Analysis of a Coupled-Mass Microrheometer

Cheneler, David

doi:10.5772/35442

Cited by 3 publications

(5 citation statements)

References 14 publications

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“…While these expressions are difficult to solve analytically, they are easily solved numerically. For instance, for the data shown in Figure 13, K Cap = 179.4 N/m and χ Cap = −0.0017 N. The maximum relative error between the linear function given by Equation (21) and the data shown in Figure 13 is 0.11%. Therefore, Equation (21) can be used to determine the correction to the squeeze force measured during rheometry due to capillary forces and to check that these forces are linear, facilitating analysis of the rheometry data.…”

Section: Linearization and Applicability To Squeeze Flow Rheometrymentioning

confidence: 95%

“…While the capillary force is still non-linear, if the change in gap is small enough, this nonlinearity will be small. This means the capillary force can be approximated by the linear relationship given in Equation (21), as demonstrated in Figure 13.…”

Section: Linearization and Applicability To Squeeze Flow Rheometrymentioning

confidence: 99%

“…However, in general these solutions are not easily adaptable for modelling capillary bridges between two planes. The study of this geometry is of increasing importance as it can explain stiction in MEMS devices [13,14] and head/disk systems [15], be used for particle transfer in microfluidics channels [16], and is the geometry increasingly being used for squeeze flow rheology [17][18][19][20][21][22]. To this end, several investigators have studied capillary bridges between flat parallel surfaces [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens

Bowen

Cheneler

2020

Colloids and Interfaces

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A closed form expression capable of predicting the evolution of the shape of liquid capillary bridges and the resultant force between parallel platens is derived. Such a scenario occurs within many micro-mechanical structures and devices, for example, in micro-squeeze flow rheometers used to ascertain the rheological properties of pico- to nano-litre volumes of complex fluids, which is an important task for the analysis of biological liquids and during the combinatorial polymer synthesis of healthcare and personal products. These liquid bridges exhibit capillary forces that can perturb the desired rheological forces, and perhaps more significantly, determine the geometry of the experiment. The liquid bridge has a curved profile characterised by a contact angle at the three-phase interface, as compared to the simple cylindrical geometry assumed during the rheological analysis. During rheometry, the geometry of the bridge will change in a complex nonlinear fashion, an issue compounded by the contact angle undergoing hysteresis. Owing to the small volumes involved, ascertaining the bridge geometry visually during experiment is very difficult. Similarly, the governing equations for the bridge geometry are highly nonlinear, precluding an exact analytical solution, hence requiring a substantial numerical solution. Here, an expression for the bridge geometry and capillary forces based on the toroidal approximation has been developed that allows the solution to be determined several orders of magnitude faster using simpler techniques than numerical or experimental methods. This expression has been applied to squeeze-flow rheometry to show how the theory proposed here is consistent with the assumptions used within rheometry. The validity of the theory has been shown through comparison with the exact numerical solution of the governing equations. The numerical solution for the shape of liquid bridges between parallel platens is provided here for the first time and is based on existing work of liquid bridges between spheres.

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Section: Linearization and Applicability To Squeeze Flow Rheometrymentioning

confidence: 95%

Section: Linearization and Applicability To Squeeze Flow Rheometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens

Bowen

Cheneler

2020

Colloids and Interfaces

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“…Square plates are supposed in some quarters to be equivalent to circular if the areas are the same on the grounds that the (final) stress is then identical. However, the flow pattern is different enough as to affect the closing velocity (19), and thus when the material is strainrate sensitive, as must be the case in general in the context (as for flow, because it depends in part on flow), the results may vary. It can be shown numerically that the closing velocity difference is about 3% lower in the case of the square plates (at any thickness).…”

Section: Film Thicknessmentioning

confidence: 99%

Mechanical test relevance—A personal perspective on some methods and requirements

Darvell

2023

Front. Dent. Med

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Mechanical tests of various kinds are widely used in dental research to study the behaviour of its materials. Unfortunately, despite often long history, the relevance of a test or its outcome is hard to discern. But even for tests that have a more apparent appropriateness many details that ensure good accuracy and reproducibility appear not to be appreciated or understood in that there is little evidence in the published literature that the necessary steps and precautions have been taken. The present purpose to is to examine a number of these aspects in the context of a selection of tests to illustrate the care and attention that are essential for sound results.

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“…according to [4] 1 . In all three analytical solutions it can be seen from the negative sign that the reaction force F acts in the opposite direction of the velocity v. This means that the fluid damps the system in the cases considered.…”

Section: Analytical Solutions For Selected Scenariosmentioning

confidence: 99%

Development of a simple substitute model to describe the normal force of fluids in narrow gaps

Bilz

Payrebrune

2023

Proc Appl Math and Mech

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Fluids in narrow gaps are employed frequently in many applications. The motivation for their use is diverse and ranges from hydrodynamic lubrication in plain bearings to the transport of hard particles into the working gap for the purpose of machining workpiece surfaces in lapping processes. Depending on the focus of the analysis, it may be useful to investigate the entire pressure field or to calculate only individual quantities. For example, in sophisticated simulations it may be of interest to know the resulting force of a fluid as a function of the external system state in order to describe its damping characteristics. Especially for the simulation of flows in narrow gaps, the Reynolds equation is a convenient choice, which, in contrast to the more general Navier‐Stokes equations, can lead to considerable savings in computational time because no three‐dimensional discretization is required, but only a two‐dimensional discretization. However, if not a highly detailed pressure field is of interest, but only simple relations such as the resulting force as a function of distance and velocity, and if this relation to be evaluated many times for different parameter combinations over a wide range of values, the use of a robust substitute model is a good choice. This article deals with the creation of such a substitute model based on the Reynolds equation taking cavitation into account.

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Analysis of a Coupled-Mass Microrheometer

Cited by 3 publications

References 14 publications

Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens

Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens

Mechanical test relevance—A personal perspective on some methods and requirements

Development of a simple substitute model to describe the normal force of fluids in narrow gaps

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