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A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series solution or some truncation of the power series solution be available and that some asymptotic behavior of the solution is known away from the series' expansion point. Here, we formalize the method of asymptotic approximants that has found recent success in its application to thermodynamic virial series where only a few to (at most) a dozen series coefficients are typically known. We demonstrate how asymptotic approximants may be constructed using simple recurrence relations, obtained through the use of a few known rules of series manipulation. The result is an approximant that bridges two asymptotic regions of the unknown exact solution, while maintaining accuracy in-between. A general algorithm is provided to construct such approximants. To demonstrate the versatility of the 1 method, approximants are constructed for three nonlinear problems relevant to mathematical physics: the Sakiadis boundary layer, the Blasius boundary layer, and the Flierl-Petviashvili monopole. The power series solution to each of these problems is underspecified since, in the absence of numerical simulation, one lower-order coefficient is not known; consequently, higher-order coefficients that depend recursively on this coefficient are also unknown. The constructed approximants are capable of predicting this unknown coefficient as well as other important properties inherent to each problem. The approximants lead to new benchmark values for the Sakiadis boundary layer and agree with recent numerical values for properties of the Blasius boundary layer and Flierl-Petviashvili monopole.

Bacterial viruses or phages have great potential in the medical and agricultural fields as alternatives to antibiotics to control nuisance populations of pathogenic bacteria. However, current analysis and purification protocols for phages tend to be resource intensive and have numbers of limitations, such as impacting phage viability. The present study explores the potential of employing the electrokinetic technique of insulator-based dielectrophoresis (iDEP) for virus assessment, separation and enrichment. In particular, the application of the parameter “trapping value” (Tv) is explored as a standardized iDEP signature for each phage species. The present study includes mathematical modeling with COMSOL Multiphysics and extensive experimentation. Three related, but genetically and structurally distinct, phages were studied: Salmonella enterica phage SPN3US, Pseudomonas aeruginosa phage ϕKZ and P. chlororaphis phage 201ϕ2-1. This is the first iDEP study on bacteriophages with large and complex virions and the results illustrate their virions can be successfully enriched with iDEP systems and still retain infectivity. In addition, our results indicate that characterization of the negative dielectrophoretic response of a phage in terms of Tv could be used for predicting individual virus behavior in iDEP systems. The findings reported here can contribute to the establishment of protocols to analyze, purify and/or enrich samples of known and unknown phages.

Mathematical modeling is a fundamental component in the development of new microfluidics techniques and devices. Modeling allows for the rapid testing of new system configurations while saving resources. Microscale electrokinetic (EK) techniques have significantly benefited by the advances in modeling programs and software packages. However, EK phenomena are complex to model, as they dynamically affect system characteristics, including the physical properties of the particles and fluid within the system. Insulator‐based dielectrophoresis (iDEP) is an EK technique that has received important attention during the last two decades. In particular, numerous research groups that study iDEP systems employ a combination of modeling and experimentation for developing new iDEP systems. An important fraction of these research groups has adopted the practice of employing “correction factors” to account for EK phenomena that cannot be accurately predicted in their models due to model complexity and limitations in computing resources. The present review article aims to provide the reader with an overview of the most common approaches in the use of correction factors for the modeling of iDEP systems.

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