Advances in computational technology and high-throughput modeling software have given rise to the tailored design of products that require accurate mathematical relationships for their assessment. Industrial emulsion-based products, ubiquitous to everyday life, are complex systems driven by interfacial phenomena that require quick property-prediction tools for their commercialization. In this work, by means of a multiscale approach, mathematical relationships to model oil-in-water emulsions and that can be applied to any commercial emulsion-based product are proposed. The energy consumption during the emulsification process ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>v</mi> </mrow> </msub> </math> , which transitions from monotonic increase to exponential growth at 80% <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>w</mi> <mo>/</mo> <mi>w</mi> </math> ), a parameter responsible for finished product performance, was linked to final product properties at three different levels: (i) molecular, through the dynamics of the interdroplet interactions given their distribution and structure at a microscopic level; (ii) microscopic, through average droplet size yielding an inversely proportional exponential relationship ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mfenced open="[" close="]" separators="|"> <mrow> <mn>4,3</mn> </mrow> </mfenced> </mrow> </msub> <mtext> </mtext> <mo>∝</mo> <mtext> </mtext> <msubsup> <mi>E</mi> <mi>v</mi> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msubsup> </math> ); and (iii) macroscopic, through the plateau value of the elastic modulus and the flow behavior index leading to inversely proportional quadratic relationships ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>∝</mo> <mtext> </mtext> <msubsup> <mi>E</mi> <mi>v</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msubsup> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi>η</mi> <mo>∝</mo> <mtext> </mtext> <msubsup> <mi>E</mi> <mi>v</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msubsup> </math> , respectively). These relationships are valid at dispersed phase concentrations beyond the 60% <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mi>w</mi> <mo>/</mo> <mi>w</mi> </math> threshold where the packing of the droplets changes the emulsion’s microscopic structure giving rise to Van der Waals forces-driven phenomena. Finding this threshold allowed expanding the concentration ranges of previously reported models. The main expectation is that these results will aid researchers and process/product designers to optimize their work in different industrial applications.
Tópico:
Pickering emulsions and particle stabilization
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2
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FuenteInternational Journal of Chemical Engineering