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Criteria for Applying the Lucas-Washburn Law.

ABSTRACT: Spontaneous imbibition happens in many natural and chemical engineering processes in which the mean advancing front usually follows Lucas-Washburn's law. However it has been found that the scaling law does not apply in many cases. There have been few criteria to determine under what conditions the Washburn law works. The effect of gravity on spontaneous imbibition in porous media was investigated both theoretically and experimentally. The mathematical model derived analytically was used to calculate the imbibition rates in porous media with different permeabilities. The results demonstrated that the effect of gravity on spontaneous imbibition was governed by the hydraulic conductivity of the porous media (permeability of the imbibition systems). The criteria for applying the Lucas-Washburn law have been proposed. The effect of gravity becomes more apparent with the increase in permeability or with the decrease in CGR number (the ratio of capillary pressure to gravity forces) and may be ignored when the CGR number is less than a specific value N(*)(cg) ≅ 3.0. The effect of gravity on imbibition in porous media can be modeled theoretically. It may not be necessary to conduct spontaneous imbibition experiments horizontally in order to exclude the effect of gravity, as has been done previously.

SUBMITTER: Li K

PROVIDER: S-EPMC4568521 | biostudies-other | 2015

REPOSITORIES: biostudies-other

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Project description:ObjectiveThe objectives of this study were to determine whether patients reporting symptoms are more likely to develop lymphedema and to describe the temporal relationship between symptom onset and lymphedema.MethodsThis was a prospective longitudinal cohort study of 647 women treated for breast cancer and screened for lymphedema using arm volume measurements and subjective questionnaires (n = 647; 2284 questionnaires [median 3.5 per patient, range = 1-24]). Primary study outcome was lymphedema (relative volume change ≥10%). The Kaplan-Meier method was used to estimate cumulative lymphedema incidence. Cox proportional hazards models were used to assess the relationship between symptoms, other risk factors, and lymphedema.ResultsA total of 64 patients (9.9%) developed lymphedema. On multivariable analysis, patients reporting increased arm size (hazard ratio = 3.09, 95% CI = 1.62-5.89) were more likely to progress to lymphedema than those who did not report this symptom. Of those who developed lymphedema, 37 (58%) reported an increased arm size a median of 6.1 months before lymphedema onset (range = 68.6 months before to 50.2 months after lymphedema onset).ConclusionPatients at risk of lymphedema who report increased arm size might do so prior to lymphedema onset and are at 3 times the risk of lymphedema as patients not reporting this symptom. Even without objective or observable edema, these patients should be followed vigilantly and considered for early intervention. Symptoms should be incorporated into screening and diagnostic criteria for lymphedema.ImpactThis study shows that patients at risk for breast cancer-related lymphedema who report increased arm size should be considered at high risk for progression to lymphedema-even without edema on measurement or clinical examination-and should be followed vigilantly, with consideration of early intervention.Lay summaryIf you are at risk of lymphedema and you feel as though your arm size has increased, you might develop lymphedema, and you are at 3 times the risk of lymphedema as patients not reporting this symptom. Even without measurable or observable edema, you should be followed vigilantly and consider early intervention.

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Criteria for Applying the Lucas-Washburn Law.

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