Microfluidic channel calculator

Hydraulic diameter D_h = 4A/P and mean velocity v = Q/A of a rectangular channel, from its internal width and height and the volumetric flow rate. With the viscosity and length come the Reynolds number, the hydraulic resistance R = 12ηL / [(1 − 0.63·(h/w))·h³·w] in Pa·s/m³, the pressure drop ΔP = R·Q in pascals, and series and parallel networks.

A is the cross-sectional area (width × height), P its wetted perimeter. For a non-circular channel, D_h stands in for the diameter in the Reynolds number and pressure-drop correlations. Re is computed from the kinematic viscosity ν (m²/s, kinematic mode) or from the dynamic viscosity µ (Pa·s) and density ρ (kg/m³, dynamic mode), depending on the chosen mode.

Hydraulic diameter (D_h)

diameter of the circular tube hydraulically equivalent to the rectangular section.

Mean velocity (v)

flow rate divided by the cross-sectional area. It differs from the velocity at the channel centre.

Full section

a channel filled with fluid over its full height, with no free surface.

Reynolds number (Re)

ratio of inertial to viscous forces. No regime is inferred from it, for lack of a verified boundary for a microfluidic channel.

• The fluid is Newtonian, with a viscosity independent of shear rate; a polymer solution, blood or a concentrated suspension is not.
• The flow is laminar and fully developed. Near the inlet the velocity profile is still developing and the real resistance is higher.
• The fluid is incompressible and does not slip at the wall. A high Knudsen or Mach number breaks these assumptions and is flagged.
• The usual laminar/turbulent thresholds come from macroscopic pipes; in a microchannel, transition may occur at another Reynolds number depending on geometry, roughness and inlet.

The model assumes a constant, full rectangular section. It does not cover a partially filled channel, a trapezoidal profile from anisotropic etching, or a circular or semicircular section.

1. Wikipedia (Wikimedia Foundation), Reynolds number, révision consultée : oldid 1362194896.

   Location: Section « Flow in a pipe », formule « Re = uD_H/ν = ρuD_H/µ = ρQD_H/(µA) = WD_H/(µA) », avec (unités SI de la source) : D_H « the hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m) » ; µ (mu) « the dynamic viscosity of the fluid (Pa·s = N·s/m² = kg/(m·s)) » ; ν (nu) « the kinematic viscosity (ν = µ/ρ) (m²/s) », explicitement DISTINCTE de µ. Jamais substituable sans diviser par ρ ; ρ (rho) « the density of the fluid (kg/m³) » ; u « the mean velocity of the fluid (m/s) ». Diamètre hydraulique défini, pour une section quelconque, par « D_H = 4A/P » (A l’aire de la section, P le périmètre mouillé du canal) : c’est cette définition, pas le diamètre d’un tube circulaire, qui rend la formule applicable à un canal microfluidique non circulaire. La source précise elle-même la limite de cette substitution : « the hydraulic diameter can be substituted for the diameter of a circular duct, with reasonable accuracy, if the aspect ratio AR of the duct cross-section remains in the range 1/4 < AR < 4 ». · accessed 2026-08-02 · Licence CC BY-SA 4.0

2. LibreTexts (Physics LibreTexts), remixé par Joshua Halpern · d'après OpenStax University Physics, 52.7: The Reynolds Number, consulté 2026-08-02.

   Location: Formule « Re = ρvD/µ » (D « the diameter of the pipe ») et seuils « Re<2000 : laminar flow », « 2000<Re<3000 : transition region », « Re>3000 : turbulent flow ». Contexte d’application exact donné par la source : « a general rule of thumb » pour l’écoulement d’un fluide visqueux dans une conduite (pipe), PAS pour un canal microfluidique (voir MICROCHANNEL_REYNOLDS_REGIME_BOUNDS dans reynoldsChannelSources.ts). · accessed 2026-08-02 · Licence CC BY-NC-SA 4.0

3. Elvesys (Elveflow) · Microfluidic reviews, Flow Resistance in Microfluidics: Principles, Calculations & Applications, consulté 2026-08-02.

   Location: Section « Introduction to microfluidics and flow resistance », équation « ΔP = QR_H », ΔP la différence de pression [Pa en unités SI], Q le débit volumique [m³/s], R_H la résistance hydraulique [Pa·s/m³]. · accessed 2026-08-02

4. Molecular Medicine Reports (Spandidos Publications) · Bao X., Li Z., Liu H. et al., Stimulation of chondrocytes and chondroinduced mesenchymal stem cells by osteoinduced mesenchymal stem cells under a fluid flow stimulus on an integrated microfluidic device, vol. 17, n° 2 (2018), p. 2277-2285, version PMC5783459.

   Location: Section « Materials and methods », sous-section « Numerical modeling of the shear stress », « R=[12ηL/(1–0.63(h/w)] × (1/h3w). In this formula, R is the hydraulic resistance of the rectangular microchambers, η the dynamic viscosity of the liquid, L the channel length, h and w (always h < w) the channel height and width, respectively. ». La parenthèse « always h < w » est la convention d'orientation du rapport d'aspect ET le domaine géométrique retenus par ce moteur. Le même paragraphe referme la chaîne sur la loi de Hagen-Poiseuille : « Δp=QR_H ». · accessed 2026-08-02 · DOI 10.3892/mmr.2017.8153 · Licence CC BY-NC-ND 4.0

5. Bar-Meir, Genick · LibreTexts (Civil Engineering), « Fluid Mechanics », Kinematic Viscosity, consulté 2026-08-02.

   Location: Définition « ν = µ/ρ », dimensions [m²/s] · accessed 2026-08-02 · Licence GNU Free Documentation License 1.3

6. Sensors (MDPI), Shayor Ahmed Abrar, Kabir Md Emamul, Rifath Md Sartaj Ahamed, Rashid Adib Bin, Oh Kwang W., A Synergistic Overview between Microfluidics and Numerical Research for Vascular Flow and Pathological Investigations, vol. 24, n° 18 (2024), article 5872, version PMC11435959.

   Location: Section 1 « Introduction », « To model the flow of Newtonian fluid via a single microchannel, the Hagen–Poiseuille law may be used. The flow profile throughout the channel is assumed to follow a parabolic shape ». · accessed 2026-08-02 · DOI 10.3390/s24185872 · Licence CC BY 4.0

7. JCGM / BIPM (Joint Committee for Guides in Metrology), Evaluation of measurement data, Guide to the expression of uncertainty in measurement (GUM), JCGM 100:2008, JCGM 100:2008 (GUM 1995 with minor corrections), première édition septembre 2008.

   Location: §5.1 « Uncorrelated input quantities », « This subclause treats the case where all input quantities are independent » ; §5.1.2, équation (10) : « u_c²(y) = Σ_{i=1}^{N} (∂f/∂x_i)² u²(x_i) », suivie de « Equation (10) […] based on a first-order Taylor series approximation of Y = f(X1, X2, ..., XN), express what is termed in this Guide the law of propagation of uncertainty » ; §5.1.3 nomme c_i = ∂f/∂x_i les coefficients de sensibilité. · accessed 2026-08-02

Provisional · Sources and assumptions are provided; the documentary review is incomplete.

Physical model. The result follows the significant figures of the least precise input.

revision 1 · reviewed on 4 August 2026

Revision log

1. revision 1 · 2026-08-04 · source update

   Affichage des sept sources et des hypothèses du modèle.

   Résultats, valeurs, formules et seuils inchangés.