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Research Highlights

Novel Equations Developed Across
Selected Publications

Concise, website-ready summaries of original analytical and predictive models

Selected Publications • Verified Equations • Plain-Language Impact

Editorial note

The equations below represent key analytical models, theoretical extensions, and quantitative relationships developed across our research group's published literature in nanoplasmonics, biosensors, dynamic nanoslip, and microfluidics.

Publication 1

Unraveling the Liquid Gliding on Vibrating Solid–Liquid Interfaces with Dynamic Nanoslip Enactment

Payam et al., Nature Communications 13, 6608 (2022) • doi:10.1038/s41467-022-34319-0
Equation (4)
$$\frac{b}{\delta} = \frac{(1+i)\left[Z^{L_s} - Z^{L_{ns}} - i\omega\varrho_f \ell_a\right]}{2\left[Z^{L_{ns}} + i\omega\varrho_f \ell_a\right]}$$
One-line summary: This dynamic-nanoslip model extracts the normalized slip length from QCM load impedance while explicitly including interfacial liquid inertia.
Key terms: $b$, slip length; $\delta$, viscous penetration depth; $Z^{L_s}$ and $Z^{L_{ns}}$, load impedances with slip and no slip; $\omega$, angular frequency; $\varrho_f$, fluid density; $\ell_a$, interfacial inertia length.
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Publication 2

Ion-Induced Hydrophilic Switching Enables Nanostructure Morphology Control for Superior Nanoplasmonic Sensing

Bhalla et al., ACS Applied Materials & Interfaces (2018) • doi:10.1021/acsami.8b14420
Equation (1)
$$\Delta\lambda = m \cdot \Delta n \cdot \left(1 - e^{-2d / l_d}\right)$$
One-line summary: Quantifies the localized surface plasmon resonance (LSPR) wavelength shift as a function of refractive index changes and biomolecular layer thickness.
Key terms: $\Delta\lambda$, wavelength shift; $m$, bulk refractive index sensitivity ($nm/RIU$); $\Delta n$, refractive index change; $d$, effective adsorbate layer thickness; $l_d$, electromagnetic field decay length.