Numerical investigation of AC electrokinetic virus trapping inside high ionic strength media

Abstract

A numerical investigation of the mechanism by which viral particles suspended in physiologically relevant (i.e., high ionic strength) media can be electrokinetically sampled on a surface is presented. Specifically, sampling of virus from a droplet is taking place by means of a high frequency non-uniform electric field, generated by energized planar quadrupolar microelectrodes deposited on an oxidized silicon chip. The numerical simulations are based on experimental conditions applied in our previous work with vesicular stomatitis virus. A 3D computer model is used to yield the spatial profiles of electric field intensity, temperature, and fluid velocity inside the droplet, as well as the force balance on the virus. The results suggest that rapid virus sampling can be achieved by the synergistic action of dielectrophoresis and electrothermal fluid flow. Specifically, electrothermal fluid flow can be used to transport the virus from the bulk of a sample to the surface, where dielectrophoretic forces, which become significant only at very small length scales away from the surface, can cause its stable capture.

Appendix

1.1 Physical parameters

• The equation for medium density, ρ_M, as a function of temperature T(K) was obtained from data given by Perry et al. (1997):

  $$\rho_{\rm M} = [- 3.9854 \times 10^{{- 6}}(T - 273.15)^{2} - 3.7765 \times 10^{{- 5}} (T - 273.15) + 1.0001]\rho_{0}$$

  The constant ρ₀ was taken equal to 1,000 kg/m³.

• Medium conductivity, σ_M, was obtained from data regression to experimental measurements on saline water of similar ionic strength (Lide 2001) over the temperature range of interest (T in K):

  $$\sigma_{\rm M} = 0.52 + 0.0171(T - 273.15)$$

• An expression for the relative permittivity of the medium was obtained from data given by Kaatze (1989):

  $$\varepsilon_{\rm M} = 87.297 - 0.3156(T - 273.15)$$

• The viscosity variation of water with temperature T (K) is described by the following equation (Perry et al. 1997):

  $$\eta_{M} = (- 0.0077426(T - 273.15)^{3} + 1.0344(T - 273.15)^{2} - 57.283(T - 273.15) + 1790.8) \times 10^{{- 6}} (\hbox{kg m}^{-1} \hbox{s}^{-1})$$

• Expressions for the parameters α and β were obtained from the derivatives of ɛ_M and σ_M (previously shown) with respect to temperature.

  $$\alpha = \frac{{^{1}}}{{\sigma_{\rm M}}}\left(\frac{{\partial \sigma_{\rm M}}}{{\partial T}}\right) = \frac{{0.0171}}{{0.471 + 0.0171(T - 273.15)}}$$
  $$\beta = \frac{{^{1}}}{{\varepsilon_{\rm M}}}\left(\frac{{\partial \varepsilon_{\rm M}}}{{\partial T}}\right) = - \frac{{0.3156}}{{87.297 - 0.3156(T - 273.15)}}$$

1.2 Boundary conditions

The following boundary conditions were applied for the solution of the numerical problem:

• Potential difference across opposite electrodes: ΔV _rms = 2.8 V

• External boundaries (medium–air and silicon dioxide–air interfaces):

  • Zero surface charge: − n·D =  0; (D: electric charge displacement)

  • Isothermal: T = T _o = 293°C

  • Slip symmetry: ${n \cdot \vec{u}\, =\,0}$ (medium–air interface)

• Medium–substrate interface:

  • No-slip condition: ${\vec{u}\, =\,0}$

• Vertical boundaries (symmetry planes in one quarter of the drop):

  • Surface charge: − n·D =  0 (symmetry)

  • Heat flux: − n·q =  0 (symmetry); ${q\, =\, - k\vec{\nabla}T\, +\,\rho_{\rm M}\,C_{p}\,T \cdot \vec{u}}$

  • Slip symmetry: ${n \cdot \vec{u}\, =\,0}$