnell crocodile clips. The anode basket was made of titanium and filled with industrial grade nickel pellets. The scaled-up disk mandrel ( D = 0.63  dm ) was made of 304 stainless-steel. For the scaled-up experiments the same electrolyte as in the RDE experiments was used and deposits of 0.07 × 10 − 3  m (nominal) were deposited for verification of model calculations. The interior tank schematics are provided in Supplementary Figure S2 of this publication.

One needs to clarify here that the shapes and sizes of the laboratory-scale and tank reactors are dissimilar. This is intentional, because RDE are usually employed in laboratories, whereas a tank system is the “work horse” in industry. In the laboratory, glassware availability dictates the reactor shape, which is mostly cylindrical, whereas in industry plastic sheets are used to form more rectangular reactor structures.

Nickel electroforming, time-dependent, models of two different scales were developed using a commercial software and were successfully validated against experimental data. The models were based on the assumptions of secondary current distribution (SCD) using Butler-Volmer kinetics. One model was developed to simulate the nickel electroforming process in a laboratory using a rotating disk electrode (RDE) while the second one represented an industrial, 18 L , electroforming reactor configuration.

Electrochemical experimental data, collected via polarisation studies were used as input for both models. The reaction at the cathode and anode were based on the overall nickel reduction and dissolution reactions, respectively. Current-potential data was used to fit exchange current density and forward and backward charge transfer coefficients. From the experimental measurements the equilibrium potential was found to be −0.52 V. The model could be used to predict current-potential data even though a detailed reaction mechanism was not used.

At first, a set of control simulations, modelling deposition processes, in both scales, at current values similar with those applied by the industry, were carried out to determine the potential and current at the electrode surface. The simulated results suggested that he total current and anode potential remain fixed, while the cathode surface local potential is adjusted by the model to calculate the local current density, which is then summed up to obtain the total current density, and compared against the value set for the simulation.

The results obtained were validated by cross-checking the thickness of an electroformed disk using the RDE as well as the electroforming reactor. It was found that the formed material on the RDE was thinner than the predicted value. The thickness of the disk formed within the electroforming reactor, on the other hand, agreed reasonably with the values computed by the model. The difference in the agreement between the calculated and experimental value for the RDE was attributed to the growth of dendrites along the circumferential edge of the disk.

Mesh sensitivity studies were conducted to determine both models’ inherent mesh spacing tolerance, as well as any differences observed between the two scales. Developed meshes for both models presented with a similar high element quality at ∼ 0.65 . The control meshes of both models were modified by ± 5 % , ± 10 % , ± 12 % , ± 15 % , ± 25 % , ± 50 % and − 75 % . Regarding the RDE model, an increase of mesh element size by 12 % and a decrease of 25 % were found to be the thresholds after which a minor deterioration of the thickness profiles’ smoothness was observed. For the electroforming reactor model, the corresponding results revealed that an increase of the element size by 15 % and a decrease by 50 % had a major effect on the predicted thickness profiles’ smoothness. However, no significant changes in the simulated thickness were observed for either model, while the computation time increased significantly for the finest meshes in both scales. Therefore, in practice, it is suggested that mesh spacing should be optimised against computation times.

Studies on the effect of anode location, which dictated the anode-cathode distance, on current uniformity within the RDE or reactor were performed using the models. It was found that anode positioning did not play a major role on the uniformity of the deposit. Secondly, the geometry of the reactor was changed to determine the effect of reactor boundaries on current uniformity.

For both scales, placing the anode frontally to the cathode, and within 10  mm of the deposition surface, resulted in increased thickness uniformity all over the electroform’s “useful” area. Outside the 10  mm proximity zone, the models suggested that changes in anode position increase the ohmic potential drop, but stop affecting current distribution. These results are relevant to industrial situations, because one would like to minimise changes to the electroforming process due to anode positioning or reactor geometry.