Electrowetting Simulator: Digital Microfluidics Droplet Control

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θ ≈ 78° — contact angle reduced from 115° by electrowetting

Applying 80V across a 5 μm dielectric (εr = 3.5) reduces the contact angle of a water droplet from 115° to approximately 78°, with an electrowetting number of 0.55.

Formula

cos θ = cos θ₀ + ε₀εrV² / (2dγ) (Lippmann-Young)
η_EW = ε₀εrV² / (2dγ) (electrowetting number)
F_EW ≈ ε₀εr V² w / (2d) (electrowetting driving force)

Electrowetting Fundamentals

Electrowetting-on-dielectric (EWOD) exploits the voltage-dependent change in wettability of a droplet sitting on a thin dielectric-coated electrode. When voltage is applied, the electric field at the solid-liquid interface modifies the effective surface energy, causing the droplet to spread. This phenomenon, described by the Lippmann-Young equation, enables precise digital control of discrete droplets without pumps, valves, or channels.

The Lippmann-Young Equation

The contact angle change follows cos θ = cos θ₀ + ε₀εrV²/(2dγ), where the electrowetting number η = ε₀εrV²/(2dγ) quantifies the ratio of electrical to surface tension energy. The quadratic voltage dependence means doubling the voltage produces four times the wetting force. Thinner dielectrics and higher permittivity materials enable lower operating voltages, critical for portable devices.

Contact Angle Saturation

At high voltages, the contact angle stops decreasing — a phenomenon called contact angle saturation that limits the minimum achievable angle to roughly 50-60°. Despite decades of research, the exact mechanism remains debated. Leading theories include charge trapping in the dielectric, local dielectric breakdown at the contact line, and thermodynamic limits related to the saturation of the double-layer capacitance. This saturation constrains the maximum driving force for droplet transport.

Digital Microfluidics Platforms

In a digital microfluidics device, an array of individually addressable electrodes beneath a hydrophobic surface enables programmable droplet routing. By sequentially activating adjacent electrodes, droplets can be transported, merged, split, and dispensed from reservoirs — all under software control. This flexibility makes EWOD platforms ideal for reconfigurable biochemical protocols, from immunoassays to DNA library preparation, replacing complex networks of channels and valves with a simple planar electrode array.

FAQ

What is electrowetting-on-dielectric (EWOD)?

EWOD is a technique for manipulating droplets by applying voltage across a thin dielectric layer beneath the droplet. The electric field modifies the solid-liquid interfacial energy, reducing the contact angle and enabling droplet transport, splitting, merging, and dispensing on an array of independently addressable electrodes.

What is the Lippmann-Young equation?

The Lippmann-Young equation cos θ = cos θ₀ + εε₀V²/(2dγ) relates the contact angle θ to the applied voltage V, where θ₀ is the initial contact angle, ε is the dielectric constant, d is the dielectric thickness, and γ is the surface tension. It predicts that contact angle decreases quadratically with voltage.

What causes contact angle saturation?

At high voltages, the contact angle stops decreasing despite the Lippmann-Young prediction of complete wetting. Proposed mechanisms include charge trapping in the dielectric, gas ionization at the contact line, dielectric breakdown, and thermodynamic limits. Saturation typically occurs at 50-60° for aqueous drops.

What are applications of digital microfluidics?

Digital microfluidics powers lab-on-a-chip devices for point-of-care diagnostics, automated sample preparation for mass spectrometry, cell-based assays, and DNA library preparation. Commercial platforms like the Illumina NeoPrep and Abbott ID NOW leverage EWOD for automated fluid handling.

Sources

Embed

<iframe src="https://homo-deus.com/lab/microfluidics/electrowetting/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub