Fluid-structure Interaction Research Articles

Microrheometric study of damage and rupture of capsules in simple shear flow

Capsules, which are potentially active fluid droplets enclosed in a thin elastic membrane, experience large deformations when placed in suspension. The induced fluid–structure interaction stresses can potentially lead to rupture of the capsule membrane. While numerous experimental studies have focused on the rheological behaviour of capsules until rupture, there remains a gap in understanding the evolution of their mechanical properties and the underlying mechanisms of damage and breakup under flow. We here investigate the damage and rupture of bioartificial microcapsules made of ovalbumin reticulated with terephthaloyl chloride and placed in simple shear flow. We characterize damage by identifying how the surface shear modulus of the capsule membrane changes over time. Rupture is then characterized by comparing the number and size distribution of capsules before and after exposure to shear, while varying the shear rates and time during which capsules are sheared. Our findings reveal how the percentage of ruptured capsules increases with their size, exposure time to shear, and the ratio of viscous to elastic forces at rupture.

Effects of ground motion characteristics on liquefaction response of earth dams using a non-Darcy hydro-mechanical model

During earthquake-induced excitations, significant pore pressure gradients can develop in earth dams, limiting the applicability of Darcy’s law for fluid flow. This study investigates the behavior of a liquefied earth dam subjected to various seismic excitations with differing frequency content, aiming to enhance insights into the effects of dynamic loading on fluid–structure interactions. To accurately capture the soil’s response, the Pastor-Zienkiewicz generalized plasticity model is employed to represent realistic soil behavior. Additionally, a modified Forchheimer equation is used to address varying permeability through a non-Darcy flow law. Numerical simulations, performed using a finite element code developed in Fortran, are validated through comparative analyses with previous studies. The results show that in low-permeability regions, changes in earthquake frequency content have minimal impact on discrepancies between the predicted results of Darcy and non-Darcy models. However, the non-Darcy model generally estimates horizontal displacements to be around 4% higher on average in these regions. This difference increases as earthquake frequency content decreases, reaching up to 6%. In contrast, in permeable regions, the non-Darcy model predicts significantly higher horizontal displacements, with an average increase of approximately 20% for high-frequency seismic events and 8% for low-frequency ones. Additionally, in high-permeability regions, the non-Darcy model deviates notably from the Darcy model as peak ground velocity increases, particularly affecting the upstream shell and clay core of the dam. This disparity becomes more pronounced as the input motion’s frequency content decreases, resulting in elevated pore pressures and slightly reduced vertical displacements in these regions.

Computational analysis of submerged submarine bow hull dynamics subjected to torpedo blunt impact and warhead detonation events

In the maritime sector, ensuring the survivability of ships and submarines against diverse threats such as torpedo impacts, Underwater Explosion (UNDEX) events, and environmental factors is paramount. Comprehensive analysis of hull dynamics under various impact scenarios is essential. Numerical simulations of these impacts utilize different material models, ship grounding tests, impact modes, UNDEX simulations, and failure mechanisms. In the current study, the blunt impact of a torpedo on the submarine bow and the surface detonation effects of the torpedo warhead (at different distances from the hull) on the submarine bow structure were analyzed within an underwater enclosure. The torpedo design was based on the MK-48, with Ti6Al4V alloy used for the torpedo hull and HY-80 steel for the submarine hull. The impact simulations were conducted using ANSYS Explicit Dynamics® computational software. For the blunt impact scenario, a torpedo speed of 55 knots (102 km/h) was used. For the UNDEX studies, the warhead at the front end of the torpedo was modeled using PBX-9501 (a commonly used high explosive in warheads). The novelty of the current work was the employment of a water enclosure in the model to simulate the underwater impacts. The analysis focused on hull deformation, equivalent plastic and elastic strains, equivalent stress and damage profiles for the different impact scenarios. To effectively capture fluid–structure interactions, the study also examined pressure variations within the Eulerian domain. Among the scenarios analyzed, the near-field detonation of the warhead emerged as the most destructive, resulting in severe structural damage to the bow hull. In contrast, the blunt impact of the torpedo induced moderate plastic deformation, while the far-field detonation resulted in minimal damage.

Attitude motion and nonlinear free-surface deformation of stone-skipping over shallow water

Stone-skipping is a common yet complex motion that involves rigid-body dynamics and fluid–structure interaction (FSI). While many computational fluid dynamics methods are used to simulate the interaction between a stone and fluid, little research has been done to consider the stone, fluid, and fluid boundary as a whole in a simulation. This study, focuses on the attitude motion and free-surface deformation of stone-skipping over shallow water to investigate how the boundary effect of FSI impacts ricochet behaviors. Initially, we establish an iteration framework for the stone-skipping FSI issue based on a weakly compressible smoothed particle hydrodynamics (SPH) method with a Riemann solver. We conduct particle-independence verification and simulate several cases under varying water heights. Additionally, we analyze and compare ricochets in deep and shallow cases with different incident angles and initial pitch angles. The numerical results demonstrate that in shallow flow scenarios, the “comma-shaped” high-pressure area is compressed by the stone and the fluid boundary, leading to a more moderate variation in pitch angle. Stone-skipping in shallow water typically covers a shorter distance and reaches a lower height compared to deep water cases. Changes in the incident angle show that shallow water hinders successful skipping. Futhermore, different initial pitch angles reveal that water height directly impact the stone's trajectory in both horizontal and vertical directions. These highlight the connection between motion patterns and parameters, offering a reliable numerical prediction for the stone-skipping problem using the Riemann SPH method.

Direct simulations of bedrock core and cuttings transport phenomena in reverse circulation drilling

Polar drilling is essential for obtaining ice and bedrock samples, providing critical insights into climate and geological history. The reverse circulation drilling method, utilizing a dual-wall drill pipe, presents a stable and efficient strategy. Nonetheless, the intricate dynamics involving drilling fluids, rock cuttings and cores necessitate sophisticated modeling to elucidate the underlying mechanism and optimize drilling efficiency. To address this, we developed a multiphase flow model that accounts for non-Newtonian fluid behavior, turbulence, particle dynamics, and fluid–structure interactions, enabling a thorough assessment of various operational parameters. The model's temporal–spatial sensitivity was evaluated, and its accuracy was confirmed by comparison with three different sets of experimental data. A detailed parametric investigation was then conducted to systematically assess the effects of various parameters, including the non-Newtonian behavior and inlet velocity of the drilling fluid, the rate of penetration, and the dimensions of the cuttings and core. The simulation results indicate that the non-Newtonian behavior of the drilling fluid has an non-negligible effect on the transport efficiency of both cuttings and core. An increase in the fluid inlet velocity leads to faster transport, albeit at the cost of higher pump pressure. The rate of penetration has a minor influence on the core transportation but largely affects the cutting transportation. More interestingly, larger cuttings demonstrate enhanced transport efficiency, attributed to a more uniform velocity distribution. Furthermore, the core diameter plays a pivotal role in transport efficiency by significantly altering the fluid dynamics, whereas the core length has a negligible effect. These results may have direct applications for optimizing polar drilling operations, potentially leading to enhanced drilling efficiency, reduced drilling costs, and informing future drilling technology advancements.

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular integral equation is derived for axially symmetrical configurations, and analytical formulas are established for calculating the hypersingular parts. It is proved that the hypersingular component of the surface integral is equal to its hypersingular component along the tangent plane. These exact formulas enable the development of an effective numerical method based on boundary element implementation. Benchmark tests are considered, and the convergence of the proposed methods is demonstrated. Problems in crack analysis are formulated and solved using both surface and contour hypersingular integral equations. A comparison of the results is made between boundary element methods and finite element methods for penny-shaped cracks. Boundary value problems in fluid-structure interaction are considered, and numerical simulations are performed. An estimation of modes and frequencies of panel and blade vibrations when interacting with liquids is carried out.

More accurate representation of interaction at the fluid–structure interface with an improved smoothed field gradient method

Flexible structures are wind-sensitive with a significant fluid–structure interaction (FSI). The FSI analysis, however, often has poor numerical stability and low convergence efficiency due to drastic changes of the physical fields induced by computation errors in local regions of the fluid–structure interface. This paper aims at addressing these problems with the proposal of a new method to smooth the gradient of the pressure field at the fluid–structure interface for an efficient convergence in the FSI analysis. The smoothed gradient theory is modified by introducing weight coefficients. The field of fluid pressure in each smoothing domain with large numerical fluctuations at the interface is then gradient smoothed with the proposed method and the modified field is obtained from the linear Taylor series expansion. The convergence of fluid and structure solvers for the proposed method is ensured within the commercial software FLUENT and ANSYS adopted. The proposed method is validated with experimental results from the literature. It is also numerically validated with a thin plate in viscous flow with different site categories and average wind velocities through comparison of results from conventional methods. The proposed method is found valid and accurate in the FSI analysis. It is relatively independent of a wide range of parameters with satisfactory robustness and notable improvement in the convergence of the FSI analysis.

A new finite element formulation unifying fluid-structure and fluid-fluid interaction problems

When the accurate simulation of two materials that interact through their common and deformable interface is of interest, the efficient treatment of the interface determines the success or failure of a numerical method. In this work, we propose a new, robust and easy-to-code finite element formulation for such interaction problems. The remedy of the interface constraints, namely the continuity of velocities and stresses, is accomplished using a single-node approach and the same continuous basis functions for the velocities in both materials. Given that only Newtonian fluids will be examined, we do not have to introduce basis functions for the stress components. The XFEM method, which enriches locally the continuous basis function of a variable that presents a discontinuity, is employed to tackle the discontinuous behavior of the pressure across the interface. The incorporation of Petrov-Galerkin stabilization schemes enhances further our formulation and allows the usage of equal order interpolants for velocities and pressure. We solve the coupled system of equations in a monolithic manner to alleviate the convergence problems of the segregated approach. The novel aspect of our method is that its ingredients do not differentiate based on the constituent materials of the problem, and it can be used interchangeably for either a fluid-structure or a fluid-fluid interaction problem. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: i) the flow through a partially collapsible channel, ii) the induced motion of a flexible elastic plate, iii) the filament stretching of a Newtonian thread surrounded by another immiscible viscous fluid. In all cases, we are in agreement with the results of the literature. Furthermore, we conduct a challenging, 3D simulation for a setup that resembles the motion of a three-leaflet stented aortic heart valve.

Estimating surface pressure on flexible structures subjected to flow-induced vibrations

A conventional flag is placed downstream of the inverted half cylinder to study pressure over the flag's surface due to fluid-flexible body interaction between the flag and the vortices generated by the half cylinder. An immersed boundary method provides a reliable and fast solution to the fluid-structure interaction problems, albeit with limitation. One such limitation is the accurate pressure profile over the Lagrangian grid, i.e., the structure boundary. A pressure prediction algorithm is proposed which couples with the improved immersed boundary method to predict pressure over flag's surface. The effect of flow patterns on flag's surface pressure is studied by varying flag's distance from the bluff body. The pressure results are analyzed as negative and positive pressure fluctuations from the assigned reference pressure in the far field. Results show high flag surface pressure at a smaller stream-wise distance. A subsequent decrease in flow pressure is observed, when the stream-wise distance is increased. Changing span-distance shows that the highest pressure occurs at Gy = 0.25 with a significant drop at span positions of 0 and 0.5. The average pressure over the flag's surface is also affected by the vibration modes and the vortex shedding from the surface of the flag. The deflected mode appears at a smaller stream-wise distance accompanied by additional vortex shedding from the flag surface resulting in a high average pressure. Whereas biased and conventional flapping modes appear as stream-wise distance is progressively decreased resulting in reduced average pressure. Hydrodynamic analysis shows that the vortices originating from the bluff body and their subsequent interaction with the flag serve as the primary source of pressure fluctuations resulting in a change in the pressure profile over the surface of the flag.

Multifidelity approach to the numerical aeroelastic simulation of flexible membrane wings

Due to their lightness, the capacity to adapt to the flow conditions, and the safety when operating near humans, the use of membrane-resistant structures has increased in fields as micro aerial vehicles and yachts sails. This work focuses on the computational methodology required for simulating the aeroelastic coupling of the structure with the incident wind flow. A semi-monocoque structure (composed of a main spar, a set of ribs, and an external membrane) inside a wind tunnel is simulated using two different methodologies. Firstly, a complete fluid-structure interaction is calculated by combining the finite element methodology for the solid and the unsteady Reynolds average Navier-Stokes computational fluid dynamics for the air, including nonlinear effects and prestress. Then, a low-fidelity model is applied, obtaining the linear aeroelastic eigenvalues and the temporal response of the wing. Both methodologies results are in agreement with estimating the transient mean deformation and flutter velocity. However, the modal analysis tends to overestimate the aeroelastic effects, as it calculates potential aerodynamics, predicting an instability velocity lower than that provided by the transient simulations.

Dynamic response of spring valve subjected to underwater pressure pulse

Spring-loaded valves are widely used to protect sealed containers filled with liquid against sudden excessive overpressure; however, the unstable vibration of a valve spool under dynamic loading may lead to safety incidents. This study aims to investigate the nonlinear vibration processes of a valve spool subjected to an underwater pressure pulse. To achieve this objective, the spring-loaded valve was simplified to an air-back mass spring with a constraint boundary (AMSCB). A modified split Hopkinson pressure bar (SHPB) was adopted to generate a controllable pressure pulse to establish the relationship between the specific impulse and the discharged water mass. Following the experimental verification, the influences of the pressure pulse parameters and dimensionless time on the motion characteristics of the mass block and flow rate were studied based on finite element (FE) simulations. Five motion modes were identified according to the number of collisions with the constraint boundary and changes in movement direction: (i) no collision, (ii) single collision, (iii) chatter, (iv) single collision with direction change, (v) multiple collisions. Moreover, a theoretical model for predicting the movement of a mass block was developed and validated against numerical results. The classification phase diagram of the motion mode is presented in a two-dimensional plane composed of specific strength coefficient ϕ and fluid-structure interaction coefficient ψ, and the influence of the geometrical parameters of the AMSCB on the classification boundary of motion modes is presented. The results indicate that, when subjected to underwater pressure pulse loading, the mass block repeatedly collides with the constraint boundary and undergoes non-periodic motion. With higher loading pressure amplitude and duration, the mass block is more likely to collide with the back boundary, leading to a transition in movement modes from mode (i), mode (ii), mode (iv) to mode (v). Increasing the stiffness coefficient and areal density will increase the threshold of ϕ and ψ for the transition from mode (i) to mode (v), while the maximum allowable displacement has little effect on the classification boundaries. These research findings are valuable for analysing the motion response of mass spring with various constraint boundaries under dynamic loading, and for guiding the design of spring-loaded valves.

Nonlinear vibrations analysis of a fuel rod in nuclear heating reactor

Nonlinear vibrations of a single fuel rod in nuclear heating reactor with fixed-fixed ends and subjected to various excitation levels are comprehensively analyzed using explicit dynamics. The responses of empty, pellet-filled, and water-submerged rod are investigated. Pellet-cladding and pellet-pellet interactions are addressed by a penalty-based contact treatment, meanwhile the fluid-structure interactions (FSI) between the vibrating fuel rod and surrounding coolants are simulated by the Arbitrary Lagrangian-Eulerian (ALE) method, wherein the water is modeled as Eulerian elements. The results reveal that both empty and pellet-filled rods exhibit frequency hardening phenomena, where eigenfrequencies increase with vibration amplitude due to geometric nonlinearity. The damping decay resulting from fuel pellet motions is found to be positively correlated with vibration amplitude, thereby enhancing the reactor safety. For submerged rod, the frequency decreases due to added mass effects, and the overall system damping increases despite structural damping from dry friction and impacts is reduced.

Fluid–structure interaction in a follow-up study of arterio-venous fistula maturation

Arteriovenous fistula (AVF) is the preferred vascular access for hemodialysed patients. AVF is created surgically using the patient’s artery and vein. Once the connection (anastomosis) is made, the maturation process begins. Studies have shown that most AVFs do not survive beyond one year. This study presents fluid–structure interaction (FSI) modelling of non-Newtonian blood flow through an end-to-side radio-cephalic AVF, investigated weekly during a 15-week follow-up period and 1.5 years postoperatively using ultrasound methods. The aim was to collect qualitative and quantitative data regarding changes in hemodynamics and alterations in the walls of AVF vasculature. Different material properties were assigned to the artery, suture zone (anastomosis), and vein, while the stiffening of the venous arm over time was also modelled. The proposed FSI methodology can be implemented in future follow-up studies involving groups of patients. The main findings revealed: a) counter-rotating vortices in the anastomosis cross-section affecting local pressure conditions; b) different temporal progression of vorticity, shear strain rate, and turbulent kinetic energy and similarity of the temporal progression of WSS obtained under the assumptions of the rigid-walled and FSI; c) a negligible low-WSS zone in the presented thrombosis-free AVF; d) migration of the zone of maximal temporal wall deformation over time.

Coupled processes of tissue oxygenation and fluid flow in biphasic vocal folds

Fluid-structure interaction (FSI) between the glottal airflow and the poroelastic tissue of the vocal folds (VFs) causes the VFs to vibrate, resulting in voice production. Prior experimental studies have reported that biological transport processes within the VF tissue play a crucial role in disease initiation and localized lesions. Particularly, it has been observed that physiological conditions during phonation influence the interstitial flow within the tissue and the associated oxygen partial pressure, which corresponds with dysfunctions such as intermittent hypoxia. The goal of this research is to develop a multiphysics computational methodology that investigates oxygen transport characteristics within the VFs. By considering transient glottal airflow and a biphasic description for the tissue, this coupled framework combines an FSI model with a mass transport model to quantify key features contributing to VF oxygenation. The Navier-Stokes equations represent the aerodynamics in the larynx, while linear elasticity for tissue dynamics is considered. Additionally, oxygen transport is simulated using the advection-diffusion-reaction equation, and the interstitial flow is solved via the Brinkman equation. Physiological parameters such as oxygen metabolic consumption, subglottal lung pressure, and tissue permeability coefficient are varied; and their contribution to oxygen supply as well as to the liquid dynamics within the VF are quantified. It is found that filtration velocity is directly proportional to subglottal pressure and tissue permeability. Oxygen flow is also found to be inversely related to reaction rate, directly related to permeability, and not noticeably affected by subglottal pressure. The findings provide insight into the VF oxygenation pathways and the potential link with some pathological states such as hypoxia and localized lesions.

Modeling and Visual Simulation of Bifurcation Aneurysms Using Smoothed Particle Hydrodynamics and Murray’s Law

Aneurysm modeling and simulation play an important role in many specialist areas in the field of medicine such as surgical education and training, clinical diagnosis and prediction, and treatment planning. Despite the considerable effort invested in developing computational fluid dynamics so far, visual simulation of blood flow dynamics in aneurysms, especially the under-explored aspect of bifurcation aneurysms, remains a challenging issue. To alleviate the situation, this study introduces a novel Smoothed Particle Hydrodynamics (SPH)-based method to model and visually simulate blood flow, bifurcation progression, and fluid–structure interaction. Firstly, this research consider blood in a vessel as a kind of incompressible fluid and model its flow dynamics using SPH; and secondly, to simulate bifurcation aneurysms at different progression stages including formation, growth, and rupture, this research models fluid particles by using aneurysm growth mechanism simulation in combination with vascular geometry simulation. The geometry incorporates an adjustable bifurcation structure based on Murray’s Law, and considers the interaction between blood flow, tissue fluid, and arterial wall resistance. Finally, this research discretizes the computation of wall shear stress using SPH and visualizes it in a novel particle-based representation. To examine the feasibility and validity of the proposed method, this research designed a series of numerical experiments and validation scenarios under varying test conditions and parameters. The experimental results based on numerical simulations demonstrate the effectiveness and efficiency of proposed method in modeling and simulating bifurcation aneurysm formation and growth. In addition, the results also indicate the feasibility of the proposed wall shear stress simulation and visualization scheme, which enriches the means of blood analysis.

Analysis of Resistance in Magnetic Flux Leakage (MFL) Detectors for Natural Gas Pipelines

This study systematically explores the sources and influencing factors of resistance encountered by magnetic flux leakage (MFL) detectors in natural gas pipelines through a theoretical analysis, experimental investigation, and numerical simulation. The research methodology involves the development of a fluid–structure interaction model using ABAQUS 2023 finite element software, complemented by the design and implementation of a pull-testing platform for MFL detectors. This platform simulates detector operation under various interference conditions and quantifies the resulting frictional resistance. The findings reveal that the primary source of frictional resistance is the contact interaction between the MFL detector and the pipeline wall. Key factors influencing the magnitude of this resistance include the detector’s mass, the structural design and materials of the sealing cups and support plates, as well as the surface roughness of the pipeline. Both experimental results and numerical simulations demonstrate a pronounced increase in frictional resistance with heightened interference levels. The theoretical model exhibits strong agreement with experimental data, though deviations are observed under conditions of severe interference. This study provides a detailed understanding of frictional resistance patterns under diverse structural and operational scenarios, offering both theoretical guidance and practical recommendations for the design of low-resistance MFL detectors.

Effects of maximum thickness position on hydrodynamic performance for fish-like swimmers

When designing the internals of robotic fish, variations in the internal arrangements of power and control systems cause differences in external morphological structures, particularly the positions of maximum thickness. These differences considerably affect swimming performance. This study examines the impact of the topological structure of self-propelled fish-like swimmers on hydrodynamic performance using fluid-structure interaction techniques. Fish-like swimmers with maximum thickness closest to the head exhibit optimal swimming performance, characterized by modest energy consumption for fast-response acceleration during the starting phase and higher swimming velocity for high-speed travel during steady swimming. As the maximum thickness moves toward the middle, acceleration performance significantly weakens and swimming speed decreases, although maximum energy consumption is relatively reduced. This study will provide a notable reference for the morphological design of underwater robotic fish.

Assessment of typhoon-induced wind and wave effects on fatigue crack growth life in offshore wind turbines

ABSTRACT Fatigue and structural failures in OWT towers are common due to sustained aerodynamic and wave loads. This study predicts the remaining service life of 2.1MW jacket-type Offshore Wind Turbine (OWT) towers, focusing on fatigue crack growth life (FCGL). Using one-way fluid-structure interaction (FSI) simulations with Typhoon "Muifa" parameters, it analyzes stress under wind, wave, and current effects. FNK theory and linear elastic fracture mechanics are applied to calculate FCGL under various loads. The results indicate that the participation of waves and currents significantly affects the stress distribution in both the tower and the tower frame. During the crack propagation process, cracks initially propagate along the thickness direction and then extend along a straight path after penetrating the thickness. Under typhoon conditions, waves and currents cause a significant reduction in the FCGL of the tower, decreasing from 2.46 years to 1.48 years numerically.

On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Abstract In this paper, we study a nonlinear fluid-structure interaction problem between a ‘square-root’ viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions in both directions, while both the beam and the fluid are under the effect of time-periodic forces. By using a decoupling approach, at least one time-periodic weak solution to this problem is constructed which has a bounded energy and a fixed prescribed mass. The lack of a priori energy bounds is overcome by a series of estimates based on a careful choice of parameters. The most challenging one is the pressure estimate, which is obtained by utilizing the specific periodic geometry and the Bogovskiǐ operator on a fixed domain that has a uniform constant. With uniform estimates and improved regularity of the beam as in (Muha and Schwarzacher 2023 Ann. Inst. Henri Poin. Anal. Non Lineaire 39 1369–412), the time-periodic solution is constructed by a series of limit procedures, following the finite-dimensional time-space construction from (Feireisl et al 2012 Arch. Rational Mech. Anal. 204 74586).

Characterization of the Dynamic Flow Response in Microfluidic Devices.

The purpose of this study is to characterize the dynamic response of fluid flow in microchannels, which can show significant delay times before reaching steady flow conditions. Two main sources of these delays are numerically and experimentally investigated, the hydraulic compliance which originates from the flexibility of the system components (microchannel, tubing, syringe, etc.), and the compressibility of the liquid dead volume in the setup, also known as the "bottleneck effect". A fluid-structure interaction model is presented for the compliance of rectangular PDMS microchannels that is used to form a numerically based relation for the compliance as a function of the pressure and geometry. This relation is successfully able to predict the dynamics of the flow inside PDMS microchannels in stop-flow experiments. The time delays associated with the bottleneck effect is also shown when using different syringe volumes, microchannel resistances, and liquid types. In these tests, the bottleneck effect has a much larger effect compared to the compliance of the PDMS microchannels. This is true even when using softer PDMS by increasing the monomer-to-curing agent mixing ratio. The characterization that is presented here allows for a simple analysis of microfluidic networks using the hydraulic-circuit approach.