Microfluidic Shear Stress Calculator: Tutorial & Examples

Universal flow control in microfluidics combines pressure-driven flow controllers with Coriolis flow sensors to achieve precise, stable fluid delivery at milli/micro/sub-micro scales for any fluid type (gases, liquids, or mixtures), offering response times down to 40ms and stability as low as 0.006% of flow rate, which enables advanced applications like droplet generation, organ-on-a-chip systems, and sequential liquid injection with high reproducibility.

In microfluidic systems, liquids are moved using three main methods: peristaltic pumps (mechanical action on flexible tubes), syringe pumps (plunger-driven with endless screw), and pressure-driven flow controllers (gas pressure applied to sealed liquid reservoirs). The fundamental principle is that liquid flow occurs according to the pressure difference (Delta P) between inlet and outlet, where flow rate is proportional to this pressure difference through the system's microfluidic resistance. While peristaltic and syringe pumps create pulsating flows due to their mechanical nature, pressure-driven flow controllers provide smoother, pulseless flow with higher control accuracy by using gas pressure to push liquids through microchannels.

Flow meters connect via AIF (Analog Interface) or CAN gate, configured by setting zero and 24 milliamps to correspond to minimum and maximum flow rates. The system offers flow control with pressure limiting, where the unit operates only up to a set pressure limit. For sensitive applications, this prevents over-pressurization. Huber also offers the Flow Control Cube as an all-in-one package with VPC, pressure sensors, and inductive flow meters for plug-and-play automation.

The restrictor valve uses pressure direction to control refrigerant flow through different orifices. When pressure enters from one side, it pushes the valve component toward the larger orifice (0.89), allowing refrigerant to pass through the larger opening. When pressure enters from the opposite side, it pushes the component toward the smaller orifice (0.67), forcing refrigerant through the smaller opening. The conical design distributes pressure radially, while rubber seals ensure tight side closure. This pressure-driven mechanism ensures refrigerant flow is always controlled and measured according to system requirements, with the valve component mechanically responding to pressure direction to select the appropriate flow path.

Flow transducers (PR1, PR2) are configured with: transducer type selection (templates or manual entry), impulse output constant, metrological ranges, and cutoff thresholds. Flow rate range configuration includes minimum/maximum flow rates and operating frequency (100 Hz or 500 Hz). The 500 Hz setting provides five times the resolution. Temperature sensors (T1, T2) are configured with characteristics and contractual values. Pressure sensors (P1, P2) are configured with measurement ranges (up to 1 MPa). Manual parameter entry prevents automatic settings from overwriting user values.

To compute viscous forces and wall shear stresses in ParaView for CFD datasets, follow this pipeline: load the dataset, extract the internal mesh, compute gradients, extract surface critical steps, calculate surface normals, use the calculator filter to compute viscous stresses using the gradient dot product, integrate the results to obtain force components, and optionally remove extraneous patches using threshold filters to reduce numerical noise; note that ParaView computes gradients at cell centers while OpenFOAM provides them at faces, which may cause a factor-of-two difference in magnitude.

COMSOL Multiphysics is a finite element simulation software supporting multiple physics disciplines. The software includes modules for multiphysics and program interaction, with COMSOL Server providing web-based application access. The interface consists of Model Builder (left), Settings (middle), Graphics (right), and Message windows. COMSOL offers Model Wizard for guided setup or Blank Model for manual construction. CFD simulations solve Navier-Stokes equations for fluid flow, with options for laminar flow (Reynolds number < 2000) and various turbulence models. The demonstration shows a channel flow simulation with abrupt expansion, using symmetry to reduce computational cost by simulating only one-eighth of the geometry.

A flow model of the bioreactor was developed using CFD. The speaker describes an embarrassing example where scaffolds were always placed at the bottom, but CFD revealed this was a bad idea because flow was not well-developed. The model combines flow through porous media (Stokes equation) in the free flow zone with flow through the scaffold using a penalty method. From the flow, shear stresses are calculated both at the interface between new tissue and free flow zone and within the new tissue. The speaker discovered that wall shear stress (often used as a measure for optimizing scaffolds) is actually much lower than the shear stress inside the neo-tissue where cells respond to flow.

Wall functions are empirical correction methods in CFD that replace the need for very fine mesh cells near solid boundaries by using nonlinear relationships (log-law for y+ > 30 and viscous sub-layer for y+ < 5) to calculate wall shear stress, allowing larger computational cells and reducing simulation cost while maintaining accuracy; CFD codes automatically switch between these treatments based on local y+ values, though users should aim for y+ < 5 for wall-resolved simulations or y+ ≈ 1 in complex flows with separation and curvature.

This webinar demonstrates how to set up a large-scale turbulent channel flow simulation in COMSOL Multiphysics, covering key aspects including model selection (ALE-based variational multiscale method), geometry creation with periodic boundaries, initial condition setup with Poiseuille profile and periodic disturbances, mesh generation with stretched wall-normal resolution, time-dependent study configuration with CFL condition-based time step restrictions, and visualization techniques for analyzing turbulent flow results.

Non-Newtonian fluids do not follow Newton's law of viscosity. Shear thinning fluids (blood, paint, polymers) decrease viscosity with increased shear rate. Shear thickening fluids (starch-water mixtures, printer ink, mud) increase viscosity with increased shear rate. A graph of viscosity versus shear rate distinguishes these behaviors: negative slope indicates shear thinning, positive slope indicates shear thickening.

Newtonian fluids (like air and water) have constant viscosity where stress is directly proportional to strain rate. Non-Newtonian fluids (like blood, paint, toothpaste) have viscosity that changes with strain rate - viscosity decreases as shear rate increases. Blood is a non-Newtonian fluid where viscosity is not constant but varies with shear rate, requiring specific mathematical models to describe its behavior.

Non-Newtonian fluids do not follow Newton's law of viscosity. Pseudoplastic fluids have viscosity decreasing with shear rate (n < 1), examples include blood, paint, and milk. Dilatant fluids have viscosity increasing with shear rate (n > 1), examples include starch solution and sugar solution. Bingham plastic fluids behave as Newtonian fluids only after a certain yield stress is applied (n = 1, b ≠ 0), examples include toothpaste and gel. Time-dependent non-Newtonian fluids include thixotropic fluids (viscosity decreases with time, examples: clay, honey) and rheopectic fluids (viscosity increases with time, examples: gypsum paste).

Non-Newtonian fluids do not follow Newton's law. The general equation is τ = a × (du/dy)^n + b. When n < 1, fluids are shear-thinning (pseudoplastic) - apparent viscosity decreases with increasing shear rate. Examples: ketchup, paint, blood, idli batter. When n > 1, fluids are shear-thickening (dilatant) - apparent viscosity increases with increasing shear rate. Examples: cornstarch-water mixture (oobleck), quicksand. The slope of stress-strain rate graph determines behavior: decreasing slope for shear-thinning, increasing slope for shear-thickening.

Non-Newtonian fluids do not obey Newton's Law of Viscosity, meaning their viscosity changes with applied shear stress or shear rate. These fluids can be shear-thinning (viscosity decreases with shear rate) or shear-thickening (viscosity increases with shear rate). The shear stress versus shear rate graph is not a straight line passing through the origin.