Electrophoresis of a small sphere in a cylinder of finite length.

The pressure due to electrophoretic motion of a charged colloidal sphere in a fluid-filled circular cylinder is determined in the limit in which the sphere radius is small compared with that of the cylinder. If the ends of the cylinder are open, pressure-driven Poiseuille flow occurs, but the magnitude of this flow is shown to be small when the cylinder is long compared to its radius. It is concluded that the flow has little effect upon electrophoretic velocities, unlike when the diameter of the sphere is comparable to that of the cylinder in which case the Poiseuille flow increases electrophoretic velocities and creates long-range interactions between spheres.

Depletion layer dynamics of polyelectrolyte solutions under Poiseuille flow.

Complex liquids flow through channels faster than expected, an effect attributed to the formation of low-viscosity depletion layers at the boundaries. Characterization of depletion layer length scale, concentration, and dynamics has remained elusive due in large part to the lack of suitable real-space experimental techniques. The short length scales associated with depletion layers have traditionally prohibited direct imaging. By overcoming this limitation via adaptations of stimulated emission depletion (STED) microscopy, we directly measure the concentration profile of polymer solutions at a nonadsorbing wall under Poiseuille flow. Using this approach, we 1) confirm the theoretically predicted concentration profile governed by entropically driven depletion, 2) observe depletion layer narrowing at low to intermediate shear rates, and 3) report depletion layer composition that approaches pure solvent at unexpectedly low shear rates.

Analytical solutions for contaminant fate and transport in parallel plate fracture-rock matrix systems with poiseuille flow.

Modeling contaminant transport in fractured-rock matrix systems often approximates the effect of the parabolic flow field in the fractures (i.e., Poiseuille flow) on transport by adding a dispersion term to the uniform flow field. In this study, an analytical solution is derived to model contaminant transport in a parallel-plate fractured-rock matrix that explicitly simulates Poiseuille flow in the fractures, eliminating the need for the dispersion approximation. In addition to simulating Poiseuille flow in the fracture, the contaminant transport model developed here includes: (1) two-dimensional contaminant diffusion in the fractures and matrix, (2) first-order decay in the aqueous phase, and (3) rate-limited sorption onto matrix solids. It should be noted, however, that this model, much like the commonly employed Taylor dispersion approximation, neglects macro dispersion, thereby limiting the model's applicability to systems having wide fracture apertures with extremely high flow velocities (P e > 104). Model equations are analytically solved in the Laplace domain and numerically inverted. In addition, analytical expressions for the zeroth, first, and second spatial moments of the concentration profiles along the fractures are derived for both the new Poiseuille flow model as well as a model that approximates the effect of Poiseuille flow on transport by using a dispersion term. The first and second moment expressions are used to quantify how well the dispersion term approximates the effect of Poiseuille flow. Simulations confirm that the dispersion approximation will be adequate for natural fractures at long times. However, if a modeler is concerned with short-time transport behavior or transport behavior in systems with relatively wide-aperture fractures and high groundwater velocities where macro dispersion can be ignored, such as may be found at engineered geothermal systems and carbon capture and storage sites, there may be significant differences between model simulations that explicitly incorporate Poiseuille flow and those that approximate Poiseuille flow with a dispersion term. The model presented here allows the modeler to analytically quantify these differences, which, depending on the modeling objective, may cause the dispersion approximation to be inadequate. Simulations were also run to examine the effect of adsorption rate on remediation of fractured-rock matrix systems. It was shown that moderate adsorption rate constants could lead to very long remediation times, if remediation success is quantified by achieving low concentrations within the fracture.

Transitional Channel Flow: A Minimal Stochastic Model.

In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

Phonon Hydrodynamic Heat Conduction and Knudsen Minimum in Graphite.

In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (∼1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (∼100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. More intriguingly, the reflection symmetry associated with a single graphene layer is broken in graphite, which opens up more momentum-conserving phonon-phonon scattering channels and results in stronger hydrodynamic features in graphite than graphene. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.

Effects of Radiative Electro-Magnetohydrodynamics Diminishing Internal Energy of Pressure-Driven Flow of Titanium Dioxide-Water Nanofluid due to Entropy Generation.

The internal average energy loss caused by entropy generation for steady mixed convective Poiseuille flow of a nanofluid, suspended with titanium dioxide (TiO2) particles in water, and passed through a wavy channel, was investigated. The models of thermal conductivity and viscosity of titanium dioxide of 21 nm size particles with a volume concentration of temperature ranging from 15 °C to 35 °C were utilized. The characteristics of the working fluid were dependent on electro-magnetohydrodynamics (EMHD) and thermal radiation. The governing equations were first modified by taking long wavelength approximations, which were then solved by a homotopy technique, whereas for numerical computation, the software package BVPh 2.0 was utilized. The results for the leading parameters, such as the electric field, the volume fraction of nanoparticles and radiation parameters for three different temperatures scenarios were examined graphically. The minimum energy loss at the center of the wavy channel due to the increase in the electric field parameter was noted. However, a rise in entropy was observed due to the change in the pressure gradient from low to high.

Study of the instability of the Poiseuille flow using a thermodynamic formalism.

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier-Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec ≈ 2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be independent of the noise amplitude. Using the puff density as the macrostate variable, the free energy of such a system is computed and analyzed. The puff density approaches zero as the critical Reynolds number is approached from above, signaling a continuous transition despite the fact that the bifurcation is subcritical for a finite-sized system. An action function is found for the probability of observing puffs in a small subregion of the flow, and this action function depends only on the Reynolds number. The strategy used here should be applicable to a wide range of other problems exhibiting subcritical instabilities.

Modelling Study on Internal Energy Loss Due to Entropy Generation for Non-Darcy Poiseuille Flow of Silver-Water Nanofluid: An Application of Purification.

In this paper, an analytical study of internal energy losses for the non-Darcy Poiseuille flow of silver-water nanofluid due to entropy generation in porous media is investigated. Spherical-shaped silver (Ag) nanosize particles with volume fraction 0.3%, 0.6%, and 0.9% are utilized. Four illustrative models are considered: (i) heat transfer irreversibility (HTI), (ii) fluid friction irreversibility (FFI), (iii) Joule dissipation irreversibility (JDI), and (iv) non-Darcy porous media irreversibility (NDI). The governing equations of continuity, momentum, energy, and entropy generation are simplified by taking long wavelength approximations on the channel walls. The results represent highly nonlinear coupled ordinary differential equations that are solved analytically with the help of the homotopy analysis method. It is shown that for minimum and maximum averaged entropy generation, 0.3% by vol and 0.9% by vol of nanoparticles, respectively, are observed. Also, a rise in entropy is evident due to an increase in pressure gradient. The current analysis provides an adequate theoretical estimate for low-cost purification of drinking water by silver nanoparticles in an industrial process.

Analytical method for calculation of deviations from intended dosages during multi-infusion.

BACKGROUND: In this paper, a new method is presented that combines mechanical compliance effects with Poiseuille flow and push-out effects ("dead volume") in one single mathematical framework for calculating dosing errors in multi-infusion set-ups. In contrast to existing numerical methods, our method produces explicit expressions that illustrate the mathematical dependencies of the dosing errors on hardware parameters and pump flow rate settings. METHODS: Our new approach uses the Z-transform to model the contents of the catheter, and after implementation in Mathematica (Wolfram), explicit expressions are produced automatically. Consistency of the resulting analytical expressions has been examined for limiting cases, and three types of in-vitro measurements have been performed to obtain a first experimental test of the validity of the theoretical results. RESULTS: The relative contribution of various factors affecting the dosing errors, such as the Poiseuille flow profile, resistance and internal volume of the catheter, mechanical compliance of the syringes and the various pump flow rate settings, can now be discerned clearly in the structure of the expressions generated by our method. The in-vitro experiments showed a standard deviation between theory and experiment of 14% for the delay time in the catheter, and of 13% for the time duration of the dosing error bolus. CONCLUSIONS: Our method provides insight and predictability in a large range of possible situations involving many variables and dependencies, which is potentially very useful for e.g. the development of a fast, bed-side tool ("calculator") that provides the clinician with a precise prediction of dosing errors and delay times interactively for many scenario's. The interactive nature of such a device has now been made feasible by the fact that, using our method, explicit expressions are available for these situations, as opposed to conventional time-consuming numerical simulations.

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory.

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone". The underlying representative volume element of the macroscopic bone material contains two types of phases: a spherical, impermeable extracellular bone matrix phase interacts with interpenetrating cylindrical pore channel phases that are oriented in all different space directions. This type of interaction is modeled by means of a self-consistent homogenization scheme. While the permeability of the bone matrix equals to zero, the permeability of the pore phase is found through expressing the classical Hagen-Poiseuille law for laminar flow in the format of a "micro-Darcy law". The upscaling scheme contains pore size and porosity as geometrical input variables; however, they can be related to each other, based on well-known relations between porosity and specific bone surface. As two key results, validated through comprehensive experimental data, it appears (i) that the famous Kozeny-Carman constant (which relates bone permeability to the cube of the porosity, the square of the specific surface, as well as to the bone fluid viscosity) needs to be replaced by an again porosity-dependent rational function, and (ii) that the overall bone permeability is strongly affected by the pore fluid viscosity, which, in case of polarized fluids, is strongly increased due to the presence of electrically charged pore walls.

Paradox of the drinking-straw model of the butterfly proboscis.

Fluid-feeding Lepidoptera use an elongated proboscis, conventionally modeled as a drinking straw, to feed from pools and films of liquid. Using the monarch butterfly, Danaus plexippus (Linnaeus), we show that the inherent structural features of the lepidopteran proboscis contradict the basic assumptions of the drinking-straw model. By experimentally characterizing permeability and flow in the proboscis, we show that tapering of the food canal in the drinking region increases resistance, significantly hindering the flow of fluid. The calculated pressure differential required for a suction pump to support flow along the entire proboscis is greater than 1 atm (~101 kPa) when the butterfly feeds from a pool of liquid. We suggest that behavioral strategies employed by butterflies and moths can resolve this paradoxical pressure anomaly. Butterflies can alter the taper, the interlegular spacing and the terminal opening of the food canal, thereby controlling fluid entry and flow, by splaying the galeal tips apart, sliding the galeae along one another, pulsing hemolymph into each galeal lumen, and pressing the proboscis against a substrate. Thus, although physical construction of the proboscis limits its mechanical capabilities, its functionality can be modified and enhanced by behavioral strategies.

Studying the influence of surface roughness with different shapes and quantities on convective heat transfer of fluid within nanochannels using molecular dynamics simulations.

CONTEXT: In the past decade, rapid advancements in microtechnology and nanotechnology have propelled modern science and technology into the nanoscale domain, where miniaturization and high integration have found extensive applications across various fields, including industry, biotechnology, and information technology. Mechanisms of nanofluid flow and heat transfer properties have received increasing attention. In the flow and convective heat transfer of fluids at the nanoscale, the shape and dimensions of the surfaces play a crucial role. So, the main purpose of our paper is to investigate the influence of surface roughness with different shapes and quantities on fluid flow and convective heat transfer. In this study, we have chosen argon atoms as the fluid and used copper atoms to simulate the nanochannel walls. In order to investigate the influence of the shape and quantity of roughness on the convective heat transfer of fluids within nanochannels, we computed and analyzed the velocity, temperature, and density distributions of fluids inside channels with triangular, hemispherical, and rectangular roughness. Through simulation results, we found that triangular, hemispherical, and rectangular surface roughness at the same height can result in differences in temperature and velocity of the fluid within nanochannels. With a nanochannel roughness number of 5, the temperature and velocity of the fluid at the middle position of the nano-channel for the triangular roughness increased by 6% and 25% compared to the rectangular roughness, and by 4% and 10% compared to the hemispherical roughness. The fluid temperature and velocity are highest in channels with triangular surface roughness and lowest in those with rectangular roughness. Furthermore, increasing the quantity of surface roughness decreases the temperature and velocity of the fluid within nanochannels. When the quantity of rectangular surface roughness is 5, the fluid temperature within the nanochannel decreases by 12%, and the velocity decreases by 38% compared to a roughness quantity of 1. We also found, through velocity contours, that the presence of roughness increases the local fluid velocity in the rough regions of nanochannels. Roughness also reduces the density fluctuations of the fluid near the walls within the nanochannel. Roughness significantly affects the heat transfer performance of the fluid during its flow, and this influence should not be overlooked. METHODS: In this study, molecular dynamics theory was employed, and simulations were conducted using the open-source software LAMMPS to investigate the influence of different shapes and quantities of surface roughness on fluid flow within nanochannels. The model in this paper was constructed using the LAMMPS software, and the surface roughness shapes on the walls were implemented as rectangular, hemispherical, and triangular. The wall surfaces were composed of copper atoms, while the fluid consisted of argon atoms. The copper atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 3.615 Å. Similarly, the argon atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 5.62 Å. The interactions between copper atoms were modeled using the EAM (Embedded Atom Method) potential, while the interactions between argon atoms were described using the LJ (Lennard-Jones) potential. The LJ potential was also employed to represent interactions between argon and copper atoms.

Intracranial pressure-flow relationships in traumatic brain injury patients expose gaps in the tenets of models and pressure-oriented management.

Background: The protocols and therapeutic guidance established for treating traumatic brain injury (TBI) in neurointensive care focus on managing cerebral blood flow (CBF) and brain tissue oxygenation based on pressure signals. The decision support process relies on assumed relationships between cerebral perfusion pressure (CPP) and blood flow, pressure-flow relationships (PFRs), and shares this framework of assumptions with mathematical intracranial hemodynamics models. These foundational assumptions are difficult to verify, and their violation can impact clinical decision-making and model validity. Methods: A hypothesis- and model-driven method for verifying and understanding the foundational intracranial hemodynamic PFRs is developed and applied to a novel multi-modality monitoring dataset. Results: Model analysis of joint observations of CPP and CBF validates the standard PFR when autoregulatory processes are impaired as well as unmodelable cases dominated by autoregulation. However, it also identifies a dynamical regime -or behavior pattern-where the PFR assumptions are wrong in a precise, data-inferable way due to negative CPP-CBF coordination over long timescales. This regime is of both clinical and research interest: its dynamics are modelable under modified assumptions while its causal direction and mechanistic pathway remain unclear. Conclusion: Motivated by the understanding of mathematical physiology, the validity of the standard PFR can be assessed a) directly by analyzing pressure reactivity and mean flow indices (PRx and Mx) or b) indirectly through the relationship between CBF and other clinical observables. This approach could potentially help to personalize TBI care by considering intracranial pressure and CPP in relation to other data, particularly CBF. The analysis suggests a threshold using clinical indices of autoregulation jointly generalizes independently set indicators to assess CA functionality. These results support the use of increasingly data-rich environments to develop more robust hybrid physiological-machine learning models.

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions.

This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm-Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods.

Colloidal stability of graphene in aqueous medium: a theoretical approach through molecular dynamics.

CONTEXT: Graphene has been used as reinforcement of polymeric nanocomposites to increase mechanical and electrical properties. Recently, graphene suspensions have been used for the development of nanofluids in automotive applications, where improvements in convection heat transfer coefficients and pressure drops have been reported. However, dispersions of graphene sheets in a polymeric matrix as well as in a solvent medium are difficult to achieve; that is because Van der Waals, [Formula: see text] and Coulombic interactions cause agglomerations. Surface chemical modifications have been considered as viable options to improve the graphene integration. In this work, we studied the colloidal stability of aqueous solutions of graphene sheets functionalized with (i) carboxylic groups, (ii) 3-amino-propyl tri-ethoxy silane (amphiphilic behavior), (iii) graphene oxide, and (iv) pristine graphene. Results show that the lower sedimentation velocity corresponds to the graphene functionalized with carboxylic groups, which presents the higher colloidal stability. However, the amphiphilic group enhances the interaction energy between graphene and the solvent; we believe that there is a threshold percentage of functionalization that improves the colloidal stability of graphene. METHOD: Transport properties of graphene solutions were estimated by using Non-Equilibrium Molecular Dynamics simulations to generate Poiseuille flow in an NVT ensemble. Simulations were developed in the LAMMPS code. The COMPASS Force Field was used for the graphene systems and the TIP3P for the water molecules. Bonds and angles of hydrogen atoms were kept rigid by using the shake algorithm. The molecular models were built through MedeA and visualized with the Ovito software.

Effect of non-return valves on the time-of-arrival of new medication in a patient after syringe exchange in an infusion set-up.

The presence of a non-return valve in an infusion set-up is expected to affect the time-of-arrival of new medication in a patient after syringe exchange. Using Computational Fluid Dynamics (CFD) we have studied the flow through a typical non-return valve, focusing on two separate effects: (A) the overall delay in the time-of-arrival, and (B) timing effects due to the distortion of the Poiseuille flow profile in the non-return valve. The results show that (A) the additional delay in time-of-arrival of new medication, caused by the non-return valve alone, corresponds to the delay that would be caused by 11.2 cm of extra infusion line instead of the valve, and that (B) the non-Poiseuille flow profile inside the non-return valve gives rise to an extra slow wash-out of the last portion of the remnant fluid of the old medication. We conclude that awareness of these extra delays may be important for clinicians in certain time-critical situations.

Bedside visualisation tool for prediction of deviation from intended dosage in multi-infusion therapy.

BACKGROUND: In multi-infusion therapy, multiple infusion pumps are connected to one single vascular access point. Interaction between pressure changes from different pumps may result in temporary dosing errors, which can be very harmful to the patient. It is known that these dosing errors occur. However, clinicians tend to find it hard to estimate the order of magnitude of these errors. METHODS: This research uses an existing mathematical model to create a bedside prediction tool that is able to provide clinicians with the dosing errors that will occur after flow rate changes in multi-infusion therapy. A panel of clinicians, consisting of both nurses and doctors, was formed, and, in order to assess the level of knowledge about dosing errors in multi-infusion, the panel was presented with four medication schedules in which a syringe exchange or change in flow rate took place. The panel was asked to predict the resulting dosing errors. RESULTS: A prediction tool was developed that describes a two pump multi-infusion system and predicts dosing errors resulting from changing the flow rate at one pump. 44% of the panel members wrongly predicted the impact of changing the set flow of liquid A on the flow of liquid B that reaches the patient. Nobody was able to correctly predict the dosing deviation if a very small catheter was used. After the prediction tool was shown, the clinicians indicated they had a improved understanding of what deviations to expect and that the tool would be useful in understanding multi-infusion dosing errors. CONCLUSIONS: Using the predictive tool to visualise the deviations from the set flow rate is an effective method to allow clinicians to gain insight in dosing errors in multi-infusion therapy. This knowledge can be used to better anticipate future dosing errors in clinical situations.

Exact Solutions for Non-Isothermal Flows of Second Grade Fluid between Parallel Plates.

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier's slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.

Fluid dynamics characterisation of a rotating bioreactor for tissue engineering.

Biological scaffolds composed of extracellular matrix (ECM) derived from decellularised tissue are increasingly used in regenerative medicine. In this project, a flow perfusion bioreactor (the rotary cell culture system (RCCS), commercially available from Synthecon (Houston, TX)) is used in order to obtain some esophageal extracellular matrix. A theoretical mechanical characterisation of this experimental set-up is provided. Due to the combination of rotation and perfusion, some spiral Poiseuille flow is created inside the tubular esophagus. In a transverse section, a particle (or cell) experiences simultaneously gravitational, Archimedes, centrifugal, Coriolis, and drag forces. In a frame of reference rotating with angular velocity ω, the particle follows a periodic nearly circular path in the clockwise direction, associated with a very slow centrifugal drift towards the esophagus wall. It appears that moderate perfusion rate and rotation speed (ω < 20 rpm and Q < 30 ml/min) are appropriate experimental conditions for esophagus tissue engineering using the RCCS Synthecon bioreactor.

Principles and Guidelines for In-Line Viscometry in Cereal Extrusion.

In the food industry, extrusion cooking finds numerous applications thanks to its high productivity and nutrient retention. More specifically, cereal extrusion, e.g., for savory snacks and breakfast products has an important market share. For such applications, rheology, which addresses viscous and elastic contributions, plays an important role in developing, optimizing, and controlling the extrusion manufacturing technique. In this context, conventional off-line rheometers are not ideal for providing data, as the goal is to replicate the exact thermomechanical history to which the food is subjected in the extrusion process. Hence, to achieve reliable analyses, in-line viscometers that have mostly been tested using oil-based polymers were introduced. Biopolymers (e.g., starch), however, are highly sensitive to both heat and mechanical degradation, and the viscometer design has to be adapted accordingly to produce an accurate measurement. Alongside a discussion of the different designs available, this review will address the most common methodologies for measuring the steady shear viscosity, extensional viscosity, and the first normal stress difference for food applications, providing researchers in the biopolymer and food engineering fields with a general introduction to this emerging topic.