Surface Tension Model
Surface tension is the cohesive force at a liquid-gas or liquid-liquid interface that causes the surface to behave like a stretched elastic membrane. At small scales it dominates over gravity and inertia, controlling droplet formation, capillary rise, wetting behavior, and bubble dynamics. At larger scales it plays a critical role in coating stability, melt pool behavior in additive manufacturing and welding, and propellant management in spacecraft fuel tanks.
One of the earliest physics models in FLOW-3D, the Surface Tension Model has been continuously applied over decades across industries from microfluidics and inkjet printing to aerospace and additive manufacturing. It is available across the FLOW-3D product family for both single-fluid free-surface flows and two-fluid problems with a sharp interface.
Modeling Capabilities
The FLOW-3D Surface Tension model accurately computes:
- Surface tension forces at free surfaces and fluid-fluid interfaces
- Wall adhesion controlled by a global or geometry-specific contact angle
- Tangential surface tension forces caused by non-uniform surface tension coefficients due to temperature or concentration gradients
- Electrowetting effects, where an applied electric potential modifies the apparent contact angle
- Contact line pinning, which fixes the fluid contact line to a solid surface rather than computing its motion from a force balance. See the Contact Line Pinning Model for more information.
Surface tension coefficients can be defined as a constant, as a linear function of temperature, or using tabular data with up to two independent variables, for example temperature and contaminant concentration. This allows complex, non-linear property dependencies to be captured directly from experimental data, which is particularly valuable for surfactant-laden fluids, polymer solutions, and liquid metals.
Industry Applications
The Surface Tension Model is used across the FLOW-3D product family for applications including:
- Lab-on-a-chip, bioassay, and microreactor design
- Inkjet and drop-on-demand printing
- Roll, curtain, gravure, and slide coating processes
- Capillary filling and wicking in porous media
- Propellant management devices and fuel acquisition in microgravity
- Laser powder bed fusion and directed energy deposition melt pool dynamics
- Laser welding keyhole and bead geometry
- Electrowetting and digital microfluidics
- Droplet impact and spreading on substrates
- MEMS and micro-electromechanical device simulation
Microfluidics and Lab-on-a-Chip
At the microscale, surface tension governs nearly everything. FLOW-3D is widely used to simulate lab-on-a-chip devices, bioassays, microreactors, and biological sensing systems where surface tension drives fluid transport, droplet generation, and capillary filling. Patterned surfaces with spatially varying wettability can be used to direct fluid flow in micro-channels without mechanical pumping, opening up new design possibilities for passive microfluidic systems.
FLOW-3D simulation of patterned surfaces using varied surface tensions, showing fluid 2 (top left) and fluid 1 (bottom left) distributions in a micro-channel, with pressure at inlet over time (right).
Inkjet Printing and Drop-on-Demand
Surface tension governs the entire lifecycle of an inkjet droplet, from pinch-off at the nozzle to spreading and drying on the substrate. FLOW-3D simulates droplet formation, satellite behavior, and substrate interaction, giving engineers the insight needed to optimize nozzle geometry, fluid formulation, and firing parameters for consistent, accurate drop placement.
FLOW-3D simulation of piezoelectric inkjet droplet ejection, showing droplet velocity (left) alongside nozzle pressure pulse and volume flow rate time histories (right).
Industrial Coating Processes
Surface tension is a primary driver of coating stability, defect formation, and contact line behavior. FLOW-3D is used to predict the onset of ribbing instabilities in roll coating, the stability of the dynamic contact line in curtain coating, and the entrainment of bubbles where the liquid front meets the substrate. The ability to capture spatially and thermally varying surface tension gives engineers accurate insight into real process conditions.
FLOW-3D simulation of a forward roll coating process showing a ribbing defect caused by a high capillary number, with surface tension and viscosity modeled through a 400 micron nip.
Aerospace Propellant Management
In microgravity, surface tension controls the location and behavior of liquid propellants far more than gravity does. FLOW-3D simulates propellant management devices, capillary vanes, and sponge structures designed to guarantee vapor-free fuel delivery to engines during spacecraft maneuvers. Engineers use the model to assess fuel acquisition under orbit conditions and to validate tank designs before flight
In microgravity, surface tension becomes the dominant force governing free-surface behavior, controlling how propellant settles once other forces are removed. This simulation depicts a baffled tank similar in size to the Agena Target Vehicle, where FLOW-3D‘s Surface Tension model captures an incoming propellant jet as it disperses and settles into its minimum-energy configuration at the tank drain.
Additive Manufacturing and Laser Welding
Surface tension governs melt pool shape, bead geometry, and the wetting of molten metal on solidified substrate in both additive manufacturing and laser welding. FLOW-3D AM and FLOW-3D WELD use the surface tension model to capture melt pool dynamics, keyhole formation, and capillary penetration of liquid metal into the powder bed, giving process engineers the data they need to optimize parameters and predict defects before committing to physical trials.
FLOW-3D AM simulation comparing stable (left) and unstable (right) melt pool conditions in laser powder bed fusion of IN718, showing how increased scan speed at constant power drives melt pool instability and balling defects
Electrowetting
By applying an electric potential across a dielectric layer, the apparent contact angle of a droplet can be modified on demand. FLOW-3D models this electrowetting effect, enabling simulation of digital microfluidic devices where droplets are steered, merged, split, and dispensed on electrode arrays without any moving parts.
FLOW-3D simulation of electrowetting showing a hydrophobic droplet transitioning to hydrophilic behavior under a 50V applied potential, with electric potential (top left), plan view (bottom left), and 3D electric charge density in fluid (right).