microfluidics

name	microfluidics
description	Microfluidics — low Reynolds number flow (Re << 1, Stokes flow), capillary number, Hele-Shaw flow, electroosmotic flow (zeta potential, Debye length), pressure-driven Poiseuille flow in microchannels, droplet microfluidics (T-junction, flow-focusing), lab-on-chip fabrication (PDMS soft lithography, silicon MEMS), diffusion-dominated mixing (Péclet number), and biomedical applications (PCR chip, cell sorting, diagnostics).
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Microfluidics — Complete Skill

Dimensionless Numbers at Micro-Scale

Reynolds Number

Reynolds number: Re = ρ × v × D_h / μ [D_h = hydraulic diameter; v = mean velocity] In microchannels: D_h = 10–500 μm; v = 0.1–100 mm/s; typical Re = 0.001–10 Consequence: completely laminar flow (Re << 2300); no turbulence; predictable, controllable

Stokes flow (Re << 1): Inertia terms neglected: ∇p = μ∇²v [Stokes equation; instantaneous response; reversible flow] Important: mixing ONLY by diffusion (no turbulent mixing); channels must be specifically designed for mixing

Capillary Number

Capillary number (viscous vs. surface tension): Ca = μ × v / γ [μ = viscosity; v = flow velocity; γ = interfacial tension] Ca << 1: surface tension dominated → droplets remain spherical Ca >> 1: viscous forces dominate → droplet deformation, Rayleigh-Plateau instability Typical droplet microfluidics: Ca = 0.001–0.1

Péclet Number (Diffusion vs. Convection)

Péclet number: Pe = v × L / D_diff [D_diff = molecular diffusion coefficient; L = channel length] Pe >> 1: convection dominates → species carried without mixing (parallel laminar streams) Pe << 1: diffusion dominates → complete mixing → desirable for analysis chips at short length scales D_diff for small molecules in water: ~10⁻⁹ m²/s; large protein: ~10⁻¹¹ m²/s

Diffusion mixing length: L_mix = v × w² / D_diff [w = channel width; time for diffusion across channel: t = w²/(2D) → L = v×t] Example: v = 1 mm/s; w = 100 μm; D = 10⁻⁹ m²/s → L_mix = 0.001 × (100×10⁻⁶)² / 10⁻⁹ = 10 mm

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Pressure-Driven Flow (Poiseuille)

Rectangular Microchannel

Hagen-Poiseuille (circular tube): Q = π × R⁴ × ΔP / (8 × μ × L) [Q = volumetric flow rate; R = radius; ΔP = pressure drop; L = length] v_max = R² × ΔP / (4μL) [centerline velocity; parabolic profile]

Rectangular channel (w × h, h < w): Q ≈ h³ × w × ΔP / (12 × μ × L) × [1 − (192h/π⁵w) × Σ tanh(nπw/(2h))/n⁵] [exact series] Simplified for h << w (thin slit): Q ≈ h³ × w × ΔP / (12 × μ × L)

Hydraulic resistance analogy (circuit analog): R_h = ΔP / Q = 12 μL / (h³w) for thin rectangular channel Series channels: R_total = Σ R_i; Parallel: 1/R_total = Σ 1/R_i [exact circuit analogy for Stokes flow]

Example: Channel: 100 μm wide × 50 μm high × 10 mm long; water (μ = 10⁻³ Pa·s); ΔP = 1000 Pa Q ≈ (50×10⁻⁶)³ × (100×10⁻⁶) × 1000 / (12 × 10⁻³ × 10×10⁻³) = (1.25×10⁻¹³ × 10⁻⁴ × 10³) / (1.2×10⁻⁴) = 1.25×10⁻¹⁴ / 1.2×10⁻⁴ = 1.04×10⁻¹⁰ m³/s = 0.104 nL/s ≈ 6.2 nL/min

Hele-Shaw Flow

Hele-Shaw cell: flow between two closely-spaced parallel plates (h << w) Velocity field is 2D potential flow (depth-averaged): ∇²p = 0 [irrotational in plan view] Streamlines follow conformal mapping patterns → used for flow visualization + analog for 2D potential problems Application: microfluidic channels designed in plan view; predicts flow splitting, junction behavior

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Electrokinetic Flow

Electroosmotic Flow (EOF)

Zeta potential (ζ): surface potential at shear plane; depends on surface chemistry + electrolyte PDMS in aqueous buffer: ζ ≈ −30 to −50 mV at pH 7.4 (negative; attracts positive counterions) Glass (SiO₂): ζ ≈ −50 to −100 mV at pH 7 (strong EOF)

Debye screening length (κ⁻¹): κ⁻¹ = √(ε₀εkT / (2n₀e²z²)) [ε = permittivity; k_B = Boltzmann constant; n₀ = ion concentration; z = valence] At 10 mM NaCl: κ⁻¹ ≈ 3 nm (thin diffuse layer; most of channel is bulk) At 1 mM: κ⁻¹ ≈ 10 nm

Electroosmotic velocity (Helmholtz-Smoluchowski): v_EOF = −(ε₀ε × ζ / μ) × E [E = electric field V/m; ε₀ = 8.85×10⁻¹² F/m; ε_water = 80; μ = viscosity] For PDMS: v_EOF ≈ −(80×8.85×10⁻¹²×(−40×10⁻³) / 10⁻³) × E = 28.3×10⁻⁹ × E [m/s per V/m] At E = 10,000 V/m (10 V/cm): v_EOF ≈ 0.28 mm/s

EOF velocity profile: plug flow (flat profile; unlike Poiseuille parabola) → no Taylor dispersion band broadening → ideal for separation Used in: capillary electrophoresis (CE), electrophoretic separations, electroosmotic pumps

Electrophoresis: Charged species: v_ep = μ_ep × E [μ_ep = electrophoretic mobility = q×ζ_particle/(6πηR)] Net velocity = v_EOF + v_ep; separation based on charge/size → DNA, protein analysis

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Droplet Microfluidics

Generation Methods

T-junction geometry: Continuous phase (oil) flows in main channel; dispersed phase (aqueous) flows in side channel At junction: aqueous neck pinches off → monodisperse droplets Droplet size: d ≈ 1.5 × w_side × (μ_c Q_c / (γ Q_d))^n [Ca-dependent; n ≈ 0.3–0.5] Monodispersity: CV (coefficient of variation) < 2% achievable

Flow-focusing geometry: Aqueous phase squeezed by two symmetric oil streams → focused thread → breaks into droplets at orifice Better control of droplet size; works over wider Ca range; typical research platform

Droplet applications: Digital PCR (100,000 droplets/sample → single molecule sensitivity) Drug screening (each droplet = one experiment; 1,000–10,000 droplets/s) Cell encapsulation (Poisson statistics → ~1 cell per droplet at λ = 0.3)

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Fabrication — Soft Lithography (PDMS)

PDMS Molding Process

PDMS (polydimethylsiloxane) — dominant microfluidics material: Optical transparency, biocompatible, gas permeable, easy molding, bond to glass by plasma

Process steps:

1. Master fabrication: SU-8 photoresist on silicon wafer; UV exposure through mask; develop → raised features = channel mold SU-8 thickness → channel height h; typically 10–200 μm
2. PDMS casting: mix Sylgard 184 base + curing agent 10:1 by mass; degas; pour over master; cure 65°C/1h
3. Peel: remove cured PDMS slab; punch inlet/outlet holes with biopsy punch
4. Bonding: plasma activate PDMS + glass slide (O₂ plasma 30 s); bring into contact → irreversible bond Bond strength: > 500 kPa (sufficient for most microfluidic pressures)
5. Test: fill with fluid; connect tubing; verify sealing

PDMS limitations: Absorbs small hydrophobic molecules (loss of drug candidates → misleading screens) Permeable to CO₂, O₂ (good for cell culture; bad for anaerobic studies) Not suitable for organic solvents → use cyclic olefin copolymer (COC), PMMA, or glass for harsh chemistry

Silicon/Glass MEMS

Silicon microfabrication: Deep Reactive Ion Etching (DRIE — Bosch process): vertical sidewalls; aspect ratio 20:1; etch rate 5–10 μm/min Anodic bonding (Si + Pyrex at 400°C, 1 kV): hermetic; high-pressure seal; for harsh chemical/high-T Used: flow cytometry chips, high-pressure microreactors, BioMEMS pressure sensors

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Biomedical Applications

Lab-on-Chip Functions

PCR (Polymerase Chain Reaction) on chip: 30 thermal cycles; T = 95°C (denature) / 55°C (anneal) / 72°C (extend) each 5–20 s On-chip: thin silicon with TEC heaters; 30 cycles in 5–20 min (vs. 2 h conventional bench PCR) Volume: 10–100 nL (vs. 50 μL conventional) → 500× less reagent cost

Cell sorting (microfluidic FACS): Electrokinetic deflection or acoustic focusing; sort rate: 1000–10,000 cells/s Deterministic lateral displacement (DLD) arrays: sort by size without label; for CTC isolation

Diagnostics (point-of-care): Lateral flow immunoassay: paper microfluidics; gold nanoparticle detection; COVID/flu test strips Fully integrated LOC: sample-in/answer-out; blood → pathogen identification in 30 min

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Standards and References

Standard	Scope
ISO 22916	Microfluidics — interoperability requirements for chip-to-chip and chip-to-world interfaces
SEMI F119	Specification for microfluidic systems
ASTM E2652	Nanomaterial safety testing (nanofluidics adjacent)
ISO 10993	Biocompatibility of medical devices (PDMS LOC devices)
IEEE MEMS standards	MEMS device characterization

Output

Provide: application (LOC type: PCR/mixing/droplet generation/sorting/filtration; fluid: aqueous/organic; target throughput [nL/min]; required resolution), dimensionless analysis (Re = ρvD/μ [confirm laminar]; Pe = vL/D [mixing regime]; Ca = μv/γ [droplet stability]; Bo = ρgL²/γ [gravity negligible if Bo < 1]), channel geometry (w [μm]; h [μm]; L [mm]; D_h = 2wh/(w+h) [μm]; material: PDMS/glass/COC/Si), pressure-driven flow (Q [nL/min]; ΔP = 12μLQ/(h³w) [Pa]; pump type: syringe/peristaltic/electroosmotic; pressure rating), electrokinetic (if EOF: E [V/m]; ζ [mV]; v_EOF = ε₀ε×ζ×E/μ [mm/s]; Debye length [nm]; band dispersion Pe effect), droplet generation (if applicable: T-junction or flow-focus; Q_continuous [nL/min]; Q_dispersed [nL/min]; Ca; droplet size d [μm]; frequency [Hz]; CV [%]), fabrication route (PDMS soft lithography: SU-8 master h [μm], plasma bonding; or silicon DRIE: aspect ratio; anodic bonding), and applicable standard (ISO 22916 for chip interfaces; ISO 10993 for biocompatibility if medical device).