Cleaning of toothpaste from vessel walls by impinging liquid jets and their falling films: Quantitative modelling of soaking effects
Introduction
Liquid jets are widely used in cleaning operations to remove soil layers from the internal surfaces of tanks and other vessels as well as exposed surfaces of process equipment. Devices commonly employed for tank cleaning operations by liquid jets include static spray balls and rotary jet heads. The selection of the device is determined by the shape and size of the unit as well as the nature of the soil on the surface to be cleaned.
There has been a noticeable increase in research activity on flow patterns and cleaning behaviour associated with a single coherent liquid jet. These studies can be categorised as either: (i) cleaning in the impingement area, where the jet hits the surface and flows radially outwards (Bhagat et al., 2017, Chee et al., 2019, Feldung Damkjær et al., 2017, Gerhards et al., 2019, Köhler et al., 2016, Rodgers et al., 2018, Wang et al., 2013b); or (ii) cleaning by the falling film that exists below the impingement point, where the liquid flows down under gravity and wets a vertical or inclined wall (Morison and Thorpe, 2002, Wang et al., 2013a).
Wilson et al. (2012) presented a simple model of the radial flow region to predict the hydraulic jump radius and the minimum width of the falling film based on momentum balances. In the radial flow region the flow was treated as a laminar film with a parabolic velocity profile, which was revised by Bhagat and Wilson (2016) to include the development of a laminar boundary layer and the transition to turbulent flow in the thin film. Wilson et al. (2014) used their flow result to develop a model for adhesive removal where the driving force for detachment is the momentum force applied at the cleaning front. They applied this to data obtained with a number of soft-solid soil layers. Glover et al. (2016) extended it to the case of viscoplastic soil layers. The removal model has also been extended to include nozzle motion (Wilson et al., 2015a, Wilson et al., 2015b) and the angle of inclination of the jet to the wall (Wang et al., 2015). Liquid losses due to jet breakup at longer jet lengths observed in industrial tank cleaning were included via an effective flow rate term (Feldung Damkjær et al., 2017).
The aim of this work was to develop a cleaning rate model for toothpaste, based on the adhesive removal models of Wilson et al., 2014, Bhagat et al., 2017. Toothpaste is a dense suspension of abrasive particles (with mean size between 10 and 20 μm) in a water soluble continuous phase, typically glycerine. This formulation introduces dissolution and dispersion mechanisms into the removal behaviour: it represents a soil which interacts with the cleaning solution, weakening as a result of soaking time. As such it represents a model material for studying the interaction of cleaning timescales with weakening phenomena. This is important for industrial application as cleaning solutions often feature formulations which promote weakening by adjusting pH, solubility and wetting behaviour so there is a dynamic variation in removal behaviour (Yang et al., 2019). This is particularly important for the soil layer below the point of jet impingement, which is subject to soaking by the falling film. Chee et al. (2019) demonstrated the importance of soaking for removal of layers of a viscoplastic soil layer (a Carbopol® gel).
This paper presents a systematic experimental investigation of the impact of soaking on jet removal in thin soil layers. The removal model is verified using cleaning tests employing static impinging jets, where the soil layer has been contacted with water for different times before removal. The time dependency of the model parameters is characterised. The model is then applied to cleaning by moving jets and falling films, and is shown to give good agreement with the experimental data.
Section snippets
Flow patterns induced by impinging jets
The flow pattern generated by a horizontal jet impinging on a vertical wall is illustrated in Fig. 1. A radial flow zone (RFZ) of radius is formed around the impingement point, where the liquid moves rapidly outwards and terminates at a jump. In the RFZ, the effect of gravity is negligible, so the model also applies to a vertical jet impinging on a horizontal wall (Fig. 1(a)). Gravity determines what happens beyond the RFZ. Above the point of impingement a rope or corona with varying
Rheology
The rheology of the toothpaste (Advanced White, Colgate) was measured on a rotational rheometer (Kinexus lab+, Malvern Panalytical, UK) using roughened parallel plates at 20 °C with 1 mm gap. The solids content of the toothpaste sample was 62.1 ± 4.5 w/w %. The measurements included undiluted or diluted (10 – 50% extra water) samples without pre-shear, as well as undiluted toothpaste with pre-shear at 5 Pa for 3 min (see Table 3). Pre-shear at 5 Pa was based on the estimated wall shear stress
Rheology
The rheological behaviour of the toothpaste and the effect of dilution are presented in Fig. 6. In the oscillatory time sweep measurement, the elastic modulus () and viscous modulus () gave steady and values over the test periods. The data in Fig. 6(a) show > , indicating that the toothpaste can be regarded as mainly elastic at low shear stress. Both moduli decrease strongly on dilution. Pre-shearing can reduce both shear moduli, but the effect is less significant than
Critique – Cleaning by falling film
The momentum flow rate in the water film differs significantly between the impingement area ( kg·s−2) and the falling film ( kg·s−2). It has been shown above that the adhesive removal model developed by Wilson et al., 2014, Bhagat et al., 2017 for cleaning near the point of jet impingement also applies to the cleaning by the falling film. However, there are two challenges in using the model to describe the cleaning of toothpaste by falling films, both related to soaking. Firstly,
Conclusions
The cleaning of toothpaste soils from glass surfaces by impinging water jets and falling films was studied experimentally. The adhesive removal model presented by Wilson et al., 2014, Bhagat et al., 2017 gave a good description of the cleaning behaviour in the RFZ and was extended to incorporate the effect of soaking and applied to removal in the falling film region below the RFZ.
Rheological studies confirmed that the toothpaste exhibited viscoplastic behaviour. The critical yield stress
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
A PhD studentship and project support for JY from DRIP (Danish partnership for Resource and water efficient Industrial food Production), partly funded by the Innovation Fund Denmark (IFD) under contract No. 5107-00003B, and by the Technical University of Denmark (DTU), is gratefully acknowledged, as are PhD scholarships for RKB and RRF from the Commonwealth Scholarship Commission and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, respectively.
Open data
Data sets and methods information related to this article can be accessed at the University of Cambridge Apollo data repository at https://doi.org/10.17863/CAM.42392.
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