Gel-walled cylindrical channels as models for the microcirculation: dynamics of flow 1

Abstract

Vessels in the microcirculation have been compared to channels in a gel. In this study a method has been developed whereby a geometrically well defined section of a flow system was composed of a cylindrical gel mantic of outer radius R _G , surrounding a cylindrical channel of radius R. Both the channel and the mantle were of length L and were contained in a rigid transparent support of inner radius R _G . Hence R _G and L were fixed (R _G = 1.3 or 4.5 mm; L = 40 mm) and the radius R ≃ 0.14 mm could be measured by mounting the whole system on the stage of a microscope fitted with an eye-piece micrometer. The gel was crosslinked polyacrylamide swollen with water. Water also served as the flow medium. It was found that R increased with absolute pressure applied statically to the system under no flow conditions. In flow the channel tended to expand upstream and contract down stream. Flow rate Q through the system and pressure drop ΔP were measured and the radius of the channel was monitored as a function of distance x along its length. At low pressure gradients now rates Q agreed with the theoretically predicted flow rates Q _o but dropped below Q _o at higher pressure gradients even though allowance was made for changes in R in calculating Q _o and flow was shown to be laminar. The extent of the deviation decreased with gel rigidity G′ and increased with thickness of the gel wall R _G − R. The results expressed as Q/Q _o could be correlated when plotted as a function of $\mathit{\alpha }=\mathrm{(}{\mathit{R}}_{\mathit{G}}\mathrm{/}2\mathit{L}{\mathit{G}}^{\prime }\mathrm{)}\mathrm{\Delta }\mathit{P}$ , and corresponded approximately to the function $\mathit{Q}\mathrm{/}{\mathit{Q}}_{\mathit{o}}={\mathrm{(}1-\mathit{\alpha }\mathrm{)}}^4$ . The relevance of these results for the microcirculation is discussed.