This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The previously developing equation for Power-Law model is a simple ordinary differential type. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Casson model) that continuously flows into a circular tube by surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that the theoretical predictions of the governing equation were in good agreement with the results for considering the Newtonian model.

A study was conducted to determine the rheological properties of pomegranate puree (PP) as affected by different gums (xanthan and guar gums) and temperatures (25, 35 and 45°C). The rheological properties of the samples were determined using a rotational rheometer at a shear range of 1 to 40 s-1. The PP added with xanthan and guar gums were found to be Non-Newtonian fluids following the Herschel-Bulkley model. The yield stress and consistency coefficient of the PP with xanthan gum at different temperatures were higher than those of the PP with guar gum but the opposite was observed for the flow behavior index. Moreover, all rheological properties of the PP regardless of type of gum addition decreased with increasing temperature. The consistency coefficient was related to temperature using an Arrhenius-type relationship. The PP with xanthan gum (16.11 kJ/mol) has higher activation energy than the PP with guar gum (11.44 kJ/mol). The yield stress values of the PP with xanthan gum and guar gum can be related to temperature by linear regression equations and the flow behavior index values by exponential regression equations.

A study was conducted to determine the rheological properties of gochujang and chogochujang at different temperatures (25, 35 and 45°C). The rheological properties of the samples were determined using a rotational rheometer at a shear range of 1 to 40 s-1. The gochujang and chogochujang were found to be Non-Newtonian fluids following the Herschel-Bulkley model. The yield stress and consistency coefficient of the gochujang at different temperatures were higher than those of the chogochujang but the opposite was observed for the flow behavior index. Moreover, all rheological properties of the gochujang and chogochujang decreased with increasing temperature. The consistency coefficient was related to temperature using an Arrhenius-type relationship. The gochujang (14.48 kJ/mol) has higher activation energy than the chogochujang (14.03 kJ/mol). The yield stress values of the gochujang and chogochujang can be related to temperature by linear regression equations and the flow behavior index values by exponential regression equations.

sodium bis-(2-ethylhexyl)sulfosuccinate-water 라멜라 액정의 비뉴톤 유동곡선을 cone-plate 레오메타를 사용하여 여러 농도와 온도 조건에서 얻었다. 이러한 비뉴톤 유동곡선을 비뉴 톤 유동식에 적용하여 유동파라메타를 구하였다. 특별히 주목할 점은 액정시료의 전단속도에 대한 전단 응력은 증가와 감소에서 틱소트로피와 다일레턴시 현상을 보여 hysteresis loop를 나타내고 있다는 점이 다. sodium bis-(2-ethylhexyl)sulfosuccinate-water 라멜라 액정은 작은 전단속도에서는 약한 젤 현상 을 보이지만 응력이 한계 응력 이상에서는 비 선형 점탄성 성질을 나타낸다. 전단속도 감소에서 분산계 는 전단속도가 증가할 때 측정된 값 보다는 큰 구조변화와 전단응력을 유지하고 있다.

The rheological properties of complex materials such as colloid dispersion show complicated non-Newtonian flow phenomena when they are subjected to shear flow. These flow properties are controlled by the characteristics of flow units and the interactions among the flow segments. The rheological parameters of relaxation time (β2)0, structure factor C2 and shear modulus X2/α2 for various thixotropic flow curves was obtained by applying thixotropic equation to flow curves. The variations of rheological parameters are directly related to non-Newtonian flows, viscosities and activation energies of flow segments.

This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The present study introduces detailed mathematical procedures for Casson viscosity model. The equations of velocity distribution and flow rate are developed to describe the displacement of a non-Newtonian fluid that continuously flew into a circular tube by surface tension. The equation of modified volumetric flow shows the complicated form of (10) due to yield stress term, and the equation of velocity distribution which includes the yield stress and inclination angle of circular tube is composed of terms of r and rc as form of (14).