Heel estimate during pressure-driven drainage of gels from tanks
Introduction
Heel refers to any residue left in a tank after its drainage. In many cases engineers are concerned about it from the point of view of tank cleaning, either when dealing with nuclear waste (see Prokopowicz and Phillips, 2011) or more ubiquitous materials, such as toothpaste (Yang et al, 2019). Process optimization is another common reason to try to minimize the heel or accelerate the drainage. The material can be discharged from the tank either under gravity or by sucking it from the tank under pressure. Generally speaking, engineers usually want the drainage to be done faster and the heel amount to be smaller. However, while there are quite a few publications on drainage rate (see, e.g., Joye and Barrett, 2003, or Toplak et al, 2007), hardly any systematic studies of the heel amount estimates were reported in literature. This paper intends to fill this gap.
The motivation of this paper comes primarily from toothpaste manufacturing, although similar problems are encountered in other industries. A typical “cold process” of toothpaste making, as described, e.g., by Pader (1992), consists of two steps. The first step is making a “liquid mix” which essentially is usually a polymeric gel containing organic gums with water and humectants (typically, glycerin) plus some water-soluble additives. The liquid mix or gel is subsequently transferred to the main mixer to which powders are added and the product becomes a paste. To maintain an efficient and cost-effective process, one wants to minimize the loss of valuable raw materials when discharging the polymeric gel from the tank. The discharge may be entirely gravity driven or, more often, accelerated by the application of negative pressure to the outlet pipe at bottom of the tank. This is where the problem of minimizing heel may become relevant. How to prevent accumulating excessive residue material on the walls of the tank?
This paper is organized as follows. First, we describe experiments on a simplified table-top device emulating gel discharge. Various gels of different rheological properties will be studied and the resulting heel left in the table-top tank estimated. We will show that the amount of the heel can be rather accurately estimated from the rheological parameters of the gel in the framework of a rather simple computational fluid dynamics (CFD) model. Next, we will discuss visualization of the gel transfer flow using magnetic resonance imaging (MRI). Our goal is to establish the most accurate and efficient way to predict the heel.
Section snippets
Materials
The gels were made by dissolving two polymeric materials, Xanthan gum by CP Kelco and carboxy-methyl cellulose (CMC) by Ashland, in a 50/50 mixture of glycerin and deionized water. CMC is a thickener which exhibits rather low yield stress values which is why it is often combined with “thixotropes”, i.e., structure-forming gums, such as Xanthan (Pader,1992). Both gums were first dispersed in glycerin using an overhead mixer after which water was added which resulted in a semitransparent gel. The
Results and discussion
A. Rheological data and model definition
Rheological data, on which subsequent calculations are based, are summarized in Fig. 3, Fig. 4. Both stress- and strain-controlled data were used as explained in Fig. 3 using as an example one of the gels- the one with 3% Xanthan and 1% CMC. In Fig. 3(a) results of the creep tests performed on this gel are shown. Viscosity is estimated as the reciprocal slope of the creep compliance curve based on the last 10% of its stress segment, as shown on this plot.
Conclusions
In this study, CFD modeling utilizing the Carreau model with fitting parameters extracted from rheometry was successful in predicting the trends in heel mass in the gel tank and the velocity field in contraction flow. The model predictions were validated by gel tank experiments and MRI velocity measurements. The following conclusions can be drawn from the experiments and modeling.
- The effect of the gel composition was studied by testing gels composed of two polymers with very different
Declaration of Competing Interest
The authors declared that there is no conflict of interest.
Acknowledgements
The authors gratefully acknowledge the Rutgers Molecular Imaging Center for providing assistance with MRI scanning. The help of Gregg Marron in performing some of the drainage tests reported in this paper is highly appreciated.
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2022, Journal of Non-Newtonian Fluid MechanicsCitation Excerpt :However, this is rarely the case with highly viscous and rheologically complex fluids. Furthermore, and to the best of our knowledge, we are only aware of one study specifically conducted on this topic, which was limited to the study of xanthan gum and CMC solutions discharged from an industrial tank [24]. Clearly, there is a significant gap in our ability to predict heel in general and especially for complex fluids, such as soaps, creams, and pastes, dispensed from commercial consumer dispensers.
The discharge of complex fluids through an orifice: A review
2022, Chemical Engineering Research and DesignCitation Excerpt :Ideally, the discharge process should occur rapidly and result in a negligible amount of heel. This could be especially important in contraction flows since the low-shear zones near the contraction contribute significantly to the mechanical energy loss (Fester et al., 2008; Potanin and Shapley, 2021). Thus, if the flow characteristics of the complex fluid of interest are not well understood, and the equipment/orifice is not designed properly, the discharge process and formation of a residual heel can become problematic.