Applicability evaluation of the stress-optic law in Newtonian fluids toward stress field measurements

Noto, Daisuke; Tasaka, Yuji; Hitomi, Jumpei; Murai, Yuichi

doi:10.1103/physrevresearch.2.043111

Cited by 4 publications

(7 citation statements)

References 32 publications

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“…The stress component along the camera's optical axis (𝑧-axis) is not considered in the first-order stress-optic law [Eq. (24)]. Therefore, the value of Δ 1st is zero at the center of the channel (𝑦 = 0 mm), where 𝜕𝑢 𝑥 /𝜕𝑦 = 0 [see Fig.…”

Section: Resultsmentioning

confidence: 99%

“…These results indicate that the first-order stress-optic law [Eq. (24)] is invalid around the center of the channel for a three-dimensional fluid flow. In contrast, the theoretical retardation calculated using the second-order stress-optic law (Δ 2nd , red solid line) is in good agreement with the experimental retardation for all flow rates, even 22) and ( 23)].…”

Section: Resultsmentioning

confidence: 99%

“…Figure 4 (d) and (e) shows the local distributions of the retardation, Δ (𝑖) 1st and Δ (𝑖) 2nd , as calculated using the first-order stress-optic law [Eq. (24)] and the second-order stress-optic law [Eqs. (22) and ( 23)], respectively.…”

Section: Theoretical Retardation Field For a Steady Laminar Flow In A...mentioning

confidence: 99%

“…1. In recent years, there have been some reports on the application of photoelasticity to quasi-two-dimensional fluid flows [15][16][17][18][19]. In particular, several measurements have used an aqueous cellulose nanocrystal suspension (hereinafter, CNC suspension) as the photoelastic fluid [15,[20][21][22] to show that the above two-dimensional measurement principle can be successfully applied [23,24]. These studies have shown the great potential of photoelasticity for flow field measurements.…”

Section: Introductionmentioning

confidence: 99%

“…(b) The line profile of the retardation measurement results at flow rates of 15, 20, 25, and 30 ml/min. (c) A comparison between the spatial distribution of the experiment results and the spatial distribution of the theoretical retardation.The first-order stress-optic law is calculated by neglecting the second-order stress term in Eq (24)…”

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confidence: 99%

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Integrated photoelasticity measurements of a three-dimensional laminar flow: second-order stress terms in the stress-optic law

Nakamine¹,

Yokoyama²,

Worby³

et al. 2023

Preprint

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This study experimentally validates a stress-optic law for a three-dimensional flow using integrated photoelasticity. In this stress-optic law, the stress is related to the two photoelastic parameters — the phase retardation Δ and orientation 𝜙 — of elliptically-polarized light. Previous studies have examined the stress-optic law of three-dimensional flows, but the importance of the second-order stress terms in the three-dimensional stress-optic law, i.e., those relating to the stress component along the camera’s optical axis, have not yet been experimentally validated. In this work, we measure the retardation of a steady Newtonian fluid laminar flow (cellulose nanocrystal suspension of 0.5 wt%) in a square channel and compare it with the theoretical prediction. Remarkably, the theoretical result including the second-order stress terms shows good agreement with the experimental result for various flow rates, while the calculation without these terms results in a significant deviation from the measurements. Therefore, proper consideration of the second-order stress terms in the three-dimensional stress-optic law is crucial for integrated photoelasticity measurements of three-dimensional flow fields.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Theoretical Retardation Field For a Steady Laminar Flow In A...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Integrated photoelasticity measurements of a three-dimensional laminar flow: second-order stress terms in the stress-optic law

Nakamine¹,

Yokoyama²,

Worby³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Flow birefringence of cellulose nanocrystal suspensions in three-dimensional flow fields: revisiting the stress-optic law

Nakamine,

Yokoyama,

Worby

et al. 2024

Cellulose

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This study systematically investigates the flow birefringence of cellulose nanocrystal (CNC) suspensions. The aim is to clarify the importance of the stress component along the camera’s optical axis in the stress-optic law (SOL), which describes the relationship between birefringence, the retardation of transmitted polarized light, and the stress field. More than 100 datasets pertaining to the retardation of CNC suspensions (concentrations of 0.1, 0.3, 0.5, and 1.0 wt%) in a laminar flow field within a rectangular channel (aspect ratios of 0.1, 1, and 3) are systematically obtained. The measured retardation data are compared with the predictions given by the conventional SOL excluding the stress component along the camera’s optical axis and by the SOL including these components as second-order terms (2nd-order SOL). The results show that the 2nd-order SOL gives a significantly better agreement with the measurements. Based on the 2nd-order SOL, the retardation at the center of the channel, where the effect of the stress component along the camera’s optical axis is most pronounced, is predicted to be proportional to the square of the flow rate, which agrees with the experimental data. The results confirm the importance of considering the stress component along the camera’s optical axis in the flow birefringence of CNC suspensions at high flow rates, even for quasi-two-dimensional channel flow.

show abstract

Flow birefringence of cellulose nanocrystal suspensions in three-dimensional flow fields: revisiting the stress-optic law

Nakamine,

Yokoyama,

Worby

et al. 2024

Preprint

View full text Add to dashboard Cite

This study systematically investigates the flow birefringence of cellulose nanocrystal (CNC) suspensions. The aim is to clarify the importance of the stress component along the camera's optical axis in the stress-optic law (SOL), which describes the relationship between birefringence, the retardation of transmitted polarized light, and the stress field. More than 100 datasets pertaining to the retardation of CNC suspensions (concentrations of 0.1, 0.3, 0.5, and 1.0 wt\%) in a laminar flow field within a rectangular channel (aspect ratios of 0.1, 1, and 3) are systematically obtained. The measured retardation data are compared with the predictions given by the conventional SOL excluding the stress component along the camera's optical axis and by the SOL including these components as second-order terms (2nd-order SOL). The results show that the 2nd-order SOL gives a significantly better agreement with the measurements. Based on the 2nd-order SOL, the retardation at the center of the channel, where the effect of the stress component along the camera's optical axis is most pronounced, is predicted to be proportional to the square of the flow rate, which agrees with the experimental data. The results confirm the importance of considering the stress component along the camera's optical axis in the flow birefringence of CNC suspensions at high flow rates, even for quasi-two-dimensional channel flow.

show abstract

Applicability evaluation of the stress-optic law in Newtonian fluids toward stress field measurements

Cited by 4 publications

References 32 publications

Integrated photoelasticity measurements of a three-dimensional laminar flow: second-order stress terms in the stress-optic law

Integrated photoelasticity measurements of a three-dimensional laminar flow: second-order stress terms in the stress-optic law

Flow birefringence of cellulose nanocrystal suspensions in three-dimensional flow fields: revisiting the stress-optic law

Flow birefringence of cellulose nanocrystal suspensions in three-dimensional flow fields: revisiting the stress-optic law

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